0-1 Knapsack Problem

0/1-Polytopes in 3D

10-23 Deoxyribozyme Design Optimization

10. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Slope of the Median to the Base

1125899906842624 Pictures

11a. Construct a Triangle Given the Lengths of Two Sides and the Bisector of Their Included Angle

11b. Construct a Triangle Given the Lengths of Two Sides and the Bisector of Their Common Angle

11 New Numerical Functions in Mathematica 7

{1,1} Surface Deposition with {-1,1} Growth

120 Rhombic Dodecahedra of the Second Kind Arranged in a Ball

120 Rhombic Triacontahedra

1, 2, 3-Parameter Logistic Rasch and Birnbaum Models and Item Analysis

12. Construct a Triangle Given the Length of Its Base, the Perimeter and the Difference of the Base Angles

12 Rhombic Triacontahedra

12x12 Icosahedra

13. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Difference of the Lengths of the Other Two Sides

14. Construct a Triangle Given the Length of the Altitude to the Base, a Base Angle and the Sum of the Lengths of the Other Two Sides

14-Piece Dissection of Juel's Pyramid into a Parallelepiped

15. Construct a Triangle Given the Lengths of Two Sides and the Median to the Third Side

15-Point Projective Space

16. Construct a Triangle Given Its Circumradius, Inradius and the Difference of Its Base Angles

17a. Construct a Triangle Given the Length of an Angle Bisector, the Angle at Another Vertex and Distance from the Third Vertex to the Angle Bisector

17b. Construct a Triangle Given the Length of an Angle Bisector, the Angle at Another Vertex and the Distance from the Third Vertex to the Angle Bisector

18. Construct a Triangle Given the Length of Its Base, the Difference of Angles at Its Base and the Point of Intersection of an Angle Bisector with Its Base

196-Algorithm: Palindromic Numbers

1992 CMO Problem: Cocircular Orthocenters

19. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Special Point of Intersection

1. Ambiguous Rings

1B Locus of Solutions of a Complex Quadratic Equation

1. Construct a Triangle Given the Length of the Base, the Difference of the Base Angles and the Foot of the Altitude to the Base

1. Constructing a Point on a Cassini Oval

1D and 2D Singular Wavefronts

1D Heat Conduction through Biological Tissue

1D Kinematics Problem Solver

1. Figures from Bilinski Dodecahedron

1. Kowalewski's Coloring of the Triacontahedron

1. Locus of the Solutions of a Complex Quadratic Equation

1. Mazes on Polyhedral Nets

1. Mendeleev Interpreted by Schrödinger and Lewis

1. Nets for Cowley's Dodecarhombus

1. Normal and Tangent to a Cassini Oval

2002-2008 New Zealand General Election Results under Varying Cutoff Procedures

200 Stars Projected to the Sphere and Platonic Solids

2015-2016 AP Football Poll Using Alternative Voting Methods

20b. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex

20. Construct a Triangle Given the Length of Its Base, the Difference of Its Base Angles and a Line Containing the Third Vertex

20 Talking Turtles

21609 Clusters of Polyhedra

21. Construct a Triangle with Equal Base Angles That Are Each Double the Third Angle

22. Construct a Triangle Given the Hypotenuse and the Length of an Angle Bisector

2,2 Turing Machines

23. Construct a Triangle Given Two Sides and the Inradius

24a. Construct a Triangle Given the Length of the Altitude to the Base, the Difference of Base Angles and the Sum of the Lengths of the Other Sides

24b. Construct a Triangle Given the Length of the Altitude to the Base, the Difference of Base Angles and the Sum of the Lengths of the Other Sides

24c. Construct a Triangle Given the Difference of Base Angles, Length of the Altitude from the Base and the Sum of the Lengths of the Other Two Sides

24-Hour Analog Clock

25. Construct a Triangle Given Its Base, the Difference of the Base Angles and the Length of One of Three Line Segments

26b. Construct a Triangle Given the Length of Its Base, the Angle Opposite the Base and the Length of That Angle's Bisector

26c. Construct a Triangle Given the Length of Its Base, the Angle Opposite the Base and the Length of That Angle's Bisector

26 Commonly Used Drugs

26-Piece Dissection of a Cube

27a. Construct a Triangle Given a Side, the Length of the Altitude to It and the Opposite Angle

27b. Construct a Triangle Given Its Perimeter, an Angle and the Length of the Altitude to the Side Opposite the Angle

27 Coins Balance Puzzle

28. Construct a Triangle ABC Given the Length of AB, the Sum of the Other Two Sides, and a Line Containing C

29. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Sum of the Other Sides

2. Ambiguous Rings Based on a Polygon

2-by-n Disk-Packing Paradox

2. Construct a Triangle Given the Circumradius, the Difference of the Base Angles, with the Circumcenter on the Incircle

2. Constructing a Point on a Cassini Oval

2D 2C R1 Cellular Automaton on a Triangular Grid

2D Acoustic Velocities in Crystalline Materials

2D Analog for Coulomb Degeneracies

2D and 3D Packard-Takens Autocorrelation Plots of Sinusoidal Functions

2D and 3D Views of the Weierstrass Function

2D Brillouin Zones

2D CA Glider Database

2D Cellular Automata for Feature Detection

2D Cellular Automata for Texture Recognition

2D Cellular Automaton Animations

2D Cellular Automaton Growth Models

2D Cellular Automaton on a Triangulated Surface

2D Coordinate System Transformations

2D Fourier Transforms

2D Heat Diffusion Using a Search-Update-Feedback Cellular Automaton (SCA) Approach

2D Jacobian

2D Kinematics on a Figure-Eight Curve

2D Logic Game with Letters

2D Perspective View of a 3D Object

2D Quantum Problem: Particle in a Disk

2D Root Systems

2D Rotation Using Matrices

2D Sine-Gaussian Lissajous Figures

2D Spring Pendulum

2D Stokes Flow in a Lid-Driven Cavity

2D Totalistic Cellular Automata

2D Triangular Cellular Automata on a Distorted Grid with Holes

2D Vector Addition

2D View of a Conformal Mapping

2D Walsh Functions

2D Wave Propagation

2. Extending the Rationals with the Square Root of Five

2. Families of Four-Point Touching Squares

2. Figures from Bilinski Dodecahedron

2. Kowalewski's Coloring of the Triacontahedron

2. Locus of the Solutions of a Complex Quadratic Equation

2. Mazes on Polyhedral Nets

2. Mendeleev Interpreted by Schrödinger and Lewis

2. Nets for Cowley's Dodecarhombus

2. Normal and Tangent to a Cassini Oval

2x2 Matrix Operations Acting on a Unit Square

2x2 Ordinal Games

30+12 Rhombic Triacontahedra

30. Construct a Triangle ABC Given the Length of AB, the Angle at C and the Difference of the Other Two Sides

31. Construct a Triangle ABC Given the Length of AB, an Adjacent Angle and the Difference of the Lengths of the Other Two Sides

32b. Construct a Triangle ABC Given the Length of AB, the Ratio of the Other Two Sides and a Line through C

32. Construct a Triangle ABC Given the Length of AB, the Ratio of the Other Two Sides and a Line through C

33. Construct a Triangle Given Its Base, Altitude to the Base and Product of the Other Two Sides

3×3 Determinants by Expansion

3×3 Determinants Using Diagonals

34. Construct a Triangle ABC Given the Length of AB and the Sum and Product of the Other Two Sides

35. Construct a Triangle Given the Angle Opposite Its Base and the Sum and Product of the Two Other Sides

3. Ambiguous Rings Based on a Rose Curve

3B Locus of Solutions of a Complex Quadratic Equation

3-Color Left/Right Mobile Automata

3. Construct a Triangle Given the Length of an Altitude, the Inradius and the Difference of the Base Angles

3. Constructing a Point on a Cassini Oval

3D Algebra Blocks

3D Anaglyph Graphics

3D Angular Momentum of a Particle

3D Band Member Mix

3D Billiard Loop in a Rectangular Box

3D Boid Model

3D Chebyshev Lissajous Figures

3D Chess

3D Construction Set

3D Coordinate System Transformations

3D Cubic B-Spline Curves

3D Curve Constructor

3D Deterministic Context-Free (DOL) Systems

3D Dissection Puzzle

3D Extrusion Using the Frenet-Serret System

3D Field of Cuboidal Magnet

3D Flower Art

3D Flying Pipe-Laying Turtle

3D Graphics with 2D Overlay

3D Graph of a General Quadratic Form

3D Grill for Secret Writing

3D Hermite Lissajous Figures

3D Image Reconstruction of a Cube from Multiple 2D Views

3D Interactive Satellite Globe

3D Kerr Black Hole Orbits

3D Knotting

3D Lambdoma

3D Layers Evolution of Five-Neighbor Outer Totalistic 2D Cellular Automaton

3D Layers Evolution View of a 2D Totalistic Cellular Automaton

3D Legendre Lissajous Figures

3D Line and Point Rendering

3D Lissajous Figures

3D Loops

3D Mazes

3D Mazes on a Rectangular Toroid

3D Mesh Generator

3D Mitsubishi Logo on Octahedron

3D Multipole Shapes

3D Object Designer Using Splines

3D Plots of Rational Functions of a Complex Variable

3D Poincaré Plot of the Logistic Map

3D Printer Model

3D Printer Template for Aperiodic Monotile

3D Printer Templates for Aperiodic Wang Tiles

3D Printer Templates for Mazes on a Cube

3D Printer Templates for Robinson's Tiles

3D Printer Templates for Two Wang Tiles

3D Printer Templates for Wang Tiles

3D Projectile Motion

3D Quantum Trajectory for a Particle in a Harmonic Potential

3D Random Walk Using Digits of Pi

3D Reachability Set for a Dubins Car

3D Rep-Tiles and Irreptiles

3D Skeletal Anatomy of the Arm

3D Skeletal Anatomy of the Foot

3D Skeletal Anatomy of the Torso

3D Snowflake Fractals

3D Spore Creations

3D Squared Trefoil

3D Stress-Strain Tensor Relations

3D Tic-Tac-Toe

3D Totalistic Cellular Automata

3D Transformations Applied to a NURBS Pavilion

3D Unit-Distance Graphs

3D Vector Decomposition

3D Vector Fields

3D Velocity Profile for Flow between Two Cylinders

3D View of Binary Logical Operations

3D Views of Elementary Cellular Automata

3D Waves

3D Zoetrope

3j Symbols

3. Locus of the Solutions of a Complex Quadratic Equation

3n+1 Flying Saucers

3n+1 Graph

3. Normal and Tangent to a Cassini Oval

3x3 Matrix Explorer

3x3 Matrix Transpose, Inverse, Trace, Determinant and Rank

4×4 Lock Problem

4. Ambiguous Rings Based on a Heart Curve

4-Band Color Code for Resistors

4. Construct a Triangle Given Its Circumradius, Inradius and a Vertex Angle

4. Constructing a Point on a Cassini Oval

4D Rotations of a Klein Bottle

4. Locus of the Solutions of a Complex Quadratic Equation

5000 Demonstrations and Counting

50-Dimensional Complex Space

54-Faced Space-Filling Polyhedron

5. Construct a Triangle Given Its Circumradius, the Difference of Base Angles and the Sum of the Other Two Sides

5x5x5 Pentacube Puzzle

600-Cell 120-Cell Duality

600 Cell Orthogonal Scale Base Projection

60 Rhombic Dodecahedron

60 Rhombic Triacontahedra in Two Different Clusters

60 Small Rhombicosidodecahedra

6. Construct a Triangle Given Its Circumradius, Inradius and the Length of Its Base

7. Construct a Triangle Given the Lengths of Two Sides and a Median of the Third Side

80 Golden Rhombohedra

8 and 8 Pitcher Puzzle

8. Construct a Triangle Given the Lengths of Two Sides and the Length of the Altitude to One of Them

9. Construct a Triangle Given the Length of Its Base, the Difference of the Base Angles and the Sum of the Other Two Sides

A 1D Random Walk with Fractal Dimension 2.0

A 2011 IMO Tangency Problem

A 2D Flow Field

A 2-pire Map

A 3D View of Modular Arithmetic

A 6×6 Grill for Secret Writing

Abacus

A Basic Property of Integrals

ABC Analysis

abc Conjecture

A Bee's Eye View of Cellular Automata

Abelian Algebras: Sums, Products, Duals, Powers

Aberration of Light

A Binary-Based Enumeration of the Primitive Pythagorean Triples

A Bitter Chocolate Problem

A Bitter Chocolate Problem That Satisfies an Inequality

A Breather Solution in the Causal Interpretation of Quantum Mechanics

Absolute Stability of an Integration Method

Absorbing Markov Chain

Absorption and Emission of Radiation by Atoms

Absorption in a Falling Thin Liquid Film at Low Reynolds Numbers

Absorption of Acetone in Air Using Water

Absorption Spectroscopy

Absorption with Chemical Reaction in a Semi-Infinite Medium

Abstract Art

Academic Admissions

Academic Ranking of World Universities (ARWU) World University Rankings

A CA-horus Line

A'Campo's Link of a Divide

A Canadian Lottery Wheel

A Canonical Optimal Stopping Problem for American Options

A Case of the Epsilon-Delta Definition of a Limit

A Catalog of Conformal Mappings

Acceleration of a Wheel

Acceleration of Particles in a Wave Obeying the Korteweg-de Vries Equation

Acceptance/Rejection Sampling

Accidentals, on Purpose

Accumulation Point

Accuracy of Series Approximations

A Cellular Automaton-Based Heat Equation

A Cellular Automaton Mapped on the Surface of a Cuboid

A Cellular Automaton Mapped on the Surface of a Cylinder

A Chain of Tangent Circles

A Chaotic Chemical Reaction Scheme Derived from Chua's Circuit Equations

A Chinese Knight's Tour

Acid-Base Titrations

Acid-Base Titration with Phenolphthalein Indicator

AC Induction Motor Rotor Design

AC Induction Motor VFD Operation

A Circle Defined from an Equilateral Triangle via Pythagoras

A Circumcircle through the Midpoint of a Triangle's Side

A Collection of 138 Nonconvex Rhombic Polyhedra

A Collection of Chaotic Attractors

A Collection of Image Processing Functions

A Collinearity between the Nine-Point Center, the Foot of an Altitude, and a Midpoint

A Collinearity from the Medial and Excentral Triangles

A Collinearity Involving an Excircle, the Incircle, and the Circumcircle

A Combinatorial Game

A Complex Gaussian Function

A Complex Wave in One Dimension

A Conceptual Model of Lapse Financed Life Insurance

A Concurrence Based on Ellipses through the Incenter

A Concurrency from a Point and a Triangle's Excenters

A Concurrency from Circumcircles of Subtriangles

A Concurrency from Midpoints of Arcs of the Circumcircle

A Concurrency from Six Pedal Points

A Concurrency from the Midpoints of Line Segments through the Circumcenter

A Concurrency from the Reflection of the Incircle's Contact Points across the Incenter

A Concurrency from the Reflections of the Contact Points with the Excircles

A Concurrency Generated by Circles about a Triangle's Sides and Lines through an Internal Point

A Concurrency Generated by Lines through the Orthocenter and Circles about a Triangle's Sides

A Concurrency Generated by the Angle Bisectors

A Concurrency Involving the Midpoints of the Sides and the Altitudes

A Concurrency of Lines Joining Orthocenters

A Concurrency of Lines through Points of Tangency with Excircles

A Conditional Probability Mass Function

A Congruent Angle inside the Incircle

A Conjecture of Apoloniusz Tyszka on the Addition of Rational Numbers

A Construction of the Square Root of Seven

A Contact Element in Rheological Models

A Continuous Analog of the 1D Thue-Morse Sequence

A Continuous Mapping That Fixes All Boundary Points but No Interior Points

A Convergent Sequence Satisfies the Cauchy Criterion

A Converging Geometric Series

Acoustic Bipole and Tripole

Acoustic Dipole in a Duct

Acoustic Multipoles

Acoustic Velocity in Crystalline Materials

Acoustic Waves Generated by a Loudspeaker

AC Power Factor Principle

AC Rotating Magnetic Field Principle

AC Synchronous Machine Vector Diagram

AC Three-Phase Neutral Current

AC Thyristor Operation

AC Thyristor Trigger Angle versus Power Factor

Action of a 2x2 Singular Transformation Matrix in 2D

Action of a Continuous Stirred-Tank Reactor

Action of a Siphon

Action of Inner Automorphisms on Subgroup Lattices

Action Potential Propagation along Myelinated Axons

Activated Sludge Process in a Batch Reactor

Activator-Inhibitor Cellular Automata

Active Negative Resistance Model That Is Not Piecewise Linear

Active Shock Absorbers

AC Transformers

A Curious Coin-Flipping Game

Acute Sets in Euclidean Spaces

A Cycle Index Spreadsheet

A Cyclic Quadrilateral Concurrency

Ada Deitz Polynomials for Handwoven Textiles

Adams' Circle and the Gergonne Point

Adaptive 3D Plotting

Adaptive Contour Plotting

Adaptive Frequency Hopf Oscillator

Adaptive Mesh Relocation-Refinement (AMrR) on Kim's Method for Options Pricing

Adaptive Mesh Trinomial Tree for Vanilla Option Pricing

Adaptive Monte Carlo Integration

Adaptive Plotting

Adaptive Thresholding of Images

Add a Component to a Mixture with an Azeotrope

Adding and Subtracting Positive and Negative Integers

Adding a Second Component to a Fixed-Volume Container

Adding a Second Component to a Single-Component Vapor-Liquid Equilibrium (VLE) Mixture

Adding Edges to Photographic Images

Adding Effects to Images

Adding Fractions

Adding in a Given Base

Adding Mixed Numbers

Adding One Component to a Binary Vapor-Liquid Equilibrium (VLE) Mixture

Adding Points on an Elliptic Curve

Adding Polarizations with Phase Shifts

Adding Polygonal Numbers

Adding to Color Channels

Adding Whole Numbers

Adding Whole Numbers Graphically

Addition and Subtraction of Integers

Addition and Subtraction of One-Decimal Numbers Using Rulers

Addition and Subtraction on a Circular Ruler

Addition Bingo

Addition Formula for Sine

Addition of Angular Momenta in Quantum Mechanics

Addition of Fractions

Addition of N Vectors in 2D

Addition of Points on an Elliptic Curve over the Reals

Addition Slide Rule

Addition Table

Additive and Multiplicative Risks

Additive Cellular Automata

Additive Cipher

Adelson's Checkershadow Illusion

A Device that Illustrates Pythagoras' Theorem

Adiabatic Compression of Pure Gases

Adiabatic Compression of Water in Vapor-Liquid Equilibrium (VLE)

Adiabatic Converter for Sulfur Trioxide Production

Adiabatic Evaporation of Water into Vacuum

Adiabatic Expansion and Compression of an Ideal Gas

Adiabatic Flash Distillation of a Benzene-Toluene Mixture

Adiabatic Flash Drum with Binary Liquid Feed

Adiabatic Gas Expansion between Two Tanks

Adiabatic Humidification

Adiabatic Mixing of Two Moist Air Streams

Adiabatic Plug Flow Reactor with Recycle

A Diagonal Inequality

A Differential Equation for Heat Transfer According to Newton's Law of Cooling

A Disappearing/Reappearing Coin

A Discrete Green's Theorem

A Discrete Model of Excitable Media

A Dissection of a Prolate Golden Rhombohedron

A Dissection Proof of Pythagoras's Theorem

Adjacency Matrices of Manipulable Graphs

Adjacent Flow of Two Immiscible Fluids

Adjusting RGB Color of Image

Adjustment of Protection Zones in an Impedance Relay for Two Adjacent Transmission Lines

A Domain Decomposition Method with Orthogonal Collocation

A Domino Puzzle

A Double Exponential Equation

A Double Parabola with Retroreflection Properties

Adsorption Column for Removing Acetone from an Air Stream

Adsorption, Diffusion and Chemical Reaction in a Slab

Adsorption Isotherms of Ethylene in NaX (Zeolite Structure FAU)

Advanced Celestial Sphere

Advanced Space Visualization Test

Advection Maps for Closed Flows

Adversarial Bifurcation

Adverse Selection

Aeration Dynamics in a Batch Reactor

Aerial Photo Scale

Aerial Tour of Differential Geometry

Aerosol-Cloud-Rain Equations with Time Delay

A Face from Words

A Family of Generalized Fibonacci and Lucas Numbers

A Family of NxN Space-Filling Z-Functions, N>1

A Family of Surfaces Including a Möbius Strip

A Few More Geometries after Ramanujan

Affine Products of Locators

Affine-Scaling Interior Point Method

Affine Transform

Affinity or Resistance Distance between Actors

A Fifth-Degree Polynomial and Its Derivatives

A Finite Automaton Editor

A Fire Spread Model: The Contagion Effect

A First Morley Triangle Concurrence

A Five-Power Algebraic Identity

A Forest Growth Curve

A Formula for Primes in Arithmetic Progressions

A Four-Power Algebraic Identity

A Four-Term Algebraic Identity for Powers 1, 2, 3 and 5

A Four-Term Algebraic Identity with Squares and Quartics

African GDP Outliers

A Function Invariant under a Group of Transformations

A Function with a Jump Discontinuity

Age Distribution in the World

Age Distributions from a Leslie Model for Age-Structured Populations

A General Cone

A Generalization of Cross's Theorem

A Generalization of Hansen's Theorem

A Generalization of IMO 2008 Problem 1

A Generalization of the Mean Value Theorem

A Geometrical Theorem of Leibniz

A Geometric Limit Problem

A Geometric Proof of the Square Pyramidal Number Formula

A Glimpse of Developing Leaf Venation

A Golden Ratio Dissection

A Gothic Window

A Graphical Analysis of the US Code

A Graphically Enhanced Method for Computing Real Roots of Nonlinear Functions

A Graph Theory Interpretation of the Sum of the First n Integers

A Grating at the End of a Tube

A Gravitational Optimization Problem

A Greeting from a Surface Plot

A Grill for Secret Writing

A Grill for Secret Writing 2

Aharonov-Bohm Effect

A Health Stories Model of Long-Term Care Insurance

A Hexagon with Opposite Sides Parallel

A Hybrid Benz-Grignani Logo

Aircraft Propeller

Aircraft Wing

Airplanes and Crosswinds

Akaike Criterion in Orbit Determination

Akrasia

Alarm Clock

A Layered Design

Albrecht Dürer's Heptagon of 1525

Albrecht Dürer's Nonagon of 1525

Albrecht Dürer's Pentagon of 1525

A Lemma in Geometry Concerning Points Generated by the Incircle of a Triangle

A Lemma of Archimedes about a Bisected Segment

A Lever with Four Weights

Algal Growth and Lipid Accumulation Stimulated by Nitrogen Concentration

Algebraic Family of Trefoil Curves

Algebraic Identities with Powers of Two or Four for Thirteen Variable Sets

Algebraic Identity for Powers 1, 2, 4 and 6

Algebraic Identity for Sum of Seven Terms with Exponents 1, 2, 4, 6 and 8

Algebraic Identity with Five Fourth Powers

Algebraic Identity with Sextics

Algebraic Identity with Six Fourth Powers

Algebraic Identity with Squares and Seventh Powers

Algebraic Identity with Twelve Variables

Algebraic Loops (1); Properties

Algebraic Loops (2); Symmetry-Conserving Vector-Division Hoop Algebras

Algebraic Numbers in the Complex Plane

Algebraic Operations on Melodies

Algebraic Problems in Propositional Logic

Algebraic Solution of the Plemelj Triangle Construction Problem

Algebraic Solutions to Polynomial Equations

Algebraic Surfaces with Many Nodes

Algebraic Values of Trigonometric Functions of Inverse Trigonometric Functions

Algebra Quiz

Algorithm for Bicubic Nonuniform B-Spline Surface Interpolation

Algorithm for Cubic Nonuniform B-Spline Curve Interpolation

Algorithm for Data Encryption Standard

Algorithmic Architecture with Cellular Automata

Algorithmic Complexity and Big-O Notation

Algorithmic Stupa Builder

Algorithmic Terrain with Cellular Automata

Algorithms for Egyptian Fractions

Algorithms for Finding Hamilton Circuits in Complete Graphs

Aliasing in Pendulum Waves

Aliasing in Time Series Analysis

A Library of Functions with Transformations

Alice and Jacobi in Determinantland

Alien Creator

A Limit Theorem from Information Theory

A Linear Homogeneous Second-Order Differential Equation with Constant Coefficients

A Line Associated with an Excircle

A Line Crossing Two Parallel Lines Makes Alternate Angles Equal

A Line Has Constant Slope

A Line Parallel to a Side of a Triangle

Alkanes

All 11 Folding Nets of the Cube

All 11 Folding Nets of the Regular Octahedron

Allan Plot of an Oscillator with Deterministic Perturbations

Allen Key

Allocation of Bandwidth by TCP

All Possible Sums and Differences of Powers

All Real Roots of a Nonlinear System of Equations

All Roots of Two Systems of Algebraic Equations

Almost-Circular Cellular Automaton

Almost Equilateral Triangles

Almost Repunit Primes

A Lockable Box

Alpha-Biharmonic Bézier Surfaces

Alpha Complex and Union of Growing Disks

Alpha-Type Stirling Engine

Alternating-Current Generator

Alternating Planar Graphs

Alternative 24-Hour Analog Clock

Alternative Forms of Maxwell's Equations

Alternative on the Island of Knights and Knaves

Altitude of a Tetrahedron Given Its Edges

Altitudes and Incircles

A Magic Box

AM and FM Modulation of ASCII Input

Amanecer con dos y tres soles (Spanish)

A Massive Bar Oscillating between Two Identical Rotating Support Rollers

Ambigram for Gardner

Amdahl's Law

A Mean-Reverting Jump Diffusion Process

American Call and Put Option

American Capped Call Options with Constant Cap

American Capped Call Options with Exponential Cap

American Options on Assets with Dividends Near Expiry

Ames Room

Am I in a Polygon?

A Minimal Circumcircle Measure of District Compactness

Ammann Chair

Ammann Tiles

Ammann Tiling A1

Ammann Tiling A4

Ammonia Inversion: Classical and Quantum Models

A Model for Fermi-Dirac Integrals

A Model for Monomer and Micellar Concentrations in Surfactant Solutions

A Model for Pedestrian Interaction with Anticipation

A Model for Photon Polarization and Detection

A Model for Population Growth

A Model for Successive Radioactive Decays

A Model Illustrating Multiple Interest Rate Analysis (MIRA)

A Model of Atmospheric Circulation

A Model of Market Shares I

A Model of Market Shares II

A Model of Plasmodium Falciparum Population Dynamics in a Patient during Treatment with Artesunate

A Model of the SCARA Robot

A Model of Vector Autoregression

Among Six People, Either Three Know Each Other or Three Are Strangers to Each Other

A Monotone Sequence Bounded by e

Amortized Loan Interest and Principal

Ampčre's Force Law: Force between Parallel Currents

Amplitude and Phase in 2D Fourier Transforms

Amplitude Modulation

A Multiobjective Optimization of a Room Configuration

Anagrams

Analemmas

An Algebraic Identity for Powers 0, 1, 2, 3 and 5

An Algorithm to Compute Square Roots of Integers

Analog & 24-Hour Digital Clocks

Analogies between Kinematics of Linear and Angular Motion

Analogies to Understand Stoichiometry

Analog Modulation

Analogous and Complementary Colors

Analogous Oscillations of a Pendulum and Liquid in a U-Tube

Analog-to-Digital Conversion Algorithm with a Single Slope

Analog-to-Discrete System Conversion Using Impulse Invariance

Analogy between Truth Tables and Venn Diagrams

An Alternative Periodic Table

An Altitude and Four Concyclic Points

Analyse einer Familie von Kurven (German)

Analysis of a Family of Curves

Analysis of an Extractive Distillation Column with Three Design Variables

Analysis of a Single-Span Euler-Bernoulli Beam under Different Loading Conditions

Analysis of Chromatographic Data

Analysis of Cumulative Triangles with the Chain-Ladder Method

Analysis of Diagnostic Accuracy Measures

Analysis of Diagnostic Accuracy Measures for Two Combined Diagnostic Tests

Analysis of Forces on a Truss

Analysis of Lattice Vibrations in Two Dimensions

Analysis of Minimum Credit Card Payments

Analytical Solution of Equations for Chemical Transport with Adsorption, Longitudinal Diffusion, Zeroth-Order Production, and First-Order Decay

Analytic Solutions for Double Deltafunction Potential

Analytic Solutions of the Helmholtz Equation for Some Polygons with 45 Degree Angles

Analyzing a Rectifying Column Using the Calculus of Finite Differences

Analyzing the Crystallography of the SH2 Domain and Its Residue Contact Map

An American High School Mathematics Examination Question

An Amoeba Problem

Anamorphic 2D Images That Look Three-Dimensional from a Particular Viewpoint

Anamorphic Origami

Anamorphic Prisms

Anamorphic Text Messages

An Analog Clock

An Angle Bisection

An Angle Invariant for Arbitrary Triangles

An Application of the Gergonne-Euler Theorem

An Application of the NestList Function

An Approximation to the n-th Prime Number

An ASCII Game of Life

Anatomy of a Quantum Jump

Anatomy of the Eye

An Automated Barrier

An Automatic Analog/Digital Clock

Ancient Aleppo Tiling

Ancient Architectural Designs with Cellular Automata

A Necklace of Equilaterals

An Efficient Test for a Point to Be in a Convex Polygon

A Negative Times a Negative Is Positive

An Elliptic Identity

An Enneper-Weierstrass Minimal Surface

Aneroid Barometer

An Essential Singularity

A Net That Folds into an Icosahedron or into a Double Biaugmented Triangular Prism

A New Kind of Casimir Energy and Its Implications for Dark Energy

A New Kind of Sunrise

A New Kind of Yin Yang Rotation

A New Model for Linear Polarizing Filter

A New Type of Polyhedron: The Scutoid

An Example of a Production Function

An Example of Subtraction of Negative Numbers

An Example of the Bolyai-Gerwien Theorem

An Example of Three-Dimensional Chaos

An Example of Two-Dimensional Chaos

An Excircle Inequality

An Expanding Structure Based on the Diamond Lattice

An Experiment with Boyle's Law

An Expert System Specific to Improving Personal Relationships

An Exploration of the "6174 Problem" and Some Generalizations

Angel Puzzle

Angle and Length Measurement of a Polygon

Angle and Velocity of Batted Baseball

Angle Bisector for an Angle Subtended by a Tangent Line

Angle Bisectors in a Triangle

Angle Bisectors of Two Intersecting Lines

Angle Bisectors on the Circumcircle

Angle Bisector Theorem

Angle Measure

Angle of Depression and Sine

Angle of Depression and Tangent

Angle of Intersection for Equiangular Spirals

Angle of Intersection of Two Circles

Angle of Torsion in the Elastic Range

AnglePath

Angles and Nature

Angles in a Cube

Angles in a Quadrilateral Total 360°

Angles in a Triangle Total 180 Degrees

Angles Measured in Degrees and Radians

Angles of a Triangle

Angry Spikey

Angular Acceleration

Angular Displacement

Angular Distribution of Gravitational Wave Radiation from Scattering by Two Point Particles

Angular Distribution of Radiated Power Emitted by an Accelerated Point Charge

Angular Function Fractals

Angular Momentum of a Rotating Particle

Angular Momentum of a Rotating Rigid Body

Angular Spheroidal Functions as a Function of Spheroidicity

Angular Velocity of a Compact Disc

Anharmonic Oscillator Phase Space Trajectories 2D

Anharmonic Oscillator Spectrum via Diagonalization of Amplitudes

An Illustration of the Argument Principle

An Illustration of the Central Limit Theorem Using Chi-Square Samples

Animal Cell Structure

Animal Sounds

Animated Binary

Animated Butterfly

Animated Model of an Industrial Robot Arm

Animated Pendulum

Animated Projectile Motion

Animated Remainder Graph

Animation of Free Kicks in Soccer

An Imitation Model for 2x2 Symmetric Games

An Imitation Model in the Hawk-Dove Game

An IMO Problem Involving Concurrency

An IMO Triangle Problem

An Increasing Preference Distribution

An Inequality for Tripolar Coordinates Related to the Brocard Angle

An Inequality Relating the Nagel Point and Exact Trilinear Coordinates

An Infinite Knight's Tour

An Infinitely Colorable Set of 3D Regions

An Infinite Tree of Circles or Spheres

An Interval Eventually Bounding Trajectories of the Logistic Map

An Intra-Population Imitation Model for Inter-Population 2x2 Symmetric Games

An Intra-Population Imitation Model in the Two-Population Hawk-Dove Game

An Introduction to Invariant Subspaces Using a Cube

An Intuitive Proof of the Pythagorean Theorem

An Inventory Control Model

Anisotropic Elasticity

Anisotropic Elasticity for HCP Crystal Structures

Anniversaries

Annotated Quadratic Polynomial

Annual Sunspot Numbers

Annual Temperature Cycles

Annulus for a Regular Polygon

An Octopus under Water

Anomalies for Planetary Motion

A Noncontinuous Limit of a Sequence of Continuous Functions

A Nonlinear Model for the Rings of Saturn

A Nonlinear Stage-Structured Cannibalism Model

An Ordinary Fractional Differential Equation

An Oscillating Pendulum

An Osculating Circle for Various Curvatures

Another Concurrency Generated by Circles about a Triangle's Sides and Lines through an Internal Point

Another Dissection of Two Rhombic Solids into an Icosidodecahedron and a Rhombicosidodecahedron

Another Generalization of Pythagoras's Theorem

Another Hinged Dissection of One Pentagon to Five Pentagons

Another Knights and Knaves Puzzle Generator

Another Octagram-To-Square Dissection

Another Relation between the Areas of Triangles Associated with an Excircle

Another Triangle into Hexagram Dissection

Another Variant of Kosnita's Theorem

Anscombe Quartet

Antarctic Sea Ice Aggregation Model

Ant Colony Optimization (ACO)

Antenna Patterns for a Laser Interferometer Gravitational Wave Detector

Antibody Production Fed-Batch

Anticycloid Curves I: A Rolling Circle

Anticycloid Curves II: A Rolling Ellipse

Antikythera Mechanism

Antipodes

Ant Puzzle

An Unfoldable Polyhedron

An Unforgettable Substitution Code

Any Quadrilateral Can Tile

Any Triangle Can Tile

A One-Parameter Family of Polyhedra with Two Kinds of Symmetries

A One-Parameter Family of Zonohedra

A Packing of the 3 x 3 x 3 Cube

A Pair of Biorthogonal Bases in the Real Plane

A Parabola Sieve for Prime Numbers

A Parabolic Mirror

A Parabolic Partial Differential Equation in Three Different Geometries

A Parallelogram Defined by the Centers of Four Circumcircles

A Parallelogram Defined by the Centers of Four Incircles

A Parallelogram Related to the Excircles

A Parallelogram with Vertices on Two Circles

A Parameterized Multistate Life Table

A Parametric Plot of a Spiral on a Paraboloid

A Passive Cochlear Model

A Path through the Lattice Points in a Quadrant

A Perfect Cognac Glass

Aperture Synthesis with VLA and ALMA Radio Telescope Arrays

Apéry's Rational Approximation to His Constant

Apollonian Circle Packings via Möbius Transformations of Hyperbolic Polygons

Apollonian Edge Circles

Apollonian Gasket

A Polygon from Its Midpoints

A Polygon That Folds into a Regular Tetrahedron or into a Rectangular Box

A Polyhedron with 420 Triangular Faces

A Polynomial Function with an Irreducible Factor

Apparent Violations of Bell's Theorem

Appearance of Spiral Behavior

Apple Image

Apple in a Carnot Refrigerator

Application of the Murphree Liquid Efficiency Method to the Study of a Binary Distillation Column

Applications of Driving-Force and McCabe-Thiele Diagrams to Binary Distillation Processes

Applications of Fresnel Equations for Light Intensities

Applications of Lanchester's Square Law

Applied Voltage on an Ideal MOS Capacitor

Applying a Clipping Mask to a Photographic Image

Applying a Coloring Function to an Image

Applying Graphics Filters Using Convolution

Applying Mohr's Circles to Stress States of Continuum

Applying the Iota-Delta Numerical Function to Describe Normal and Anomalous Diffusion Using the Rules 26 and 146

Applying the Pólya-Burnside Enumeration Theorem

Applying the Smith-Waterman Similarity to Cellular Automata

Applying the Soave-Redlich-Kwong Equation of State

Apply the Hunter-Nash Method to Liquid-Liquid Extraction

Approach of a System of Particles towards Thermal Equilibrium

Approximate Area and Circumference of a Circle Using Isosceles Triangles

Approximate Bubble Temperature Distribution for Benzene, Toluene, p-Xylene Ternary Mixture

Approximate Distributions Using Moments in Gram-Charlier Expansion

Approximate pH Calculation of Acids

Approximate Rhombic Icosahedron

Approximate Rhombic Triacontahedron

Approximate Solutions of a Functional Differential Equation

Approximate Spikey

Approximating Ackermann Steering Geometry with a Trapezoidal Linkage

Approximating a Double Integral with Cuboids

Approximating a Judge

Approximating Catalan's Constant

Approximating Circles with Pixels

Approximating Continuous Functions with Haar Approximations

Approximating Pi by the Monte Carlo Method

Approximating Pi Using Inscribed and Circumscribed Circles of Regular Polygons

Approximating Pi with Continued Fractions

Approximating Pi with Inscribed Non-Regular Polygons

Approximating Pi with Inscribed Polygons

Approximating Pi with Trigonometric-Polynomial Integrals

Approximating Polar Area with Sectors

Approximating Spheres with Boxes

Approximating the Brachistochrone by Line Segments

Approximating the Derivative by the Symmetric Difference Quotient

Approximating the Derivatives of a Function Using Chebyshev-Gauss-Lobatto Points

Approximating the Jacobian Elliptic Functions

Approximating the Length of Viviani's Curve

Approximating the Logarithm of Any Base with Continued Fractions

Approximating the Riemann Zeta Function with Continued Fractions

Approximating the Tangent to a Curve with Secants

Approximating the Volume of a Sphere Using Cylindrical Slices

Approximating the Yin-Yang Symbol with Rhombuses

Approximating Volumes by Summation

Approximation by Orthogonal Polynomials

Approximation by Rationals

Approximation of Discontinuous Functions by Fourier Series

Approximation of Irrationals

Approximations to the Distribution of Primes

A Primer on Stoichiometry

A Probabilistic Forest Fire Model

A Probabilistic Model for Population Extinction

A Procedure to Compute the Digit Sequence of a Rational Number

A Procedure to Compute the Digit Sequence of a Square Root

A Product of Chord Lengths in a Circle

A Projective Tetrahedral Surface

A Proof of Euler's Formula

A Proof of the Difference Identity for Cosine

A Puzzle about Labeled Logicians

A Quintuple Triangle Inequality

A Quiz for the Longest Rivers and Largest Lakes

A Random Meeting

A Random Walk on a Random Rock-Paper-Scissors Graph

A Rational Bicentric Quadrilateral with a Rational Area

A Rational Function that Iterates to the Identity

Arbitrary Curves of Constant Width

Arc Form Design Widget

Arc Form Discovery Widget

Archaic Trigonometry

Archimedean Screw

Archimedean Solids

Archimedes' Approximation of Pi

Archimedes' Hat Box Theorem

Archimedes's Method for Determining the Area of a Circle

Archimedes's Neusis Angle-Trisection

Archimedes's Spiral and Its Tangents

Archimedes's Tomb

Archimedes' Twin Circles in an Arbelos

Architectural Applications of Several 3D Geometric Transformations

Arc Length

Arc Length and Polygonal Approximations

Arc Length Approximation

Arc-Length Continuation Applied to the Haber Process

Arc Length of a Logarithmic Spiral

Arc Length of Cycloid

Arc Length of the Hyperbolic Cosine

Arc Resolution

Area Among Four Curves In A Square

Area and Perimeter of a Rectangle

Area and Volume of n-Dimensional Spheres

Area Approximation for Polar Plot

Area between a Line and the Graph of a Function

Area between Curves

Area Bisectors via Monte Carlo

Area Function for a Piecewise Curve

Area Maze

Area Maze Race

Area of a Circle from Sectors

Area of a Disk

Area of a Hexagon Formed by the Vertices and Altitude Extensions of a Triangle

Area of an Ellipse

Area of an Inscribed Triangle in Terms of the Product of Its Sides

Area of a Normal Distribution

Area of a Parallelogram

Area of a Pentagon

Area of a Polygon

Area of a Polygon on the Integer Lattice

Area of a Quadrilateral by Triangulation

Area of a Quadrilateral within a Triangle

Area of a Triangle

Area of a Triangle inside the Incircle

Area of a Triangle in the Poincaré Disk

Area of a Triangle on an Integer Grid

Area of a Triangle Using Sine

Area of Epicycloid and Hypocycloid

Area of Parallelogram in Terms of Its Diagonals

Area of the Arbelos

Area of Triangles Formed by Tangents on the Reciprocal Curve

Area, Perimeter, and Diagonal of a Rectangle with Uncertain Sides

Area Puzzle

Areas in a Multiplication Table

Areas of Parallelograms

Areas of Parallelograms and Trapezoids

Areas of Squares from the Pedals of a Triangle

Areas of the Lens and Two Lunes of Two Intersecting Circles

Areas of Triangles

Area Under a Curve

Area under a Cycloid

Area under a Cycloid (II)

Area under a Parabola by Symmetries

Area under the Exponential Curve

Area Under the Tractrix

Arecibo Signal Generator

A Recursive Behavior of Words in Different Languages

A Recursive Integration Method for Options Pricing

A Recursive Sequence Convergent to e

A Regular Polygon with an Even Number of Sides Is the Union of Rhombuses

A Relation between Altitudes of Four Triangles

A Relation between Incircles and Excircles

A Relation between the Areas of Four Triangles

A Relation between the Contact Triangles of a Triangle

A Relationship between the Cube, Tetrahedron, Octahedron, and Rhombic Dodecahedron

A Reluctant Random Walk

A Remarkable Formula Of Ramanujan

Are the Lines Parallel?

Are the Red Lines the Same Length?

Are These Lines Straight?

Argand Diagram

Argentometric Titration by Precipitation of Silver Salts

A Rhombic Dodecahedron in the Skeleton of a Tesseract

A Rhombic Dodecahedron Made of Rhombic Triacontahedra

A Ring Game

Aristotle's Wheel Paradox

Arithmetic in Lambda Calculus

Arithmetic Mean, Geometric Mean, Root Mean Square and Harmonic Mean for Two Numbers

Arithmetic Operation Game

Arithmetic Operation Game 2

Arithmetic Sculpture for Addition and Multiplication

Arithmetic Sequences

Arithmetic Series

Armed Balloons Puzzle

Arm Manipulations

Arm-Z Modular Manipulator

Arnold-Beltrami-Childress (ABC) Flows

Arnold's Cat Map

Arnold Tongues

A Rod Sliding in a Semicircular Well

A Rolling Reuleaux Triangle

A Rose for Valentine's Day

A Rotating Hinged Parallelogram

A Rotating Puzzle

A Rotating Reuleaux Triangle

A Rotating Waveplate Polarization Analyzer

Arrangements of Golden Prolate Rhombohedra

Arranging Balls into Boxes

Arrhenius Equation for Chemical Reaction

Arrhenius Equations for Reaction Rate and Viscosity

Arrhenius versus Exponential Model for Chemical Reactions

Arrhenius versus Eyring-Polanyi Model

Art Gallery Problem

Artificial Metropolis

Art of Tangent Circles

Aryabhata's Algorithm for the Square Root of an Integer

ASCII Images of Portraits

A Sculpture Based on the Diamond Unit Lattice

A Second-Order Chemical Reaction

A Selection and Analysis Tool for Fluorescence Recovery after Photobleaching (FRAP) Region of Interest (ROI)

A Semi-Discrete Analog to The Mean Value Theorem

A Sequence of Inscribed Platonic Solids

A Sequence of Spheres

A Shapeshifting Flexible Frame

Asian Tour Puzzle

A Signed Rank Test of Hypotheses about a Median

Asimov's Ladder of Physical Constants

A Simple 2x2 Cooperative Game

A Simple Inventory Control Model

A Simple Lever

A Simple Lofting Function

A Simple Logic Game

A Simple Metronome

A Simple Model for Leaf Placement

A Simple Model for Multiple Epidemics

A Simple Model of Magnetization

A Simple, Standard Linear Programming Scenario

A Simplified Epidemic Model

A Simplified Model for the Big Bang

A Sine/Cosine Identity

A Six-Variable Algebraic Identity with Squares and Cubes

A Sketch of American Gothic

A Sliding Element in Rheological Models

A Snowball's Rate of Change

A Solution of Euler's Type for an Exact Differential Equation

A Spatial Dynamic Jury Model

A Special Case of the Sum of Two Cosines

A Special Parameter Value for the Logistic Map

A Sphere Divided by Planes and a Cone

A Sphere Visits Flatland

A Spider Walking on a Polygon

A Spikey Made of Tetrahedra and Octahedra

Aspirin Metabolism in the Body

A Squaring Cellular Automaton

Assembling a Golden Great Rhombicosidodecahedron

Assembling a Great Rhombic Triacontahedron

Assembling a Rhombic Triacontahedron

Assembly of 60 Rhombic Dodecahedra

Assessing the Risk of Food Poisoning

Assessing Total Risk from Interacting Factors

Assessor Model for Simulated Test Markets

Asset Allocation

Associated Surface of a Minimal Möbius Strip

A Strategy for Exploring k=2, r=2 Cellular Automata

Astroid-Shaped Tent Made of Rectangles

AstroMast

AstroMesh Reflector

Astronaut Training Centrifuge

Astronomical CCD Camera Noise

Astronomical Clock

Astronomical Data

Astronomical Units of Length

A Study of the Dynamic Behavior of a Three-Variable Autocatalator

A Sturm-Liouville Eigenvalue Problem

A Subfamily of Julia Sets

A Subset of Phi Space

Asylum in the United States

Asymmetric Heavy Top

Asymmetric Propeller

Asymmetric Simple Exclusion Processes

Asymmetric Spirographs

Asymptotic Expansions

Asymptotic Expansions for Some Special Functions

Asymptotic Stability of Dynamical System by Lyapunov's Direct Method

Asymptotic Stability of Steady States for Two-Component Logistic Map

A Tessellation from a Square Twist Fold

A Tessellation of the Sphere

A Tessellation of the Torus

A Test for the Convexity of a Quadrilateral

A Tetrahedron with Edges of Given Length

A Theo Jansen Walking Linkage

A Theorem about Two Tangent Circles

A Theorem on the Dihedral Angles of a Tetrahedron

A Theory of Insurance Lapses

A Third-Order Differential Equation with Chaotic Solutions

A Three-Term Algebraic Identity with Squares or Quartics

Atínale a la bola (Spanish)

Atmospheric Radar Wave Absorption

Atomium

A Tour of Second-Order Ordinary Differential Equations

ATP Synthesis

A Triangle and an External Contact Triangle

A Triangle Formed by the Centers of Three Circles

A Triangle Formed by the Centers of Three Nine-Point Circles

A Triangle Inequality Involving the Altitudes, Semiperimeter, Inradius, and Circumradius

A Triangle Model of Criminality

A Triangle Semiperimeter Inequality

Attainable Region for van de Vusse Kinetics

Attainable Regions for Maleic Anhydride Manufacture in a Plug-Flow Reactor

Attenuation of a Sinusoidal Magnetic Field in a Halfspace Conductor

Attenuator Values in Resistor Families

Attraction and Repulsion in Dynamical Systems

Attractors of Iterated Affine Transform Systems

Attributing Portfolio Value at Risk: Relations with Component VaR, Marginal VaR, and Incremental VaR

A Twist-Hinged Dissection of Triangles

A Two-Link Inverse-Kinematic Mechanism

Atwood's Machine

Atwood's Machine with Rotational Inertia

A Two-Phase Anneal: The Beauty of Interface Dynamics

A Two-Power Algebraic Identity

A Two-Power Diophantine Identity

A Two-State, Discrete-Time Markov Chain

Audio File Size Calculator

Audio Spectrogram

Augmenting Polyhedra with Prisms or Pyramids

Aurifeuillean Factorization

Autocorrelation and Partial Autocorrelation Functions of AR(1) Process

Auto Lease Calculator

Auto Loan Calculator

Automata Generative Networks 1

Automata Generative Networks 2

Automated Graph Layout

Automatically Selecting Histogram Bins

Automatic Differentiation

Automatic Feedback Control of a Pendulum-and-Cart System

Automatic Stabilizers in Krugman's Cross Diagram

Autoregressive Moving-Average Generator

Autoregressive Moving-Average Simulation (First Order)

Auto-Regressive Simulation (Second-Order)

Autostereogram with Depth Adjustment

Autothermal Reactor

A Variable Can Be Anything

A Variation of Banach Matchbox Problem

Averaged Cellular Automaton Patterns

Averaged Gosper Curves

Average Force on a Batted Ball

Average Rate of Change: Exploring More Functions

Averages of Totalistic Automaton States

Average Value of a Function

Average Value via Integrals

Average Vertex Degree of Connected Graphs

A Vertex Distance Relation for Two Triangles

A Very Tough Puzzle

A Visit to Flatland

A Visit to Sphereland

A Visualization of Logarithms

A Visual Proof of Girard's Theorem

A Visual Proof of Nicomachus's Theorem

A Visual Proof of Ptolemy's Theorem

A Visual Proof of Thales's Intercept Theorem

A Visual Proof of the Cauchy-Schwarz Inequality in 2D

A Visual Proof of the Double-Angle Formula for Sine

A Visual Proof of Viviani's Theorem

A Wave Collapse in the Causal Interpretation of Quantum Theory

A Wavy Parametric Cliff Overlooking the Sea

A Wide-Tie-Cross-to-Square Dissection

A Word Problem about Boats

Axial Electric Field of a Charged Disk

Axial Gradient

Axial Tilts of Planets

Axis of Revolution

Azeotropes of Binary Mixtures Containing Ethanol

Babylonian Algorithm for Computing Square Roots

Babylonian Numerals

Bad Fraction Simplification

Balanced Annihilation

Balanced Bracket Sequences

Balanced Configurations of Multislot Centrifuges

Balanced T-Coil Parameters

Balanced Ternary Notation

Balancing Abstract Chemical Equations

Balancing Abstract Chemical Equations with One Kind of Atom

Balancing a Can on Its Edge

Balancing a Double Inverted Pendulum in 2D or 3D

Balancing Redox Reactions

Ball Bearings

Ball Bouncing in a Potential Well

Ball Bouncing on a Moving Piston

Ball Bouncing on an Elliptical Slope

Ball in a Box

Ball in V Groove Geometry

Ballistic Pendulum

Ballistic Trajectories

Ball of 30 Octahedra

Ball on the Border of a Rectangle

Balloon Dog

Ball Rolling without Slipping inside a Vertical Cylinder

Balls and Sticks Geometrical Sculpture

Balls Bouncing off Walls

Balls Rolling on a Sphere

Ball Valve

Balmer Series for the Bohr Atom

Banach Matchbox Problem

Banchoff's Chmutov Surfaces

Banchoff's Klein Bottle

Bands of Faces for the Rhombic Dodecahedron and Triacontahedron

Band Spectrum in a Periodic Potential

Band Structure of a Quantum Wire with Rashba and Zeeman Interactions

Band Structure of Graphene

Band Structure of P-N Junction Semiconductor

Band Structures in Zigzag Graphene Nanoribbons and Armchair Carbon Nanotubes

Bankoff Circle

Banzhaf Power Index

Barlow's Wheel

Barnsley's Tree

Barrel Cactus

Barrier Option Pricing within the Black-Scholes Model

Barrow's Inequality

Bars of a Hyperboloid

Bars of an Astroid

Bars with an L-Shaped Cross Section

Barycenter for Three Masses at the Vertices of a Triangle

Bascule (Seesaw) Bridge

Baseball Batting Metrics

Baseball Card Collecting

Baseball: Graph of On-Base Percentage

Baseball: Graph of Slugging Percentage

Baseball without Swings

Base Conversions from Base 2 through 100 Using Radix Points

Basel II Capital Adequacy: Internal Ratings-Based (IRB) Approach

Basic Angles

Basic Arithmetic in Other Bases

Basic Examples of Propositional Calculus

Basic FM Synthesis of Sounds

Basic Graphics Tool

Basic One-Step Graphical Operations on Complex Numbers

Basic Option Trading Strategies

Basic Parameters of the Bevan Point (X40)

Basic Parameters of the Brocard Midpoint X(39)

Basic Parameters of the Circumcenter

Basic Parameters of the Clawson Point

Basic Parameters of the de Longchamps Point

Basic Parameters of the Exeter Point

Basic Parameters of the Far-Out Point

Basic Parameters of the Feuerbach Point

Basic Parameters of the First Fermat Point

Basic Parameters of the First Isodynamic Point

Basic Parameters of the First Napoleon Point

Basic Parameters of the Gergonne Point

Basic Parameters of the Incenter of a Triangle

Basic Parameters of the Kimberling Center X12

Basic Parameters of the Kimberling Center X25

Basic Parameters of the Kimberling Center X26

Basic Parameters of the Kimberling Center X27

Basic Parameters of the Kimberling Center X28

Basic Parameters of the Kimberling Center X29

Basic Parameters of the Kimberling Center X33

Basic Parameters of the Kimberling Center X34

Basic Parameters of the Kimberling Center X35

Basic Parameters of the Kimberling Center X36

Basic Parameters of the Kimberling Center X37

Basic Parameters of the Kimberling Center X(38)

Basic Parameters of the Kimberling Center X41

Basic Parameters of the Kimberling Center X(42)

Basic Parameters of the Kimberling Center X(43)

Basic Parameters of the Kimberling Center X(44)

Basic Parameters of the Kimberling Center X(45)

Basic Parameters of the Kimberling Center X(46)

Basic Parameters of the Kimberling Center X(47)

Basic Parameters of the Kimberling Center X(48)

Basic Parameters of the Kimberling Center X(49)

Basic Parameters of the Kimberling Center X(50)

Basic Parameters of the Kimberling Center X(51)

Basic Parameters of the Mittenpunkt

Basic Parameters of the Nagel Point

Basic Parameters of the Nine-Point Center

Basic Parameters of the Orthocenter

Basic Parameters of the Schiffler Point

Basic Parameters of the Second Fermat Point

Basic Parameters of the Second Isodynamic Point

Basic Parameters of the Second Napoleon Point

Basic Parameters of the Second Power Point X(31)

Basic Parameters of the Spieker Center

Basic Parameters of the Symmedian Point

Basic Parameters of the Triangle Centroid

Basic Performance Measures for Information Retrieval

Basic Statistics of Movable Points

Basic Structure, Plane Orientation, and Facetting in the Face-Centered and Body-Centered Cubic Crystal Structures

Basic Supply and Demand

Basic Ternary Phase Diagram

Basic Views in Technical Drawing

Basis for a Topology

Basis for Pure Geodetic Angles

Basis Instruments Contracts (BICs) in Baseball World Series Odds

Basketball Seam Pattern Designer

Basketball Shot

Batch Distillation

Batch Distillation of a Non-Miscible Binary Mixture

Batch Fermentation with Product Inhibition

Batch Reactors at Constant Volume or Constant Pressure

Batch Reactor Using the Segregation Model

Batch Reactor with Multiple Reactions

Batch Rectification of a Binary Mixture at Total Reflux

Batch Rectification of an Acetone/Chloroform Binary Mixture

Batch Rectification of an Ethanol/Ethyl-Acetate Binary Mixture

Batch Rectification of an Ideal Benzene/Toluene Binary Mixture

Batch Rectification of a Partially Miscible Binary Mixture

Bat Occupancy at a Wind Facility

Bat Occupancy Probabilities

Battery Requirements for Electric Vehicles

Batting Averages, Weighted Averages, and Simpson's Paradox

Baum-Sweet Sequence

Bayesian Distribution of Sample Mean

Bayesian Range Weighting for Sonar

Bayes's Theorem and Inverse Probability

bct-Carbon

Bead on a Horizontally Rotating Hoop: Variable Initial Displacement and Tilted Axis

Bead on a Horizontally Rotating Hoop with Movable Axis

Bead on a Rotating Hoop

Bead on a Rotating Wire

Beat Chebyshev

Beat Frequency of Sound Waves

Beating and Roughness

Beats Produced by Two Tuning Forks

Beats Working

Beautiful Designs Made from the Knight's Tour

Beautiful Designs Made from Two Knights' Tours

Bedford-McMullen Carpets

Bed of Nails

Bee Honeycomb

Beer's Law

Behavior of Equilibrium Points in Two-Dimensional Systems of Differential Equations

Bell Curves

Bell Number Diagrams

Bell's Theorem

Bell Wave Machine

Bending and Stretching of an Elastic L-Beam

Bending and Stretching of an Elastic U-Beam

Bending and Wrinkling as Competing Relaxation Pathways of Strained Free-Hanging Films

Bending a Wire on a Cylinder

Bending of Light by a Star

Benford's Law and Data Spread

Benford's Law from Ratios of Random Numbers

Benford's Law in Statistical Physics

Bennett's Octagon-to-Square Dissection

Beraha's Conjecture and Cyclic Graphs

Beraha's Conjecture, Wheels, and Cyclic Graphs

Bernoulli-Euler Double Generation Theorem

Bernoulli Inequality

Bernoulli's Differential Equation

Bernoulli's Lemniscate Formed from an Isosceles Trapezoid

Bernoulli's Theorem

Bernstein Polynomials

Bernstein Polynomials and Convex Bézier Sums

Berry Pseudorotation in Phosphorus Pentafluoride

Bertrand Competition with Linear or Quadratic Costs

Bertrand's Box Paradox

Bessel Function Lissajous Figures

Bessel Functions in the Complex Plane

Best Effort Global Warming Trajectories

Best Response in Static Two-Player Games

Best Response Learning in a Cournot Framework

Beta Cube

Beta Distribution

Beta Distributions for a Given Mean, Median or Mode

Betting Strategies: Should I Play or Run Away?

Between Ellipsoid and Spindle in Stereo

Between Sphere and Torus

Beverton and Holt's Yield per Recruit Model

Bezdek's Unistable Polyhedron With 18 Faces

Bézier Curve Approximation of an Arc

Bézier Curve by de Casteljau's Algorithm

Bézier Curve Flowers

Bézier Curves

Bhargava's Theorem

Bicolor Towers of Hanoi

Bicycle Gear Ratios and Meters of Development

Bicycle or Unicycle Tracks?

Bicycle Rides

Bicycle Wheels Using Curves of Constant Width

Bidirectional Variant of Josephus Problem

Bifurcation Analysis of a Cubic Memristor Model

Bifurcation Diagram for a Generalized Logistic Map

Bifurcation Diagram for a Simple Nonlinear Optical Fiber Ring Resonator

Bifurcation Diagram for the Gauss Map

Bifurcation Diagram for the Rössler Attractor

Bifurcation Diagram for the Tent Map

Bifurcation Diagram for the Three-Variable Autocatalator

Bifurcation Diagram of the Hénon Map

Bifurcation Diagrams with Flow Fields

Bifurcation in a Biochemical Reactor

Bifurcation in a Model of Spruce Budworm Populations

Bifurcation of Boundary Wavefronts for Some Graphs

Bifurcations in First-Order ODEs

Bifurcations of the Logistic Map

Big Circles on Small Tiles

Biggest Little Polyhedron

Bijective Mapping of an Interval to a Square

Bilateral Accident Model

Bilinski's Vase

Billiard Ball Fredkin Gate

Billiard in a 4D Hypercube

Billiards in Regular Polygons

Bimetallic Spiral Thermometer

Bimetallic Strip

Bimodal Normal Distribution Mixtures

Bimodal Size Distributions in Grinding and Attrition

Binary-Based Cryptosystem

Binary Card Game

Binary Card Game on an Unfolded Cube

Binary-Coded Decimal Clock

Binary Coding Functions for Generalized Logistic Maps with z-Unimodality

Binary Counting Sequence

Binary de Bruijn 2D Hex Maps

Binary Diffusion Coefficients for Gases

Binary Distillation of Non-Ideal Mixtures Using Driving-Force Diagrams

Binary Election Sequences

Binary Gray Code

Binary Indexed Tree

Binary Inspiral Gravitational Waves from a Post-Newtonian Expansion

Binary Numbers, Subsets and Compositions

Binary Operations with Cellular Automata

Binary Operators Satisfying Two Axioms

Binary Options: Pricing and Greeks

Binary Patterns of Integer Functions

Binary Program Pattern

Binary Relations among Elements in a Set

Binary Run-Length Encoding

Binary Tree Enumeration

Binaural Beats

Binding Energies of Isotopes

Binet-Cauchy Identity

Binet's Ellipsoid

Bingham Fluid Flow in a Circular Tube

Bingo Card Generator

Binocular Disparity versus Depth (Visual Depth Perception 9)

Binocular Disparity (Visual Depth Perception 7)

Binomial Approximation to a Hypergeometric Random Variable

Binomial Approximation to a Poisson Random Variable

Binomial Black-Scholes with Richardson Extrapolation (BBSR) Method

Binomial Coefficients in the Multiple-Angle Tangent Formula

Binomial Cube

Binomial Distribution

Binomial Distributions Are Bernstein Vectors

Binomial Distribution via Coin Flips

Binomial Option Pricing Model

Binomial Probability Distribution

Binomial Theorem

Binomial Theorem (Step-by-Step)

Binomial Tree

Bin Width and Histogram Shape

Biodiversity in Spatial Rock-Paper-Scissors Games

Bioeconomics of a Discrete Ricker Model with Delayed Recruitment

Biphasic Exponential Decay and Growth

Biradial Matrix

Birds on a Wire

Birds on a Wire Revisited

Birefringence at an Isotropic-Uniaxial Interface: Waves, Rays, and Fresnel Coefficients

Biregular Star Graphs

Birthday Paradox Probability Estimates

Bisecting a Line Segment through the Orthocenter

Bisecting a Line Segment Using Sticks of Equal Length

Bisecting a Line Segment with a Ruler Given a Parallel Line

Bisecting an Angle Efficiently

Bisecting an Angle with a Two-Edged Ruler

Bisecting a Triangle

Bisecting the Area and Perimeter of a Triangle

Bisection Method

Bisection of Line Segment

Bisection of Segments by the Sides of a Triangle

Bisectors of Quadrilaterals

Bisectors of the Angles of the Orthic Triangle

Bishop Edge Coloring

Bit Count Classification of Binary Numbers

Bit Plane Effects

Bit Response of a PR4 Encoded Magnetic Medium

Bitwise Operations Mod n

Bitwise XOR Game

Bivariate First-Order Vector Autoregression Model with Correlated Random Shocks

Black and White Point Adjustments of Photographic Images

Blackbody Curves and Telescope Sensitivity

Blackbody Radiation

Blackbody Radiation: from Rayleigh?Jeans to Planck and Vice Versa

Blackbody Spectrum

Blackjack Player

Black-Scholes Option Model

Blasting Radii for Various Entropic Explosives

Blended Fonts

Blended Quadrilaterals

Blind Algorithm

Blind Spot and "Filling In" Illusions

Blip Solitons

Block and Tackle

Block Bootstrap for Time Series

Block Builder

Block in Three-Point Perspective

Block in Two-Point Perspective

Block on a Frictionless Inclined Plane

Blocks in Cellular Automaton Patterns

Blood Donation Protocols

Blood Lactate Concentration in "Good" and "Bad" Runners

Blood Spatter Trigonometry

Blood Type Inheritance

Blooms from the Campanus Sphere

Blue Sky and Red Sunset

Board Inversion

Bochvar's Three-Valued Logic

Bode, Nyquist, and Nichols Diagrams of Second-Order Systems

Body Mass and Onset of Hypothermia

Body-Mass Index

Bohmian Quantum Trajectories for Coherent States of the Pöschl-Teller Potential

Bohm Trajectories

Bohm Trajectories for a Coupled Two-Dimensional Harmonic Oscillator

Bohm Trajectories for an Isotropic Harmonic Oscillator with Added Inverse Quadratic Potential

Bohm Trajectories for a Particle in an Infinite 3D Box

Bohm Trajectories for a Particle in a Two-Dimensional Calogero-Moser Potential

Bohm Trajectories for a Particle in a Two-Dimensional Circular Billiard

Bohm Trajectories for a Special Type of a Pseudoharmonic Potential

Bohm Trajectories for a Type of Derivative Nonlinear Schrödinger Equation

Bohm Trajectories for Quantum Airy Waves in a Time-Dependent Linear Potential

Bohm Trajectories for Quantum Particles in a Time-Dependent Linear Potential

Bohm Trajectories for Quantum Particles in a Uniform Gravitational Field

Bohm Trajectories for the Anisotropic Coulomb Potential with Constant Phase Shift

Bohm Trajectories for the Noncentral Hartmann Potential

Bohm Trajectories for the Two-Dimensional Coulomb Potential

Bohm Trajectories in an LCAO Approximation for the Hydrogen Molecule H_2

Bohr's Model for the Hydrogen Molecule

Bohr's Orbits

Boids: Simulated Flocking Behavior

Boiling Point Elevation of Solutions

Boiling Point of Water as a Function of Altitude

Boiling Point of Water on Several Planets

Boltyanski's Cake Problem

Boltzmann Gas

Boltzmann's Analysis of Macroscopic and Microscopic Aspects of Reversible Thermodynamic Processes

Bolyai Memorial in Marosvásárhely

Bolzano's Continuous but Nowhere Differentiable Function

Bolzano's Function

Bolzano's Theorem

Bonding and Antibonding Molecular Orbitals

Bond Pricing

Book Reader

Boolean Algebra

Boolean Algebra with Eight Elements

Boolean Algebra with Eight Elements 2

Boolean and Gene Regulatory Networks

Boolean Dissimilarities

Boolean NK Networks

Boolean Operations in Geometry

Boolean Operations on Graphs

Boolean Primitives as Symmetric Boolean Functions

Boolean Ring Cryptography

Boolean Symmetric Functions

Boole Differential Equation with Continued Fractions

Boost Composition and Wigner Rotation in Rhodes-Semon Rapidity Space

Bootstrap Percentile Confidence Intervals

Bootstrap Percolation Automaton

Bootstrapping Credit Default Swap Data

Bootstrapping to Compute Value-at-Risk Standard Errors

Border Patterns

Boron Suboxide

Borromean Mesh

Borromean Ring Removal

Borromean Rings Logo of the International Mathematical Union (IMU)

Bose-Einstein Condensation (Free Boson Gas)

Bose-Einstein Condensation in a Harmonic Trap

Bose-Einstein, Fermi-Dirac, and Maxwell-Boltzmann Statistics

Boson and Fermion Effects in Helium-Helium Scattering

Bottema's Theorem

Bouc-Wen Model: Magnetorheological Fluid Damping for Micro-Vibration Control

Bouncer

Bounce Time for a Bouncing Ball

Bouncing a Superball

Bouncing Ball in a Closed Room

Bouncing Bob Pendulum

Bouncing Mass-Spring System

Boundary and Hole Detection

Boundary Conditions for a Semi-Infinite Potential Well

Boundary Control of a 1D Wave Equation by the Filtered Finite-Difference Method

Boundary-Feedback Control of Vibrations on a String with and without Filtering

Boundary-Layer Flow Past a Semi-Infinite Wedge: The Falkner-Skan Problem

Boundary Layer in Flow between Parallel Plates

Boundary Stabilization of Euler-Bernoulli and Rayleigh Beam Vibrations

Boundary Value Problems for Cone Geodesics

Boundary Value Problem Using Galerkin's Method

Boundary Value Problem Using Series of Bessel Functions

Bounding Partial Sums of the Harmonic Series

Bound States in a Square Potential Well

Bound States of a Finite Potential Well

Bound States of a Semi-Infinite Potential Well

Bound-State Solutions of the Schrödinger Equation by Numerical Integration

Bound-State Spectra for Two Delta Function Potentials

Bour's Minimal Surface and Variations

Bowls Puzzle

Box-Counting Algorithm of the Hénon Map

Box-Counting the Dimension of Coastlines

Box Packing

Box Toppling Patterns

Box Volume and Surface Area

Boy Scouts' Compass Course

Boy Surface and Variations

Brachistochrone Problem

Brachistochrones

Bracket with Cylindrical Hinge

Bradley's Hexagram-to-Square Dissection

Bradley's Triangles for a 3-4-5 Triangle

Bradley's Two-Triangles-to-One Dissection

Bragg's Law

Brake Shoes

Braking a Car

Branched Pipe Connection

Branching Ratios for Higgs Boson Decays

Brauer's Cassini Ovals versus Gershgorin Circles

Breadth-First Search Enumeration

Breadth-First Search Robot Motion Planning

Break Even

Breaking Azeotropes with Hybrid Separation Systems

Breaking the Acetone-Methanol Azeotrope with Different Extraction Solvents

Breaking the Azeotrope between Cyclohexane and Benzene Using Aniline

Breaking the Azeotrope between Methanol and Acetone with an Entrainer

Breakthrough Curves for Adsorption with Longitudinal Diffusion Assuming Linear Equilibrium

Breeding Outcomes with Two Autosomal Linked Genes

Breit-Rabi Diagram

Brianchon's Theorem

Bricard's Flexible Octahedron

Bridges with Catenary Shaped Supports

Bridge Varieties

Briggs-Rauscher Mechanism: The Chemical Color Clock

Brightness and Magnitude

Brillouin Zone of a 2D Square Lattice: Tight Binding Approximation

Brillouin Zone of a Single-Walled Carbon Nanotube

Brillouin Zone Sampling of a Periodic Chain with N Sites

Brillouin Zone Sampling of Chain with N Sites and Modified Periodic Boundary Conditions

Brinell Hardness of Materials

Brix Corrections for Citric Acid and Temperature

Broadcasting Satellite in a Geocentric Kepler Orbit

Brodie's Pentagon-to-Square Dissection

Broken Heart

Broken Heart Tangram

Broken Heart Tangram (Variation)

Broken Stick Rule

Brouwer Fixed Point Theorem

Brownian Bridge

Brownian Motion in 2D and the Fokker-Planck Equation

Brownian Motion Path and Maximum Drawdown

Browser of Lattice Data

Brute-Force String Matching

Bryant Surfaces

B-Spline Basis Functions

B-Spline Curves from Voronoi Polygon Vertices

B-Spline Curve with Boundary Conditions

B-Spline Curve with Knots

B-Spline Curve with Periodic Knot Vector

B-Spline Surfaces

Bubble Chain Puzzle

Bubble Chart Comparisons of Countries

Bubbles in a Simple Behavioral Finance Model

Bubble Sort Algorithm

Buckminster Fuller's Dymaxion Map

Buckyball in Icosahedron

Buckyball of Buckyballs

Budworm Population Dynamics

Buffon's Needle Experiment for Three Types of Grids

Buffon's Needle Problem

Build a Frustum

Building a Small Stellated Dodecahedron

Building a Snowman

Building a Velocity Sensor

Building Cylinders from Congruent Triangles

Building Frame with Catenary Roof Beams

Building on 12 Polar Zonohedra

Building on an Icosahedron

Building the London Tower Bridge

Build the Periodic Table

Build Your Own Atoms

Build Your Own Spaceship

Bulls and Cows

Bullseye Illusion

Bump Map of Mars

Bump Puzzle

Bungee Jumping

Buoyancy, Gravity, and Drag on a Sphere Immersed in a Liquid

Buoyancy of a Balloon

Buoyancy of a Floating Cylinder

Buoyancy Ventilation in Multistory Buildings

Burgers Turbulence

Burning Ship Fractal

Business Benefits of Releasing Software in Multiple Increments

Busschop's Hexagon-to-Square Dissection

Busy Beaver

Butler-Volmer Equation for Electrochemical Reaction

Butterfly Curve and Variations

Butterworth-Van Dyke Circuit

Buttons in Manipulate

Buying Gas at Midnight

Buying Watermelons Intelligently

Buy or Rent Investment Return Calculator

Byte Value Display (Maybe It Is EBCDIC?)

C3v Group Operations

C80 Fullerene

Cable Tension Needed to Support Platform

Cafe Wall Illusion

CAGED Fretboard System

Cahn-Hilliard Equation for Phase Separation

Cahn-Ingold-Prelog Priority Rules

Cairo Tiling

Calabi-Yau Space

Calculating 24

Calculating and Plotting B-Spline Basis Functions

Calculating Area, Perimeter, and Diagonal Length of a Rectangle

Calculating Integer Logarithms in Different Bases

Calculating Logarithms with a Series

Calculating Sample Size

Calculating the Area of a Country Using Green's Theorem

Calculating the Distance between Two Inaccessible Points

Calculating the Earth's Circumference at Any Date from Any Location

Calculating the Path of a Point on a Sliding Ladder

Calculating Your Grade

Calculation of Diagnostic Accuracy Measures

Calculations for Reduced Carbon Emissions

Calculator for Diagnostic Accuracy Measures

Calculus-Free Derivatives of Sine and Cosine

Calculus Game

Calculus Slalom

Calendar Calculator

Calendar on a Bilinski Dodecahedron

Calendar on Dodecahedron

Calendar on Icosidodecahedron

Calendar on Two Cubes

Calendar on Various Archimedean Solids

Calendar with Op Art Motifs

Calkin-Wilf Tree of Fractions

Call Graphs of Fibonacci-Like Functions

Call Graphs of Nestedly Recursive Functions

Calories Burned While Walking

Camera Animations on Circles, Spirals, Helices, and Conical Spirals

Camera Obscura

Campanus's Sphere

Canonical Integrals for Diffraction Catastrophes

Canonical Polygons

Canonical Polyhedra

Cantilever Bridge

Cantor Function

Cantor Set

Capacitors in Circuits

Capacity Planning for Short Life Cycle Products: The Newsvendor Model

Capetown Puzzle

Capillary Action

Capitalization Rate Probability

Capitals of the World

Captain Cook's Voyages

Captain Cook's Voyages around the Globe

Carbon Dating

Carbon Dioxide Absorption in Water

Carbon Dioxide Sublimation and Dissolution Equilibria

Carbon Nanotubes

Cardinal Elements of an Aging Human Eye Model with a Gradient-Index Crystalline Lens

Carlyle Circle

Carnot Cycle on Ideal Gas

Carnot Cycles with Irreversible Heat Transfer

Carnot's Theorem

Car on a Banked Road

Carotid-Kundalini Fractal

Car Racing Game

Carramba Puzzle

Car Steering with a Trapezoidal Mechanism

Carta Psicrométrica (Portuguese)

Cartesian Color Coordinate Spaces

Cartesian Coordinates Exercise

Car Traveling at Night

Cart with Pendulum

Cascade of Two Continuous Stirred-Tank Reactors with Recycle

Cassegrain Telescope

Cassini Ovals

Cassini Ovals and Other Curves

Cassini Spaceflight

Catacaustics for Some Graphs

Catacaustics Generated by a Point Source

Catalan Number Trees

Catalan's Surface

Catalan Unrank

Catalog of Some Elementary Functions

Catalyst Regeneration Using a Shrinking Core Model

Catastrophe Set of the Plane Projection of a Movable Surface

Catching a Point within a Teragon

Catenary Stability for Variable-Length Cables

Catenary: The Hanging Chain

Cauchy and Engineering Strain Deformation in 3D

Cauchy Mean-Value Theorem

Cauchy-Schwarz Inequality for Integrals

Cauchy's Problem

Causal Interpretation for an Electron Passing through Two Narrow Slits

Causal Interpretation for Electron Scattering

Causal Interpretation of the Double-Slit Experiment in Quantum Theory

Causal Interpretation of the Free Quantum Particle

Causal Interpretation of the Nonlinear Schrödinger Equation: An Analytic Example

Causal Interpretation of the Quantum Harmonic Oscillator

Causal Interpretation of Transitions in a Two-Level System

Causal Interpretation of Two-Dimensional Time-Dependent Scattering

Causal Network Generated by a Mobile Automaton

Causal Networks for the Wolfram 2,3 Turing Machine

Caustics from Radiants at Finite Distance Generated by Rolling Circles

Caustics Generated by Rolling Circles

Caustics on Spline Curves

Cavalieri's Principle

Cavity Quantum Electrodynamics with Bosons: Emission Spectra in the Strong and Weak Coupling Regimes

Cayley Graphs

Cayley Graphs for Weyl Groups

Cayley Tables for Small Groups and Moufang Loops

Celestial Map of Constellations, Stars, and Planets

Celestial Navigation

Celestial Sphere Basics

Cell Signaling by an Intracellular Receptor

Cellular Automata as Mappings

Cellular Automata Based on Permutation Groups

Cellular Automata Coupled by Overlap or Common Boundary

Cellular Automata Entropy

Cellular Automata Evaluation

Cellular Automata Model of an MPA Fishery

Cellular Automata on Trivalent Networks

Cellular Automata Ordered by Entropy

Cellular Automata Sensitivity to Initial Conditions

Cellular Automata That Generate Triangles

Cellular Automata with Global Control

Cellular Automata with Globally Determined Neighborhoods

Cellular Automata with Majority Rule

Cellular Automata with Modified Game-of-Life Rules

Cellular Automata without Redundant Information

Cellular Automata with Repetitive Initial Conditions

Cellular Automaton Browser

Cellular Automaton Carpets

Cellular Automaton Classification according to Attractor Type

Cellular Automaton Coil Representation

Cellular Automaton Compressibility

Cellular Automaton Difference Pattern and Distribution

Cellular Automaton Explorer

Cellular Automaton Fluids

Cellular Automaton Fonts

Cellular-Automaton-Like Neural Network in a Toroidal Vector Field

Cellular Automaton Media Strategy

Cellular Automaton Model of Pine Savanna Dynamics in Response to Fire and Hurricanes

Cellular Automaton Rules on Dendrites

Cellular Automaton State Transition Diagrams

Cellular Shading

Cellular Structures from Superposition of Waves

Celsius and Fahrenheit Thermometers

Center of a Golden Rectangle

Center of an Equilateral Triangle Circumscribing a Given Parabola

Center of Gravity of an L-Shaped Sheet and the Golden Ratio

Center of Mass in a Canoe

Center of Mass of a Circular Arc

Center of Mass of a Perforated Square Plate

Center of Mass of a Polygon

Center of Mass of Disk with Circular Hole

Center of Mass of Disk with Square Hole

Center of Mass of n Points

Centipede3D

Central Cross Sections of Polyhedra

Central Limit Theorem Applied to Samples of Different Sizes and Ranges

Central Limit Theorem for the Continuous Uniform Distribution

Central Limit Theorem Illustrated with Four Probability Distributions

Centre d'un triangle équilatéral circonscrit ŕ une parabole (French)

Centro de Massa de Partículas (Portuguese)

Centroid Hexagon

Centroid of an Arbitrary Hexagon

Centroid of a Planar System of Particles

Centroids of Triangles with Vertices on the Unit Circle

Cepheid Variable Star Light Curve Analysis

Certainty Equivalent Wealth

Cesŕro Summation

Cesŕro Sums of Some Unit Sequences

Ceva's Theorem

Chain-Growth Polymerization Using Monte Carlo Simulation: Termination by Combination

Chain Length Distribution of Polymers after Degradation by Random Chain Scission

Chain Mail

Chain Puzzle on Triangular Grid

Chain Rule

Chains of Amicable Numbers

Chains of Regular Polygons and Polyhedra

Chair-O-Plane

Chamomile

Champernowne Constant

Change in Inflection for a Basic Polynomial

Change of Basis in 2D

Changes in Key Signature with Addition of Sharps or Flats

Changes in the Budget Line

Change the Dog: Matrix Transformations

Change the Dog: Transformations 2

Change the Dog: Transformations 3

Change the Dog: Transformations 4

Changing a Coefficient in Polynomials of Low Degree

Changing Hexecontahedron

Changing Proportions into Percents

Changing Sea Levels

Chaos and Order in the Damped Forced Pendulum in a Plane

Chaos Game

Chaos Game 2D/3D

Chaos Game Fractals

Chaos in a Continuous Stirred Tank Reactor

Chaos in a Plant Pathogen/Hyperparasite Population Model

Chaos in a Rotating Pendulum

Chaos Induced by Delay in Model of the Immune Response

Chaos in the Shift Map

Chaos in Tumor Growth Model with Time-Delayed Immune Response

Chaos While Sledding on a Bumpy Slope

Chaotic Attractor for the Solar Cycle

Chaotic Attractor in Tumor Growth

Chaotic Data: Correlation Dimension

Chaotic Data: Delay Time and Embedding Dimension

Chaotic Data: Maximal Lyapunov Exponent

Chaotic Dynamics for Ball Bouncing between Two Constant Slopes

Chaotic Dynamics of a Bouncing Ball in a Sinusoidal Channel

Chaotic Dynamics of a Magnetic Pendulum

Chaotic Dynamics of a Modulated Semiconductor Laser

Chaotic Itinerary but Regular Pattern

Chaotic Motion of a Bouncing Ball on a Harmonically Forced Oscillator

Chaotic Motion of a Damped Driven Pendulum: Bifurcation, Poincaré Map, Power Spectrum, and Phase Portrait

Chaotic Motion of Perturbed Pendulum

Chaotic Oscillation Circuit

Chaotic Quantum Motion of Two Particles in a 3D Harmonic Oscillator Potential

Characteristics of Three-Phase Asynchronous Motors

Characteristic Times in Accumulation and Decay

Character Rotation Patterns

Charged Harmonic Oscillator in Electric Field

Charged Particle Fired between Parallel Plates

Charged Particle in a Constant Electric Field Produced by Two Plates

Charged Particle in a Four-Wire Potential

Charged Particle in a Uniform Magnetic Field

Charged Particle in Uniform Electric and Magnetic Fields

Charged Particle Subjected to Lorentz Force

Charged Particle Subjected to Lorentz Force: Analytical Solution

Charles's Law

Chart for a Torus

Charting with BarChart

Chatter Stability with Orthogonal Rotation

Chay-Keizer Model for Electrical Activity of Pancreatic Beta Cell

Chebyshev Collocation Method for 2D Boundary Value Problems

Chebyshev Collocation Method for Linear and Nonlinear Boundary Value Problems

Chebyshev Collocation Method for the Helmholtz Problem

Chebyshev Polynomials

Chebyshev's Inequality

Chebyshev's Inequality and the Weak Law of Large Numbers

Chebyshev's Inequality and the Weak Law of Large Numbers for iid Two-Vectors

Chebyshev's Lambda Mechanism

Chebyshev Spectral Differentiation via Fast Fourier Transform

Chebyshev Walking Machine

Check Digit Schemes

Checkerboard Bulge Illusion

Checking a Net by Rolling a Cube

Checking Finite Difference Errors

Chemical Abundances and Properties

Chemical Compound Class Browser

Chemical Equilibrium and Kinetics for HI Reaction

Chemical Equilibrium in the Haber Process

Chemical Potential Dependence on Temperature and Pressure

Chemical Reaction and Diffusion in a Spherical Catalyst Pellet (the Nonisothermal Effectiveness Factor)

Chemical Reaction in a Non-Newtonian Fluid

Chemical Reactions Described by the Lorenz Equations

Chemical Reactions Represented on a 2D Simplex

Chemical Reactions Represented via a 3D Simplex

Chemical Reaction Trajectories Using Bézier Curves

Chen-Gackstatter Surfaces

Chess

Chestnut Shell

Chicken Life Cycle

Chinese Postman Problem

Chinese Remainder Theorem

Chip-Firing Graph Configurations

Chip Stack Game

Chirality of Substituted Methanes

Chiral Polyhedra

Chiral Tunneling and the Klein Paradox in Graphene

Chirplet Signals

Chi-Squared Distribution and the Central Limit Theorem

Chladni Figures

Chlorite-Iodide-Malonic Acid (CIMA) Reaction

Choe's Hexagon and Cairo Tiling

Chooser Options

Choosing a Data Transformation with the Box-Whisker Plot

Choosing Initial Parameter Values for Nonlinear Regression

Choosing Taxes with a Constant Elasticity of Substitution (CES) Utility Function

Choosing the Aspect Ratio

Chord Diagrams for Motzkin Numbers

Chords in Equal Temperament and Just Intonation

Choreographic Motions of N Bodies

Christmas Flower

Christmas Stocking Identity

Chromatic Polynomials

Chromatic Spindles

Chromatographic Reactions of Three Components

Chromatographic Reactor

Chronological Interpretation of Mayan Numerals

Chrysanthemum-Like Curves

CIE Chromaticity Diagram

CIE xyY Color Space

Cigarette Smoke Concentration in an Automobile

Cipher Encoder

Circle Chord Envelope

Circle Covering by Arcs

Circle, Ellipse, Hyperbola, and Astroid

Circle Illusion

Circle Images

Circle Intersection Patterns

Circle Inversion of Basic Figures

Circle Involute

Circle Involute 3D Art

Circle of Curvature

Circle of Disks

Circle of Fifths

Circle of Lamps

Circle Packing and Hamiltonian Mappings

Circle Packings with Linear Fractional Transformations

Circle-Point Midpoint Theorem

Circle Reflections

Circle Rolling inside Another

Circle Rolling on a Curve

Circles and Ellipses

Circles of Apollonius

Circles on a Grid

Circles on a Sphere

Circles Packed in a Circle

Circles through the Orthocenter

Circles & Triangles

Circuit Phasor Diagram for Transformers

Circulant Ring Systems

Circular and Elliptic Polarization of Light Waves

Circular Asymptote

Circular Coverings

Circular Hole Drilled in a Cone

Circular Hole Drilled in a Cylinder

Circular Hole Drilled in a Sphere

Circular Law for Random Matrices

Circular Mass Accelerator

Circular Motion and Newton's First Law

Circular Rectangle

Circular Regression

Circular Scissors Lift

Circular Slide Rule

Circular View of the Means of Two-Color Totalistic 2D Cellular Automata

Circumcenter of a Triangle

Circumcircle and Incircle of a Triangle

Circumcircles Intersecting at the First Fermat Point

Circumcircles of Two Midpoints and an Altitude

Circumference of a Circle

Circumnavigating the Critical Point

Circumradii Perpendicular to the Sides of the Orthic Triangle

Circumscribing Polygons

Cissoid of Diocles

Cities of Countries

Clairaut's Angle Trisection

Clairaut's Differential Equation

Classes of Isomers

Classical and Quantum Hall Effects

Classical Approximations of Pi

Classical Barrier Crossing and Phase Space

Classical Correlation Function via Generalized Langevin Equation

Classical Electron in the Field of a Magnetic Monopole

Classical Motion and Phase Space for a Harmonic Oscillator

Classical Motion and Phase Space for a Morse Oscillator

Classical Particle in a Coulomb-Like Radial Potential

Classical Qualitative Inorganic Analysis

Classical Relativistic Particle in a Linearly Polarized Laser Field

Classical Scattering with a Penetrable Square-Well Potential

Classic Logistic Map

Classifying Quadrilaterals

Classifying the Complexity and Information of Cellular Automata

Clausen Functions

Clausius-Clapeyron Equation for Some Common Liquids

Claviatures for Generalized Cellular Automata

Claw Crane

Clean Tile Problem

Cleanup Puzzle

Clebsch-Gordan Coefficients

Click a Country

Cliff Walking Problem

Clinking Wineglasses

Clock Hand Tips

Clocks in Different Relativistic Inertial Frames

Closed-Form Approximations of Euler's Number e

Closed-Form Full Life Cycle Distribution

Closed Form Solutions for Spheroidal Functions

Closed Spline Ball

Closest Packing of Disks and Spheres; Kepler's Conjecture

Closure Property of Eigenfunctions

Clovers

Clumping by Surface Tension

Cluster Algebras

Cluster Analysis

Cluster Analysis for 2D Points

Cluster Cellular Automata

Cluster Coloring in Machine Learning

Clustered Power-Law Networks

Cluster of 117 Polyhedra Around a Rhombic Triacontahedron

Cluster of 120 Spheres

Cluster of 14 Rhombic Triacontahedra

Cluster of 195 Dodecahedra

Cluster of 195 Spheres

Cluster of 20 Icosahedra

Cluster of 30 Cubes

Cluster of 30 Tetrahedra

Cluster of 45 Polyhedra around a Rhombic Hexacontahedron

Cluster of 92 Dodecahedra

Cluster of 92 Spheres

Cluster of Spheres

Clusters of 60 Polyhedra

Clusters on Regular Polygons

Cnoidal Waves from Korteweg-de Vries Equation

CNOT and Toffoli Gates in Multi-Qubit Setting

CO_2 Sublimation and Dissolution in Water

Coalescent Gene Genealogies

Coalitions

Coated Wall Photocatalytic Reactor

Coaxial Cable

Cobb-Douglas Formulation of Marshallian and Hicksian Demand Functions

Cobb-Douglas Production Functions

Cobb-Douglas Utility Function

Cobweb Diagram for Generalized Logistic Maps with z-Unimodality

Cobweb Diagram of the Logistic Map

Cobweb Diagrams of Elementary Cellular Automata

Cobweb Model

Coconuts, Sailors, and a Monkey

Code 20 Cellular Automaton Calculates R110

Code 686 Builds the Chair Tiling

Coevolving Complements

Coexistence of Qubit Effects

Coffee Mug to Donut

Cofunction Identities for Sine and Cosine

Cogwheel Drive

Coherent States of the Harmonic Oscillator

Coherent-State Time Evolution under an Inverted Oscillator Potential

Coherent Transition Radiation from Bunches of Charged Particles

Coils, Knots, and Rosettes

Coincidences in Powers of Integers

Coinciding Faces among the Regular Icosahedron, Tetrahedron and Cube

Coinciding Faces of Six Archimedean Solids

Coin Flips

Coin Fountains with a Given Base

Coin Machine

Coin Shuffle

Coldice Puzzle

Coldice Puzzle 2

Cold Wave Plasma Dispersion

Collaboration Graph for Paul Erdos Coauthors

Collapsible Cup

Collapsible Umbrella

Collatz Conjecture on a Circle

Collatz Paths

Collatz Problem as a Cellular Automaton

Collatz Sequence Computed by a Tag System

Collatz Sequence Computed by a Turing Machine

Collatz Sequence Maximums

Collatz Sequence Paths

Collection Efficiency of a Rotating Ring-Disk Electrode

Collection of Graph Styles

Colliding Cars

Colliding Galaxies

Collinear Apexes of Cones

Collinear Classical Helium Atom

Collinearity of an Incenter and Two Circumcenters

Collinearity of an Orthocenter, the Incenter, and the Circumcenter

Collinearity of a Triangle's Circumcenter, Incenter, and the Contact Triangle's Orthocenter

Collinear Orthocenters

Collisionless Periodic Orbits in the Free-Fall Three-Body Problem

Collision of Two Droplets

Collision of Two Neutrons in the de Broglie?Bohm Approach

Collocation by Chi Square

Collocation by Symmetric Conditional Probability

Color Angles

Color Blades

Color-Blended Circular Tiles

Color Blindness

Color-Changing Origami Star

Colorcoded Country Comparison

Color Cube

Color Cube 2x2x2 Puzzle

Color Cube 3x3x3 Puzzle

Color Drill Down

Colored Klein Bottle

Colored Lights

Colored Nets of Various Polyhedra

Colored Spherical Projections of Polyhedra

Colored Sudoku

Colored Szilassi Polyhedron

Color Filters in Black and White Photography

Color Gradient Sliders

Color Image Compression via the Higher-Order Singular Value Decomposition (HOSVD)

Coloring 2D Metallic-Mean Quasicrystal Tilings with a Mesh-Based Method

Coloring Cycle Decompositions in Complete Graphs on a Prime Number of Vertices

Coloring Polyhedra Given by Map Projections

Coloring Polyhedra with Four Colors

Coloring the Plane with a Rolling Cube

Coloring the Plane with a Rolling Tetrahedron

Color Islands

Colorization of Cellular Automata

Colorizing an Image

Color Lambdoma

Color-Matching Dissection of the Rhombic Icosahedron

Color-Matching Dissection of the Rhombic Triacontahedron

Color Mixing

Color Quantization of Photographic Images III: Palette from Colors out of a ColorSlider

Color Quantization of Photographic Images II: Palette from Colors out of Color Schemes

Color Quantization of Photographic Images I: Palette from Colors in the Image

Color Relationships

Color Representations of Numbers

Color Schemes

Colors of the Visible Spectrum

Color Space

Color the Faces of a Polyhedron by the Number of Corners

Color Triangles

Color Tuning of CdSe Semiconductor Nanocrystals

Color versus Name

Color versus Wavelength

Color Visual Cryptography Scheme

Color-Word Game

Color Your Pies

Colpitts Oscillator

Column of Hexagons

Combination of Linear and Icosahedral Structures

Combination of Triangular Patches

Combinations of Sines in the Complex Plane

Combinatorics of Love from A Midsummer Night's Dream

Combined Free and Forced Convection

Combined Loading and Reaction Stresses

Combining Blocks

Combining Cellular Automata Patterns Using Binary Operations

Combining Colored Quarks

Combining Functions

Combining Image Color Layers

Combining Ions to Form Chemical Compounds

Combining Quarks into Hadrons

Combining Sine Waves

Combining Two 3D Rotations

Combustion of Methane Using Block Cellular Automata (BCA) with Feedback

Combustion Reactions in a Furnace

Comet ISON Passes over the Earth

Comet Moving about the Sun

Comet Tails

Common-Factor Graph of Fibonacci Numbers

Common Font Families

Common Methods of Estimating the Area under a Curve

Common Point of Tangents

Common Robot Arm Configurations

Common Subsequences of Words

Common Units for Measuring Concentrations

Communities of Nations Bridged by Language Similarity

Commutative Matrices Associated with Vector Rotations

Commutativity of 3D Vector Addition

Commute p to the Left

Comparative and Absolute Advantage

Compare Compressors or Turbines with Different Efficiencies

Comparing Algorithms for the Traveling Salesman Problem

Comparing Ambiguous Inferences when Probabilities Are Imprecise

Comparing and Weighting Two Weibull Models

Comparing Basic Numerical Integration Methods

Comparing Binomial Generalized Linear Models

Comparing Data on Countries

Comparing Errors for Chebyshev Interpolation

Comparing Exact and Approximate Censored Normal Likelihoods

Comparing Fourier Series and Fourier Transform

Comparing Four Methods of Numerical Inversion of Laplace Transforms (NILT)

Comparing Fractions

Comparing Fractions, Decimals, and Percents

Comparing Gamma and Log-Normal Distributions

Comparing Information Retrieval Evaluation Measures

Comparing Integers

Comparing Iterative Root-Finding Methods

Comparing Leapfrog Methods with Other Numerical Methods for Differential Equations

Comparing Least-Squares Fit and Least Absolute Deviations Fit

Comparing Loxodromes and Great Circle Routes

Comparing Measures of Line Jaggedness

Comparing Models for Two-Way Contingency Tables

Comparing Normal and Student's t-Distributions

Comparing Open-Loop and Closed-Loop Operation of a Synchronous Motor

Comparing Parametrizations

Comparing Pokémon

Comparing Properties of Chemical Elements

Comparing Real Mathematical Constants and Random Numbers

Comparing Regression Models with and without Data Transformation

Comparing Resistances of Wires of Different Compositions, Dimensions and Temperatures

Comparing Roots of Unity

Comparing Rule 30 Pseudorandoms to a Uniform Distribution

Comparing Sampling Schemes for Photographic Images

Comparing Simple Crank/Slider and Scotch Yoke Mechanisms

Comparing Some Residuals for Generalized Linear Models

Comparing Sorting Algorithms on Rainbow-Colored Bar Charts

Comparing Standard Error of the Means

Comparing Standard Errors of the Means

Comparing Temperature Scales

Comparing the Cook-Torrance BRDF Model with Diffuse Reflection Simulation

Comparing the Dynamical Behavior of Elementary CA Rules

Comparing the Iterative and Recursive Flood Fill Algorithms

Comparing the Lengths of Two Zigzag Lines

Comparing the Normal Ogive and Logistic Item Characteristic Curves

Comparing the Primes in Base 2

Comparing the Regions of Polar and Cartesian Graphs

Comparing Two Discrete Lowpass Filters with Low Distortion

Comparing Two Isochronous Oscillators

Comparing Two Means Using Independent Samples of Unknown Variance

Comparing Voting Systems for a Normal Distribution of Voters

Comparing Writing Styles of Famous Texts

Comparing x, y Curves and Z-Order Curves for Texture Coding

Comparison of Different Methods for the Binary Classification of Points in the Plane

Comparison of Factorials and Primorials

Comparison of Food Moisture Sorption Isotherm Equations

Comparison of One- and Two-Dimensional Models of Plate Reactors

Comparison of Performance of Recycle Reactors with Plug Flow Reactors

Comparison of Real and Plug Flow Reactors for a First-Order Reaction

Comparison of Six Sigmoid Growth Curve Models

Comparison of Trigonometric Functions

Compass Needle in Uniform and Rotating Magnetic Fields

Compass Tiling

Competing Bid-Rents under Monocentric Assumptions

Competing Cellular Automata

Competing Species Model with Two Species

Competition for Territory: The Levins Model for Two Species

Competitive Model

Complement Tiling

Complete-Mixing Model for Gas Separation by Membranes

Completing a Tetrahedron to a Parallelepiped

Completing the Square

Complex Addition

Complex Addition of Harmonic Motions and the Phenomenon of Beats

Complex and Real Planes of Discrete Fourier Transforms

Complex Branching of Inverse Monomial Mappings from Lissajous Figures

Complex Exponential and Logarithm Functions

Complex Exponential Circle Fractal

Complex Exponential Resonance

Complex Fibonacci Residues

Complex Functions Applied to a Square

Complexified Pseudosphere

Complex Image Transformation

Complex Mapping of Contours and Regions

Complex Multiplication

Complex Networks

Complex Networks from Simple Rewrite Rules

Complex Newton Iteration for a Cubic Polynomial

Complex Newton Map

Complex Number

Complex Number Game

Complex Numbers in Rectangular and Polar Form

Complex Numbers with Different Norms

Complex One-Time Pad

Complex Pendulum Oscillations at Complex Times

Complex Polynomials

Complex Power Plot

Complex Power Spirals

Complex Product and Quotient Using Similar Triangles

Complex Quadratic Residues

Complex Reaction with Segregation in a Semi-Continuous Reactor

Complex Roots of a Polynomial and Its Derivative

Complex Roots of Polynomials with Generalized Fibonacci Coefficients

Complex Rotation of Minimal Surfaces

Complex Slide Rule

Complex Spherical Harmonics

Complex Views of Logistic Maps

Complex Zeros of Quadratic Functions

Component Identification and Boundary Delineation

Components and Nets of Regular Polyhedra

Components of a Great Rhombic Triacontahedron

Composing Functions Using Dynagraphs

Composing Rotations

Composing Rotations via Hamilton Turns

Composition and Transformations

Composition Changes during Processing of Asti Spumante Extra-Dry

Composition of a Table Tennis Blade

Composition of Binary Relations in Sets

Composition of Functions

Composition of Vapor and Liquid Phases for a Ternary Ideal Mixture

Compound-Hemisphere Reflector (Cat's Eye)

Compound Interest Table

Compound of 30 Tetrahedra in a Rhombic Triacontahedron

Compound of 5 Cubes

Compound of Five Cubes and Small Rhombicosidodecahedron

Compound of Five Octahedra

Compound of Tetrahedron and Cube

Compound of Two Dodecahedra

Compound of Two Icosahedra

Compounds of 5 and 10 Tetrahedra

Compounds of Cubes and Their Nets

Compounds of Tetrahedra

Compressed Constrained Cellular Automaton Initialization

Compressed-Gas Spray

Compressibility Factor Charts

Compressibility Factors for van der Waals Gases

Compressibility Factors Using the Soave-Redlich-Kwong Equation of State

Compressible Flow through a Nozzle/Diffuser

Compressible Helical Beltrami Flow

Compressing Elementary Cellular Automaton Rules

Compressing Ideal Fermi and Bose Gases at Low Temperatures

Compression Ratio of Spheres in a Curved Tube

Compression Waves

Compressive Stress-Strain Relationships of Layered Solid Foams

Compton Effect

Compton Scattering Angle

Compton Scattering of Subatomic Particles

Computable General Equilibrium (CGE) of Multiregion Input-Output Model

Computational Complexity of the Logistic Map

Computation of Radiative Transfer

Computation of the Residue Curve Map

Computation of the Volume of a CSTR and a PFR

Computation of Tie Lines for Ternary Mixtures

Computed Tomography Simulation Using the Radon Transform

Compute the Euler Axis and Angle Geometrically

Computing Eigenvalues Using the QR Algorithm

Computing Excess Thermodynamic Properties Using the Wilson Model

Computing Gas Permeation Using the Complete Mixing Model

Computing Individual and Cumulative Hypergeometric Probabilities

Computing Pi the Chudnovsky Way

Concave Random Quadrilaterals from Four Points in a Disk

Concentration and Temperature Profiles in an Axially Dispersed Adiabatic Tubular Reactor

Concentration Distributions with a Position-Dependent Diffusion Coefficient

Concentration of Sugar Solution in a Bubble Column

Concentration Profile in a Tubular Reactor

Concentration Profiles in Electrochemical Impedance Spectroscopy (EIS)

Concentrations of Multiple Reacting Species in a Semi-Infinite Region

Concentric Circles

Concentric Circles around a Circle

Concentric Sphere Capacitor

Concurrence of the Median, a Chord and a Diameter of the Incircle

Concurrency Induced by a Cevian

Concurrency via Midpoints

Concurrent and Countercurrent Cooling in Tubular Reactors with Exothermic Chemical Reactions

Concurrent Diagonals in a 30-Gon

Concurrent Line Segments Related to the Incircle

Concurrent Lines that Intersect on the Euler Line

Concyclic Circumcenters

Concyclic Points

Concyclic Points Associated with an Angle Bisector and an Excircle

Concyclic Points Derived from Midpoints of Altitudes

Concyclic Points from Reflections of the Circumcenter about the Altitudes

Concyclic Points Related to a Midpoint and the Incircle

Condensed Cellular Automaton States

Conditionally Reversible Elementary Cellular Automata

Conditional Probability

Condition for Free Fall around Earth

Conduction through a Composite Wall

Cone-Based Graphs

Cone Geodesics

Cone of Pythagorean Triplets

Cone Placed on a Sphere

Cone, Tent, and Cylinder

Confidence and Prediction Bands

Confidence Interval Exploration

Confidence Interval for a Population Mean

Confidence Intervals: Confidence Level, Sample Size, and Margin of Error

Confidence Intervals, Confidence Levels, and Average Interval Length

Confidence Intervals for a Mean

Confidence Intervals for the Binomial Distribution

Confidence Intervals for the Erlang Distribution

Configuration Interaction for the Helium Isoelectronic Series

Configuration of a Sessile Drop

Configuration Space for Four-Bar Linkage

Confluent Hypergeometric Functions

Conformal Map of Exponential

Conformal Mapping of the Unit Disk

Conformal Maps

Conformal Pixel Transformation

Conformational Analysis of Ethane, Butane and 2-Butanol

Congressional Apportionment Using General Divisor Methods

Congruence Classes of Geoboard Triangles

Congruential Color Sequences

Congruent Numbers

Conical Anamorphic Projection of Photographic Images

Conical Anamorphic Projection of Polar Plots

Conical Perspective Anamorphosis of Polygons

Conic Pendulum

Conic Section

Conic Section as Bézier Curve

Conic Section Curves

Conic Sections: Equations and Graphs

Conic Sections: Move Foci

Conic Sections: Polar Equations

Conic Sections: The Double Cone

Conjecture de Beraha pour les cycles (French)

Conjecture de Beraha pour les roues (French)

Connected Astroids

Connected Components

Connecting Skew Axles with Hyperboloidal Gears

Connecting the CDF and the PDF

Connecting Towns Using Kruskal's Algorithm

Connection between Quantum-Mechanical Hydrogen Atom and Harmonic Oscillator

Connectivity-Based Phase Transition

Connect the Dots

Consecutive Digits in the Expansion of Pi

Consecutive Exponential Decay

Consecutive Heads or Tails

Consecutive Smooth Numbers

Conservation of Energy with a Simple Pendulum

Conservation of Momentum in a Canoe

Conservative Byte Drift Machine

Conservative Hex Drift Machine

Constant-Addition Continuous Cellular Automaton

Constant Angle of Incidence Contours for an Air-SiO2-Si System

Constant Coordinate Curves for Elliptic Coordinates

Constant Coordinate Curves for Parabolic and Polar Coordinates

Constante d'Euler-Mascheroni (French)

Constant Elasticity of Substitution (CES) for Marshallian and Hicksian Demand Functions

Constant Elasticity of Substitution Production

Constant Price Elasticity of Demand

Constant Risk Aversion Utility Functions

Constant-Sum Figures

Constrained Optimal Routes in 3D Space

Constrained Optimization

Constrained Optimization: Cobb-Douglas Utility and Interior Solutions Using a Lagrangian

Constrained Random Walk

Constraint Tiling on a Truncated Icosahedron

Construct a Conversion-Temperature Diagram for a Reversible Adiabatic Reaction

Construct a Dihedral Angle of a Tetrahedron Given Its Plane Angles at a Vertex

Construct a McCabe-Thiele Diagram for Distillation

Construct an x-y Diagram for an Absorption Column

Construct an x-y Diagram for a Stripping Column

Construct an x-y Diagram for Flash Distillation

Construct a Pressure-Composition Diagram for Immiscible Liquids

Construct a P-x-y Diagram for Vapor-Liquid Equilibrium (VLE)

Construct a Segment with a Given Midpoint and Endpoints on Two Given Lines

Construct a T-x-y Diagram for Vapor-Liquid Equilibrium (VLE)

Construct Euclid's Regular Dodecahedron

Constructing a Cassegrain Telescope

Constructing a Line through a Given Point and an Inaccessible Point

Constructing an Autostereogram

Constructing and Manipulating Graphs

Constructing and Solving Nonograms

Constructing an Ellipse with a Tusi Couple

Constructing an Op Art Cube

Constructing an Open Flexible Projection of an Op Art Tesseract

Constructing a Parabola from Tangent Circles

Constructing a Parallel Line through an Inaccessible Point

Constructing a Rational Rectangle

Constructing a Rectangle with the Same Area as a Pentagon

Constructing a Regular Heptadecagon (17-gon) with Ruler and Compass

Constructing a Regular Heptagon Using Gleason's Method

Constructing a Regular Heptagon Using Lill's Method

Constructing a Regular Heptagon Using Plemelj's Method

Constructing a Regular Pentagon with Ruler and Compass

Constructing a Rhombic Hexecontahedron with Zometool

Constructing A Simple Optical System

Constructing a Square Pyramid without Gluing

Constructing a Square with Sticks of Equal Length

Constructing a Steiner Tree for Five Points

Constructing a Swung Surface around a B-Spline Curve

Constructing a Wooden Bilinski Dodecahedron

Constructing Op Art

Constructing Polyhedra Using the Icosahedral Group

Constructing Quadratic Curves

Constructing the Arithmetic, Geometric and Harmonic Means

Constructing the Cube Root of Two

Constructing the Harmonic Mean 1

Constructing the Harmonic Mean 2

Constructing the Perfect Piston

Constructing the Radius of a Ball

Constructing the Regular Icosahedron

Constructing the Square Root of a Positive Integer Geometrically

Constructing Vector Geometry Solutions

Constructing Voronoi Diagrams with Expanding Cells

Construction Based on Kepler's Mysterium Cosmographicum

Construction for Three Vectors with Sum Zero

Construction of a Bézier Curve

Construction of an SSA Triangle

Construction of Near-Miss Johnson Solid

Construction of Sierpinski Triangle in Two or Three Dimensions

Construction of Squares from a Parallelogram

Construction of Temperature-Composition Diagrams for Immiscible Liquids

Construction of the Rate-Conversion-Temperature Chart from Kinetic Data

Constructions around a Rhombic Enneacontahedron

Constructions by Reflecting in a Line

Constructions with Paper Folding

Constructive and Destructive Interference

Construct Single-Stage, Liquid-Liquid Extraction

Consumer and Producer Surplus

Consumer Choice: Income, Tastes, and Prices

Consumer Demand

Contact Angle Relaxation during Droplet Spreading

Contact Binary Star Envelopes

Contact Triangles of a Triangle

Contagion in a Grid and a Random Network

Contagion in Random and Scale-Free Networks

Container Filled with Particulates

Continental Plate Configurations through Time

Continued Fraction Approximations

Continued Fraction Approximations of the Tangent Function

Continued Fractions

Continuity of a Complex Function

Continuity of Polynomials in the Complex Plane

Continuous and Discrete Time Discounting

Continuous Binomial Function in 3D

Continuous Cellular Automaton with Math Rules I

Continuous Cellular Automaton with Math Rules II

Continuous Cellular Automaton with Math Rules III

Continuous Changes in Self-Similar Fractals

Continuous Exponential Growth

Continuous Functions Are Integrable

Continuously Stirred Tank Reactor Using Arc-Length Parameter

Continuously Variable Planetary Transmission

Continuously Variable Transmission

Continuous Stirred-Tank Reactor That Loses Cooling

Continuous Stirred Tank Reactor with Activated Sludge Recycle

Continuous-Time Quantum Walk

Continuous Transition between Classical and Bohm Quantum Pictures for Young's Interference Experiment

Continuous Transition between Quantum and Classical Behavior for a Harmonic Oscillator

Continuous versus Compounded Interest

Contour Integral around a Simple Pole

Contour Integration

Contour Plot on a Hemisphere

Contour Plots for Reaction Rates

Contour Plots of the Zeta Function

Contours of Algebraic Surfaces

Contours of Constant Principal Angle in the Complex Dielectric Plane

Contracting the Double-Twist in SO(3)

Contrast Illusion

Controlled Release of a Drug from a Hemispherical Matrix

Controlling Airplane Flight

Controlling Chaos on the Logistic Map

Controlling Liquid Height within Two Tanks in Series Using a PID Controller

Control of Thermal Runaway of an Exothermic Reaction by Coupling with an Endothermic Reaction

Convection

Convection between Two Vertical Walls

Convection-Diffusion in a Semi-Infinite Region

Convective Energy Flow through a Window

Convergence d'une série de Taylor vers la fonction développée (French)

Convergence of a Hyperpower Sequence

Convergence of a Monotonic Sequence

Convergence of a Power Series for Polylogarithm

Convergence of a Recursive Sequence

Convergence of Binomial, Binomial Black-Scholes, and Trinomial Option Pricing Methods

Convergence of Binomial Option Pricing under Nonconstant Volatility

Convergence of Minimization Methods

Convergence of Newton's Method for Approximating Square Roots

Convergence of Probability I: Condorcet's Jury Theorem, Part 3

Convergence of Probability II: Condorcet's Jury Theorem, Part 4

Convergence of the Binomial Series

Convergence of the Empirical Distribution Function of a Sample

Convergent Series of Rectangles to Fill a Unit Square

Conversion of Ethylbenzene to Styrene in the Presence of Steam

Conversion of Methanol to Formaldehyde

Conversion versus Reactor Volume for CSTR and PFTR

Convert an Image to Binary

Converting among Dyadic, Decimal, and Binary Notation

Converting an Image into Music

Converting a Positive Integer from Base 10 to Base b

Converting Fractions

Converting Potentials between Different Reference Electrodes

Converting Syngas to Ethanol

Convex Golden Rhombic Polyhedra

Convex Golden Rhomboidal Polyhedra

Convex Hull

Convex Hull and Delaunay Triangulation

Convexification

Convolution Method in Hydrologic Computations

Convolution of Two Densities

Convolutions of Shifted Densities

Convolution Sum

Convolution with a Rectangular Pulse

Conway Criterion

Conway Criterion for Bézier Curves

Conway's Billiard Ball Loop

Conway Sequence with Varying Initial Conditions

Conway's Look and Say Sequence

Conway's M(13) Puzzle

Conway's Toroid with 36 Equilateral Triangular Faces

Conway Triangle Notation

Cooke (Taylor) Triplet

Cookie Cutting

Cooking a Turkey

Coolest Shirt and Necktie

Cooling by a Cylindrical Pin Fin

Cooling of a Composite Slab

Cooling of a Rod with Initial Temperature Distribution

Cooling with a Shaped Pin Fin

Cooperation in Heterogeneous Populations

Coordinates of a Point Relative to a Basis in 2D

Coordinate Sonification

Coordinate Transformation of a-Matrix and alpha-Matrix

Coordination in Ionic Compounds

Coordination of Insurance Policies

Copeland-Erdos and Champernowne Numbers for Small Bases

Copernicus Epicycles versus Kepler's Ellipses

Copernicus's Chord Tables

Copernicus's Chord Tables from De Revolutionibus Orbium Coelestium

Copernicus's Theorem

Coprime Triples

Core Intensity Profiles for Linearly Polarized Modes in Optical Fibers

Coriolis Acceleration

Corner Cabinet with Rotating Shelves

Corner Reflector

Correction Factor for Shell and Tube Heat Exchanger

Correction Trees

Correlated Binary Decision Rules

Correlated Gamma Variance Processes with Common Subordinator

Correlated Lévy Processes via Lévy Copulas

Correlated Wiener Processes

Correlating the Mertens Function with the Farey Sequence

Correlation and Covariance of Random Discrete Signals

Correlation and Regression Explorer

Correlation of Bivariate Random Data

Correlation of Positive and Negative Predictive Values of Diagnostic Tests

Corrosion Mechanism for Stainless Steel

Cosine and Sine Identities with Dihedral Transformations

Cosine and Sine of the Sum of Two Angles

Cosine of a Cubic Polynomial

Cosine Offset Curves

Cosinor Analysis of Biorhythm Data

Cosinor Analysis Using Rotating Ellipse Tangents and Circle Collisions

Cosmology of Einstein-de Sitter Universe

Co-Sputtering Simulation (CO-SS)

Cost and Revenue for Monopoly and Monopolistic Competition

Costarring Actors

Cotes Identity

Cotter Pin (Split Pin)

Cottrell Equation for the Potential-Step Experiment

Couette Flow

Coulomb's Law for Three Aligned Charges

Coulomb's Law for Three Point Charges

Coulomb-Sturmian Functions in Configuration Space

Coulomb Wavefunctions

Countercurrent Extraction with Extract Reflux (the Janecke Diagram)

Countercurrent Flow Hemodialyzer

Countercurrent Leaching of Oil from Meal

Counterexamples to Euler's Formula for Nonconvex Polyhedra

Counterintuitive Intersection of Two Line Segments

Counting by Steps

Counting Exercise

Counting in Binary

Counting in Triangles

Counting Lattice Paths

Counting Necklaces

Counting Objects in Images

Counting Order Puzzle

Counting Paths through a Grid

Counting Sheep

Counting the Number of Roots of Transcendental Functions in Bounded Regions Using Winding Numbers

Counting T-Shirts

Country Curves

Country Data and Benford's Law

CountryData Globe with Tooltip Atlas

Country Flag Quiz

Country Flags and Descriptions

Country Groups

Country Interior: Two Solutions to the Nonconvex Polygon Interior Problem

Country Quiz

Country Ranking Maps

Country Statistics over Time

Coupled Cellular Automata: Symbiotic Patterns and Synchronization

Coupled Coils

Coupled Lorenz Oscillators

Coupled Oscillators

Coupled Pendulum Oscillations

Coupled Pendulums with a Spring

Coupled Point Masses on a Circle

Coupled Quantum Harmonic Oscillators

Coupler Curve Atlas for the Four-Bar Linkage

Coupler Curves of a Four-Bar Linkage

Coupling Cellular Automata with Substitution Systems

Coupon Collector Problem

Cournot and Stackelberg Equilibria and Best Responses

Cournot Competition with Two Firms

Covariant Derivative of a Field along a Curve

Coverage in Fuzzy Subset Relations

Coverage of a Unit Square by Random Discs

Coverage Probability with the Occupancy Problem

Covering Maze

Covering the Plane with Polygons

Crack Propagation and Stress Field for 2D Tensile Loads

Crack Propagation for 2D Tensile Loading

Crane Model

Crankshaft-Driven Pendulum

Crazy Surfaces

Create a 3D Character

Create a Face

Create Alternative Koch Snowflakes

Create Your Own Quick Response Code

Creating a Cardioid, a Nephroid and Other Epicycloids

Creating a GCD Grid

Creating and Manipulating Knots

Creating a Voronoi Mesh from an Image

Creating Posters from Photographic Images

Creating Self-Similar Fractals with Hutchinson Operators

Creating Word Clouds

Creation of a Magnetic Field by an Electric Current

Credit Risk

Creep and Stress Relaxation for Four-Element Viscoelastic Solids and Liquids

Cremona Diagram for Truss Analysis

Crisscrossing a Polygon

Crisscross Puzzle

Critical Thickness of Insulation

Critical Value z* for z-Scores for Confidence Levels

Crooked Church Spire

Crookes Radiometer: A Comedy of Errors

Cross-Cap Surface and Variations

Crossed Ladders Theorem

Cross-Flow Liquid-Liquid Extraction

Cross Menger (Jerusalem) Fractal

Cross Product in Spherical Coordinates

Cross Product of Vectors

Cross Product of Vectors in the y-z Plane

Cross Ratios in the Complex Plane

Cross Recurrence Plot of Two Elementary Cellular Automata

Cross-Sections of a Surface and Partial Derivatives

Cross Sections of Graphs of Functions of Two Variables

Cross Sections of Quadratic Surfaces

Cross Sections of Regular Polyhedra

Cross Sections of Three Solids

Cross's Theorem

Crossword Grid Maker

Crossword Helper

Cryogenic Recovery of Acetone from Air

Cryptic Crosswords

Cryptography on Polyhedral Nets 2

Cryptography on Surfaces

Cryptography Using a 3D Maze

Cryptography with Mazes on Polyhedra Maps

Crystal Art

Crystal Field Theory for Coordination Complexes

Crystal Lattices in Reciprocal Space

Crystallographic Planes for Cubic Lattices

Crystallographic Point Groups

Crystal Viewer

CSTR and PFR Holding-Time Ratio versus Conversion for Various Reaction Orders

Cube and Hyperboloid

Cube and Octahedron Movement

Cube and Octahedron Sculpture

Cube Drilled by Triangular Prism

Cube-in-a-Sphere Illusion

Cube Net

Cube Net or Not

Cube of Cubes

Cube of Cubic Koalas

Cube of Koalas

Cube Packing

Cubes on a Hyperbolic Paraboloid

Cubes on a Rhombic Hexecontahedron

Cube to Small Rhombicuboctahedron

Cubic Autocatalysis by Successive Bimolecular Steps

Cubic Big Bang

Cubic Close Packing

Cubic Close Packing Cube

Cubic Close Packing versus Hexagonal Close Packing

Cubic Crystal Lattices

Cubic Equation of State for the Compressibility Factor

Cubic Polynomial

Cubic Spline Interpolation versus Interpolating Polynomial

Cubic Symmetry Types

Cubic Twist

Cumulation

Cumulative Area under a Cycloid versus the Area of Its Rolling Circle

Cumulative Cooling and Heating Degree Days

Cumulative Distribution and Residence Time Distribution Curves

Cumulative Frequency Curves

Cumulative Sums and Visual Change Detection between Two Random Processes

Cunningham's Simply Connected Kakeya Set

Cupid's Arrow

Curated Collections of Graphs

Curlicue Fractal

Curling Structures Made of Square Pyramids

Curl of Some Vector Fields

Curly Torus

Current and Potential Distributions for a Freely Corroding Disk Electrode

Current-Carrying Coil in an External Magnetic Field

Current-Carrying Wire in Uniform Magnetic Field

Current versus Cohort Life Tables and the Regulation of Life Insurance

Current-Voltage Characteristics of a Memristor

Curry Triangle Paradox

Curvas de nivel (Spanish)

Curvature and Torsion

Curvature Extrema for Constrained Bézier Curves

Curvature of the Projection of a Trefoil Knot

Curvature of the Trefoil Knot

Curve Fitting

Curve Fitting to Find Missing Elements in Mendeleev's Periodic Table

Curves and Surfaces of Constant Width

Curves of Steepest Descent for 3D Functions

Curves through Given Points in the Plane

Curving Grades with Two Constraints

Customer Profitability with the Whale Curve

Custom Iterated Maps

Custom Orthogonal Axes for 3D Graphics

Custom Vertex and Edge Labeling

Cutoff Parallelepipeds

Cutting a Key for a Cylinder Lock

Cutting Polygons

Cutting Space into Regions with Four Planes

Cycles from Permutations

Cycles in Random Sample Permutations

Cycles in Sums of Prime Factors

Cyclic Functions under Differentiation

Cyclic Numbers

Cyclic Patterns

Cyclic Quadrilaterals, Subtriangles, and Incenters

Cyclic Staircase versus Cyclic Voltammetry for Reversible Electron Transfer Reaction

Cyclic Tag Systems

Cyclic Voltammetry: Characteristic Points

Cyclic Voltammetry Corrupted by Ohmic Drop

Cyclic Voltammetry for an Electro-Adsorption Reaction (EAR)

Cyclic Voltammetry for a Redox Reaction with Diffusion

Cyclogons

Cycloidal Gears

Cycloidal Path of a Charged Particle in Uniform Perpendicular Electric and Magnetic Fields

Cycloidal Pendulum

Cycloid and Archimedes's Spiral

Cycloid Curves

Cycloid from a Rolling Ellipse

Cycloids and Their Tangents

Cycloids and Trochoids of an Elliptic Base Curve

Cyclotron 4000

Cylinder and Cone Sectors

Cylinder Area Paradox

Cylinder Hemisphere Cone

Cylinder Net

Cylinders on a Helix

Cylinders through Five Points

Cylinder Volume and Area

Cylindrical Anamorphosis of 3D Polygonal Meshes

Cylindrical Anamorphosis of Parametric Surfaces

Cylindrical Anamorphosis of Some Popular Images

Cylindrical Asymptote

Cylindrical Cam

Cylindrical Cavity Resonator

Cylindrical Chess

Cylindrical Coordinates

Cylindrical Mazes on Surfaces

Cylindrical Mirror Anamorphosis

Cylindrical Segment Used as Shaft for a Switch

Cylindrical Surfaces from NURBS Curves

Cylindrical Waves Passing through a Double Slit

D4 Symmetric Stratum of Quartic Plane Curves

D'Alembert's Differential Equation

Dalton's Law of Partial Pressures

Damped 2D Lissajous Figures

Damped 3D Lissajous Figures

Damped Spherical Pendulum

Damped Spherical Spring Pendulum

Damped Swing Pendulum

Damping in RLC Circuits

Dancing Tubes

Dandelin Sphere for the Parabola

Dandelin Spheres for an Ellipse

Dandelin Spheres for the Elliptic Case

Dandelin Spheres for the Hyperbola

Dandelion

Daniell Cell: Charging and Discharging

Dante's Medieval Cosmology

Darboux and the Dog's Tail

Darboux Cubic

D'Arcy Thompson's Affine Fish Transformations

Dark Fraction of the Moon

Dart Practice

Data Compression Using Asymmetric Numeral Systems

Data Sampling and Interpolation

Data Smoothing

Da Vinci's Construction of an Ellipse

Da Vinci's Perpetual Wheel

Da Vinci's Proof of the Pythagorean Theorem

Dawn Spaceflight

Day and Night World Clock

Daylight Calculator

DC and AC Josephson Effects

Deadweight Loss for a Monopoly

Deaf Island Puzzle Generator

Dealer's Odds in Blackjack

Death Penalty Regressions

De Bruijn Graph Arcs

De Bruijn Initialization of 2D Automata

De Bruijn Sequences

De Bruijn Sequences Provide Compact Initial Conditions

Debye Length in a Symmetric Electrolyte Solution

Decagonal Clusters of Polyhedra

Decagon-to-Square Dissection

de Casteljau Algorithm for a Tensor-Product Bézier Surface

Deciding Rain-Affected Cricket Matches: The Duckworth-Lewis Method

Decimal Division

Decimal Multiplication

Decimals as Fractions

Decimal to Binary Floating-Point Conversion

Decisions Based on P-Values and Significance Levels

Decoding the Arecibo Message

Decoherence and Trajectories Implied by a Modified Schrodinger Equation

Decomposing a Cuboctahedron into Three Rhombic Dodecahedra and Two Tetrahedra

Decomposing a Random Newton Polygon

Decomposing a Regular Polygon with an Odd Number of Sides into Rhombuses and Triangles

Decomposing a Rhombic Dodecahedron into a Trapezoid-Rhombic Dodecahedron

Decomposing a Rhombic Solid into a Truncated Octahedron

Decomposing Rotations into Shear Mappings

Decomposition into Isosceles Triangles with Angles That Are Multiples of Pi/4

Decomposition of 2,3 Turing Machine Evolutions

Decomposition of a Double Triacontahedron

Decomposition of a Rhombic Dodecahedron

Decomposition of a Tetrahedron into Four Congruent Parts

Decomposition of a Vector in 2D

Decomposition of Some Polygons to Iso-Penta Triangles

Decomposition of the Tetrahedron into Four Congruent Symmetrical Parts

Deconvolution of a Chromatogram

Decorated Polar Zonohedra

Decorated Spirallohedra

Decorating a Tree with a Ribbon

Decorative Holiday Stars

Decreasing the Freezing Point of Water with Dissolved Sodium Chloride

Dedekind Cut

Deduce Linear Order from Relations

Deduce the Net for a Die

Deduce the Net for a Die's Net

Deduce the Net for an Octahedral Die

Deep Drawing of Metals

Defects in an Optical Fiber

De Finetti's Game

Define Your Own Koch Curve

Definition and Equations of an Ellipse

Definitions of Hill's Tetrahedra

Definitions of Two-Placed Connectives in Lesniewski's Protothetic

Deflection of a Diving Board

Déformation d'une particule fluide (French)

Deformation of a Tennis Ball and Racket Strings

Deformation of Noncylindrical Compression Springs

Deformation of Noncylindrical Extension Springs

Deformation Pattern in an Earthquake Source Region

Deforming a Möbius Band with a Triangular Boundary

Deforming Nets of Polyhedra

Degenerate Critical Points and Catastrophes: Fold Catastrophe

Degenerate Eigenstates

Degenerate Energy States

Degenerate Power Simplices

Degradation Parameters from Concentration Ratios

Degree Distribution on a Random Network

Degree-of-Freedom Analysis on a Distillation Process

Degrees of Freedom of a Moving Rigid Body

Degrees of Microbial Injury and Survival

Dehn Invariant of Some Disjoint Unions of Polyhedra with Icosahedral Symmetry

Dehn Invariant of Some Disjoint Unions of Polyhedra with Octahedral Symmetry

Dehydration by a Desiccant

De La Hire's Construction of an Ellipse

Delannoy Number Carpet

Delannoy Path Exhaustion Diagonal

Delaunay Nodoids

De Laval Nozzle

Delayed CA

Delayed Ikeda Difference Equation

Delay Logistic Equation

Delboeuf Illusion

Delta and Perceptron Training Rules for Neuron Training

Deltic Engine

Deltoidal Hexecontahedron

Deltoid Kite Tiling

Demanda, Oferta y Equilibrio (Spanish)

De Moivre's Theorem for Trig Identities

Denavit-Hartenberg Parameters for a Three-Link Robot

Dendrimer to Linear Polymer Transition

De Novo Growth Processes with Competing Mechanisms

Densest Tetrahedral Packing

Density

Density Estimation

Density Functional Computations on Noble Gas Atoms

Density Map for the 3n+1 Problem

Density Mapping of Elementary Cellular Automata

Density of the Kou Jump Diffusion Process

Deploying and Steering a Parabolic Antenna

DePriester Chart for Hydrocarbons

Depth Map

Derangement Diagrams

Derivation of Thermodynamic Derivatives Using Jacobians

Derivative as a Function

Derivative of a Vector-Valued Function in 2D

Derivative of log(x!)

Derivatives: A Look at Graphs

Derivatives of a 2D Gaussian

Derivatives of Exponential Functions

Derivatives of Quintic Polynomials

Derivatives of Sine

Derivatives of the Sum of Two Sines

Derivatives of Trig and Hyperbolic Functions

Derived Polygon

Deriving a Bilunabirotunda from Rhombic Solids

Deriving Hypergeometric Picard-Fuchs Equations

Deriving the Formula for the Area of a Parallelogram

Deriving the Labor Demand Curve

Deriving the Liquidity Preference-Money Supply (LM) Curve

Descartes's Angle Trisection

Descartes's Geometric Solution of a Quadratic Equation

Descartes Signature Explorer

Descartes's Method of Evaluating the Principal Cube Root

Descartes's Rule of Signs

Descriptions of Univariate Data

Descriptive Reaction Kinetics

Design a Tile for the p3 Wallpaper Group

Designer Baby

Designing a Car Body with Splines

Designing a Logo

Designing a Mercury Tumbling Machine

Designing End-Blown Flutes

Designing Four-Bar Linkages

Designing Optical Systems

Design of a Helical Extension Spring

Design of Alphabets with Fourier Transforms

Design of a Shell and Tube Heat Exchanger

Design of Mass Timber Panels as Heat Exchangers

Design of Optimal Multistage Heat Exchanger

Design of Street Gutter

Designs Based on Dissecting Regular Polygons into Rhombuses

Designs by Colorful Circles

Designs for Ribbons and Friezes Based on Trigonometric Functions

Designs from Mechanical Linkages

Design Your Own Commemorative Coin

Desk Lamp

Desmodromic Valve Train

Destructive Tomography of Red Cabbage

Desynchronization Dynamics of Two Coupled Oscillators

Detachment and Tendency of a Single Variable Function

Detailed Analysis of Rutherford Scattering of Alpha Particles

Detecting a Discontinuity Using a Wavelet Scalogram

Detecting a Signal with Background Noise

Detecting Periodicity in Short Time Series

Determinants of the NPV of a Bond

Determinants of the Weighted Average Cost of Capital (WACC)

Determinants Seen Geometrically

Determine a Vector in 2D

Determine a Vector in 3D

Determine if a Truss Can Be Solved

Determine the Figures

Determine the Properties of a Figure

Determine the Type of Stress in Each Member of a Truss

Determining a House-Like Solid from Three Orthogonal Projections

Determining Latitude from Maximum Solar Altitude

Determining Shelf Life by Two Criteria

Determining the Area of a Rhombus

Determining the Intersection of Two Lines Graphically

Deterministic Context Free (DOL) Systems

Deterministic versus Stochastic Chemical Kinetics

Deutsch's Algorithm on a Quantum Computer

Developing a Perspective Anamorphic Image

Device for Tube Extraction

Devilish Mazes

Devil's Staircase

Diagonal Planes of a Cube

Diagonals of Polyhedra

Diagrammatic Representations of Scientific Formulas

Dialectical Cellular Automata

Diamond Lattice

Diamond-Square Algorithm for Creating Landscapes

Diaphragm Shutter

Diauxic Behavior of Yeast in a Fed-Batch Reactor

Diauxic Growth of Bacteria on Two Substrates

Dice Probabilities

Dice Roller & Penny Flipper

Dice Rolls as an Example of the Coupon Collector's Problem

Dice Transitivity

Dichotomy Paradox Joke

Dichtefunktion der Chi-Quadrat Verteilung (German)

Dichtefunktion der Studentschen t-Verteilung (German)

Dielectric Sphere in a Uniform Electric Field

Dieterici Compressibility

Dieterici Equation of State

Difference Equation versus Differential Equation

Difference Formula for Cosine

Difference in Digit Sequences by Changing Initial Conditions

Difference of Cubes

Difference of Squares

Difference Set

Differences of the Union of Two Arithmetic Progressions and Christoffel Paths

Differential Element dA

Differential Equation with a Discontinuous Forcing Function

Differential of a Function

Differential of the Arc

Differentiation for Athletes

Differentiation Microscope

Different Perspectives on Achieving the Mean of a Distribution

Different Perspectives on the Median of a Distribution

Different Slants on Simple Geometric Figures

Diffraction Grating Intensities

Diffuse and Specular Reflection

Diffusional Impedance of a Recessed Microelectrode

Diffusion and Kinetic Controlled Electrochemical Reactions

Diffusion and Reaction in a Catalyst Pellet

Diffusion and Reaction in a Falling Liquid Film

Diffusion Coefficients for Multicomponent Gases

Diffusion Coefficients of Tracers in Capillary Tube Experiments

Diffusion-Controlled Drug Delivery

Diffusion-Controlled Evaporation of an Aerosol Droplet

Diffusion Impedance in a Thin Layer Cell

Diffusion in One Dimension

Diffusion in Solids

Diffusion-Limited Aggregation

Diffusion-Limited Aggregation: A Real-Time Agent-Based Simulation

Diffusion-Limited Clogging

Diffusion of Gases in a Tube

Diffusion of Ions in Soil

Diffusion of Oxygen Molecules across a Membrane Using Fick's Law

Diffusion of Oxygen through the Placenta

Diffusion on a Macro-Electrode

Diffusion Rates Across the Blood-Brain Barrier

Diffusion-Reaction in a Catalytic Particle

Diffusion through a Membrane

Diffusion to a Spherical Reactor

Digital Determination of Output Voltage Harmonics in a Single-Phase Voltage Controller

Digital Filters with Windowed Sinc Finite Impulse Response

Digital IIR Filter Design Showing Poles and Zeros

Digital Kaleidoscope: Triangular Tiling with Textures

Digital Modulation: Quadrature Phase-Shift Keying (QPSK) Signal Constellation and Eye Diagrams

Digital Representation of a Nonlinear ODE with Small Differences in Initial Conditions

Digital Tilt-Shift Photography

Digit Counts in Integers

Digit Frequencies in Digit Expansions

Digit Frequencies in the Columns of Cellular Automata

Digit Frequencies in the Copeland-Erdos Constant

Digit Frequency Plot for Transcendental Numbers

Digit Mosaics

Digit Patterns in Integer Powers

Digit Patterns of Successive Numbers

Digit-Reversal Sequences

Digits in Powers of Integers for Various Bases

Digits of Hyperfactorial and Barnes G

Digits of Successive Fractions

Digits of the First 30 Mersenne Primes

Digit Sum in Different Bases

Digit Sums

Digits Walks of Transcendental Numbers

Digon Tiling of a Hosohedron

Dihedral Effects in Aircraft Flight

Dihedral Group n of Order 2n

Dihedral Group of the Square

Dijkstra's Algorithm

Dijkstra's and A* Search Algorithms for Pathfinding with Obstacles

Dim City

Dimension and Euler Characteristics of Graphs

Dimensions of a Stranded Wire

Dini's Surface

Dinitrogen Tetroxide Dissociation Equilibrium

Dintzl's Law of Cosines Dissection

Diocles's Solution of the Delian Problem

Dipole Antenna Radiation Pattern

Dipole Fields Are Complicated

Dirac Belt Trick Simulation Showing Double Cover of SO(3) by SU(2)

Dirac Matrices in Higher Dimensions

Dirac Tunneling

Direct Control for Hex Machine

Direct-Current Generator

Directed Angles and Their Types

Directional Dependence of Acousto-Optic Figure of Merit

Directional Derivatives

Directional Derivatives and the Gradient

Directional Derivatives in 3D

Direction Fields for Differential Equations

Direct Isometries of the Hyperbolic Plane

Directivity Pattern of Line Arrays

Direct Rule Control for 2,2 Turing Machines

Direct Rule Control for 2,3 Turing Machines

Direct Rule Control for 3,2 Turing Machines

Direct Rule Control for 3,3 Turing Machines

Direct Sum of Rings

Dirichlet Characters

Dirichlet L-Functions and Their Zeros

Dirichlet L-Functions near the Critical Line

Dirichlet's Theorem

Disappearing Dot Illusion

Disappearing Fluff

Disappearing Lines around a Circle

Disappearing Lines in a Rectangle

Discontinuity

Discounted Present Value

Discrepancy Conjecture

Discrete and Continuous Quartic Anharmonic Oscillation

Discrete Fourier Sine and Cosine Transforms

Discrete Fourier Transform of a Two-Tone Signal

Discrete Fourier Transform of Windowing Functions

Discrete Function Composition

Discrete Harmonic Functions and Dirichlet's Relaxation Method

Discrete Logistic Equation

Discrete Marginal Distributions

Discrete Minimal Surfaces

Discrete Number Theory Plots

Discrete Population Model for Fishery Stocks

Discrete Reaction-Diffusion

Discrete Rogue Waves

Discrete Spiral

Discrete-Time Convolution

Discrete Versions of Continuous Functions

Discriminant of a Polynomial

Discriminating Monopolist with Two Independent Markets

Discus Flight

Disentangling Wire-and-String Puzzles in 3D

Disk Rolling inside a Rotating Ring

Disk Rolling on a Horizontal Plane

Disks Centered on Vertices of Regular Polygons

Disk Sliding or Rolling in a Semicircular Well

Disk to Oval Seat Tops

Disk to Oval Seat Tops II

Disk with a Hole Rolling in a Semicircular Well

Disparity, Convergence, and Depth (Visual Depth Perception 10)

Dispersion of Light through a Prism

Dispersion Properties of a Spin-Orbit-Coupled Bose-Einstein Condensate

Displacement along a Curve

Displacement versus Distance

Displaying Molecules with Multiple Bonds

Dissecting a Bilinski Dodecahedron into a Near Cube

Dissecting a Concave Rhombic Triacontahedron into 13 Cubes

Dissecting a Cross of Lorraine into a Square

Dissecting a Cross of Lorraine to a Greek Cross

Dissecting a Cube into a Golden Acute Rhombohedron and Three Congruent Rectangular Solids

Dissecting a Cube into an Acute Golden Rhombohedron and Three-Quarters of a Bilinski Dodecahedron

Dissecting a Cube into an H Shape and Two Cubes

Dissecting a Cube into an Obtuse Rhombohedron, Three Congruent Rectangular Solids and Two Congruent Cubes

Dissecting a Cube into a Rectangular Solid with a Square Base

Dissecting a Cube into a Rhombohedron and Three Congruent Cubes

Dissecting a Cube into a Tetrahedron and a Square Pyramid

Dissecting a Cube into Two Rhombic Triacontahedra

Dissecting a Decagon into a Pentagram and Two Pentagons

Dissecting a Decagon into Two Pentagons and Two Pentagrams

Dissecting a Decagram {10/4} into Two Decagons

Dissecting a Disk with Six Segments Deleted to a Hexagon

Dissecting a Dodecagram {12/2} into a Hexagram {6/2}

Dissecting a Dodecagram {12/2} to a Square

Dissecting a Dodecagram into a Triangle

Dissecting a Dodecagram into Two Hexagrams

Dissecting a Generalized Greek Cross to a Square

Dissecting a Globular Greek Cross to a Square

Dissecting a Hexagon into Four Smaller Hexagons

Dissecting a Hexagram into Three Hexagrams

Dissecting a Large Cube into a Bilinski Dodecahedron and a Small Cube

Dissecting a Latin Cross into a Greek Cross

Dissecting an Acute Golden Rhombohedron into a Rectangular Solid

Dissecting and Reassembling a Cube into Three Different Solids

Dissecting an Ellipsoid to Form a Heart Shape

Dissecting an Equilateral Triangle into Four Equilateral Triangles

Dissecting an Equilateral Triangle into Three Smaller Ones

Dissecting a Net of a Gyroelongated Square Dipyramid

Dissecting an Even-Sided Regular Polygon into Rhombuses

Dissecting an N-gram into Two Smaller N-grams

Dissecting an Octagon into Four Smaller Octagons

Dissecting a Pyramid into Four Equal Pieces

Dissecting a Quarter of a Rhombic Dodecahedron of the Second Kind into a Skew Triangular Prism

Dissecting a Rectangular Solid into an Acute Golden Rhombohedron and Half a Bilinski Dodecahedron

Dissecting a Rectangular Solid into an Obtuse Golden Rhombohedron and Half a Bilinski Dodecahedron

Dissecting a Regular 2n-gon into Four Smaller 2n-gons

Dissecting a Regular Hexagon into Five Congruent Regular Hexagons

Dissecting a Regular Triangle into Three Similar Tiles

Dissecting a Rhombic Dodecahedron into an Octahedron and Two Tetrahedra

Dissecting a Rhombic Dodecahedron into Two Cubes

Dissecting a Rhombic Dodecahedron into Two Solids

Dissecting a Rhombic Dodecahedron of the Second Kind to Half a Cube

Dissecting a Rhombic Triacontahedron

Dissecting a Rhombic Triacontahedron into Twenty Congruent Cubes

Dissecting a Rhombohedron into Two Congruent Rhombohedra

Dissecting a Square into a Sphinx

Dissecting a Square Pyramid into 15 Pieces

Dissecting a Square to Four Squares

Dissecting a Trapezoid into a Parallellogram

Dissecting a Truncated Octahedron to a Rectangular Solid

Dissecting Five Cubes into a Rectangular Solid with a Square Base

Dissecting Five Cubes into One

Dissecting One Equilateral Triangle into Seven

Dissecting One Isonona Triangle into Two

Dissecting the Net of an Octahedron to the Net of a Tetrahedron

Dissecting the Triangular Hebesphenorotunda (Johnson Solid 92)

Dissecting Two Bilinski Dodecahedra into a Cube

Dissecting Two Cubes into Golden Rhombohedra

Dissecting Two Rhombic Dodecahedra of the Second Kind into a Cube

Dissection and Reassembly of Parallelogram of Given Base and Altitude

Dissection Fallacy

Dissection of a Bilinski Dodecahedron into a Rectangular Solid

Dissection of a Composite Spherical Triangle

Dissection of a Concave Rhombic Triacontahedron

Dissection of a Cube into a Cuboctahedron and an Octahedron

Dissection of a Cube into Five Polyhedra

Dissection of a Cube into Five Solids

Dissection of a Cube into Three Bilunabirotundas, a Dodecahedron, and a Smaller Cube

Dissection of a Cube into Two Kinds of Triacontahedra

Dissection of a Cube to a Quarter of a Rhombic Dodecahedron of the Second Kind

Dissection of a Dodecagram {12/5} to a Square

Dissection of a Latin Cross into a Square

Dissection of a Maltese Cross to a Square

Dissection of an Dodecagram into Three Dodecagrams

Dissection of an Equilateral Spherical Triangle into Two Congruent Equilateral Spherical Triangles

Dissection of an Equilateral Triangle into Five Equilateral Triangles

Dissection of an Irregular Triangle to a Square

Dissection of an Oblique into a Right Prism

Dissection of an Obtuse and an Acute Golden Rhombohedron into a Rectangular Solid

Dissection of an Obtuse Golden Rhombohedron into Rectangular Solids

Dissection of an Octagram into Five Octagrams

Dissection of a Pentagonal Antiprism into a Metabidiminished Icosahedron

Dissection of a Pentagon to Almost a Square

Dissection of a Prismatoid into Prisms

Dissection of a Quarter of a Bilinski Dodecahedron into a Rectangular Solid

Dissection of a Regular Decagon into Three Pentagrams and Eight Pentagons

Dissection of a Regular Decagon into Two Pentagrams and Six Pentagons

Dissection of a Regular Dodecagon into Six Smaller Ones

Dissection of a Regular Dodecagon into Three

Dissection of a Regular Enneagon into Four Congruent Regular Enneagons

Dissection of a Regular Heptagon into Eight

Dissection of a Regular Pentagon into Three Pentagons

Dissection of a Rhombic 210-hedron into a Combination of Icosahedron and Truncated Dodecahedron

Dissection of a Rhombic Dodecahedron of the Second Kind into a Rectangular Solid

Dissection of a Rhombohedron into a Right Prism with the Same Base

Dissection of a Special Rectangular Solid to a Cube

Dissection of a Spherical Equilateral Triangle into Three Isosceles Triangles

Dissection of a Spherical Square into a Spherical Lune

Dissection of a Spherical Square into Two Spherical Regular Pentagons

Dissection of a Spherical Triangle into a Spherical Lune

Dissection of a Spherical Triangle into a Square

Dissection of a Spherical Triangle into Three Spherical Triangles around a Spherical Hexagon

Dissection of a Sphinx into a Triangle

Dissection of a Square and an Isosceles Right Triangle into a Square

Dissection of a Square into Three Squares

Dissection of a Square to a Parallelogram with the Same Base

Dissection of a Triangle to Its Mirror Image I

Dissection of a Triangle to Its Mirror Image II

Dissection of a Truncated Octahedron into Hexagonal Skew Prisms and Parallelepipeds

Dissection of Bilunabirotunda into Two Pentagonal Dipyramids and a Rhombic Dodecahedron of the Second Kind

Dissection of Five Bilinski Dodecahedra into a Rhombic Triacontahedron

Dissection of Five Equilateral Triangles into One

Dissection of Four Rhombic Dodecahedra into a Truncated Tetrahedron and a Tetrahedron

Dissection of Gerwien's Triangle into a Saccheri Quadrilateral on the Sphere

Dissection of Half an Obtuse Golden Rhombohedron and Half an Acute Golden Rhombohedron into a Cube

Dissection of Hill's Tetrahedron of Type 1

Dissection of One Hexagram into Seven

Dissection of One Quadrilateral to Another

Dissection of One Regular Heptagon into Seven

Dissection of One Triangle to Another

Dissection of Rhombic Dodecahedron into 24 Nonregular Tetrahedra

Dissection of the Great Rhombicosidodecahedron into Prisms

Dissection of the Oblate Golden Rhombohedron

Dissection of Three Bilunabirotundas and a Dodecahedron into Rhombic Solids

Dissection of Three Polyhedra into Two

Dissection of Three Regular Spherical Pentagons into Five Equilateral Spherical Triangles

Dissection of Three Rhombic Solids into an Icosahedron, a Dodecahedron, and an Icosidodecahedron

Dissection of Truncated Icosidodecahedron

Dissection of Two {8/2}-Prisms into One

Dissection of Two Bilinski Dodecahedra into a Dali Cross

Dissection of Two Rhombic Dodecahedra of the Second Kind

Dissection of Two Rhombic Solids into an Icosidodecahedron and a Rhomb-Icosi-Dodecahedron

Dissection of Two Savnik Gravestones into a Latin Cross

Dissection of Two Spherical Triangles to Three Spherical Squares

Dissection of Two Squares into Three Congruent Squares

Dissection of Two Squares into Three Squares

Dissection of Two Stellated Dodecahedra

Dissection of Two Truncated Octahedra into a Cube

Dissection Proof of the Addition Formula for Sines

Dissolution of Common Medications as Modeled by Drug Release Kinetics

Dissolving a Solute

Dissolving Partnerships

Distance and Average Velocity for Piecewise Trajectory

Distance and Dissimilarity Patterns

Distance and Polygons

Distance between Gergonne Point and Fletcher Point

Distance between Incenter and Fletcher Point

Distance between Inner and Outer Soddy Centers

Distance between Orthocenter and Center of Taylor Circle

Distance between the Centers of the Nine-Point and Apollonius Circles

Distance between the Incenter and the Center of the Apollonius Circle

Distance between Two Fermat Points

Distance between Two Napoleon Points

Distance between Two Points

Distance between Two Points Based on a Triangle

Distance between Two Vecten Points

Distance Distributions in Finite Uniformly Random Point Processes

Distance from a Point to a Line

Distance Functions

Distance Norms in Robot Workspace and Phase Space

Distance of a Point to a Polygon

Distance of a Point to a Segment

Distances from the Centroid

Distances from the Incenter to the Fermat Points

Distance Transforms

Distillate and Still Compositions for Batch Rectification of a Binary Mixture at a Very Large Reflux Ratio

Distillation Column Calculation Incorporating Pressure Drop Effect

Distillation-Column Product Purity as Function of Feed Thermal Quality

Distillation Column Using the Francis Formula for Flow through Weirs

Distillation Column with an Intermediate Reboiler

Distillation Column with Liquid Side Stream

Distillation Column with Two Feeds

Distillation Lines for a Mixture of Chloroform, Acetone, and Methanol at 1 atm

Distillation Lines versus Residue Curves for a Mixture of Oxygen, Argon, and Nitrogen at 1 atm

Distillation of an Ethanol-Water Mixture

Distillation of a Ternary Ideal Mixture

Distillation of Substances with Widely Differing Heats of Vaporization: The Peters Transform

Distorted Cube

Distorting a Square to Form a Hyperbolic Paraboloid

Distorting Jessen's Orthogonal Icosahedron to an Octahedron

Distortions in Map Projections

Distribution of a Robot Swarm in a Square under Gravity

Distribution of a Swarm of Robots in a Circular Workplace under Gravity

Distribution of Colloidal Particles during Solvent Evaporation

Distribution of Conformers in Rotational Isomerism

Distribution of Digits in Several Math Constants

Distribution of Discrete Records

Distribution of End-to-End Distances in Linear Substituted Polymethylenes

Distribution of Normal Means with Different Sample Sizes

Distribution of Palindromes in Base b

Distribution of Primes

Distribution of Records

Distribution of Returns from Merton's Jump Diffusion Model

Distribution of Spore Custom Content

Distribution of the Last Digit of the Primes

Distribution of the Means of Samples Having Random Sizes

Distribution of the Sample Range of Continuous Random Variables

Distribution of the Sample Range of Discrete Random Variables

Distributions for a Concentration-Dependent Diffusion Coefficient

Distributions in Direction-Biased Random Walk

Distributions of Continuous Order Statistics

Distributions of Discrete Order Statistics

Distributions of Leading Digits

Distributions of Order Statistics

Distributions Using Slice Sampling

Distributive Property of Multiplication over Addition

Divergence from the Mandelbrot Set

Divide Triangles

Dividing a Circle with Half-Circles

Dividing a Regular Tetrahedron into Four Congruent Pieces

Dividing a Right Triangle by the Altitude to the Hypotenuse

Dividing a Triangle by Lines Parallel to Two Sides

Dividing Circles, Rectangles, and Triangles into Equal Pieces

Dividing Fractions

Dividing Integers

Dividing Mixed Numbers

Dividing Segments by Origami

Diving Bell

Divisibility Graph

Divisibility Networks

Division by Successive Subtraction

Division in the Ring of Algebraic Integers Generated by the Square Root of Five

Division of an Angle Bisector by the Incenter

Division of Polynomials up to Degree Six

Division of the Opposite Side by an Angle Bisector

Divisors of a Number

Dixon Model for Magnetic Field of a Neutron Star

DMSO as an Entrainer to Separate a Water-Isopropyl Alcohol Mixture

DNA Base Pairing

DNA Replication

DNA Rotator Walk

DNA Screening Incidentalome

DNA Translation at a Ribosome

Dodecagon-to-Hexagon Dissection

Dodecahedra and Rhombic Hexecontahedra in Fractal Arrangement

Dodecahedral Cluster of RTs and RHs

Dodecahedral Rhombic Monohedra

Dodecahedral Star with Astroidal Spikes

Dodecahedron and Bilunabirotunda

Dodecahedron Made of 20 Blocks

Dodecahedron Measures

Dodecahedron to Small Rhombicosidodecahedron

Doehlert Design for Wet Pelletization

Dollar Duration

Domain and Range of Inverse Trigonometric Functions

Domain Coloring for Common Functions in Complex Analysis

Domain of a Function of Two Variables

Domany-Kinzel Stochastic Cellular Automata

Dome Frames Made of Arches

Dome Made of Cylindrical Segments

Dome of Viviani Windows

Domino and Triomino Tilings of a Chessboard

Domino Substitution Tilings

Do Not Divide by Zero

Don't Let The Pig Escape

Doors Puzzle

Doped Silicon Semiconductors

Doppler Effect

d-Orbitals in an Octahedral Field

Doshu Puzzle

Dot and Cross Products Related to Complex Multiplication

Do the Rich Live Longer?

Dot Plot

Dot Product

Dots and Boxes

Double Atwood Machine

Double Delta Function Scattering Potential

Double Helix

Double Integral for Volume

Double Integrals by Summing Values of a Cumulative Distribution Function

Double Marginalization and Supply Chains

Double Pendulum

Double P-Slide Dissection

Double Refraction by a Uniaxial Crystal

Double Rhombic Icosahedron

Double-Sided Couette Flow

Double Slit Diffraction for Particles

Double Spiral

Double-Spring Pendulum

Doublets

Double-Well Reaction Dynamics

Doubling a Distance with a Compass

Doubling a Line Segment Using a Right Angle

Doubling Cellular Automata

Doubling Time Using the Rule of 72

Doubly Recursive Integer Factorizations

Doug-all Theorem II: Inscribed Triangles

Dovetail Joint

Downbursts and the Moody Diagram

Doyle Spirals

Doyle Spirals and Möbius Transformations

Drag and Gravity Forces on a Falling Sphere

Dragon Curves Using Multiple Different Angles

Drainage of a Hemispherical Tank

Draining of Two Connected Tanks

Drawbar/Harmonic Waveform Viewer

Drawdown Pressure in a Naturally Fractured Reservoir

Drawing a Colored Polygon

Drawing a Line on a Digital Display

Drawing a Logarithmic Spiral

Drawing an Ellipse Using Circles and Lines

Drawing an Oval with a String and Three Nails

Drawing a Regular Polygon

Drawing a Spiral on the Surface of an Egg

Drawing a Triangle

Drawing a Wire

Drawing Chemical Structures

Drawing Paths on the Sierpinski Carpet

Drawing Some Plane Curves Using Envelopes of Lines

Draw Polygons on Grids

Draw Your Own Electrical Circuit

Draw Your Smiley Face

Dressed Multi-Particle Electron Wave Functions

Drill Down into Chemical Data

Drilled Truncated Octahedron

Drilling a Hexagonal Hole

Drilling an n-Gon Hole for Odd n

Drilling a Pentagonal Hole

Drilling a Square Hole

Drilling a Triangular Hole

Driven Damped Oscillator

Driven Damped Oscillator with Resonance Effect

Driven Spherical Pendulum

Driving a Piston

Driving a Reaction by Chemical Coupling

Driving out of a Parking Space

Dropping a Test Charge into an Electric Field

Drop Shadows

Droste Effect

Drude-Lorentz Model for Dispersion in Dielectrics

Drum Machine

Dry Friction

Dry Screening Stratification: A Particle Climbing and Settling Problem

Dual Billiards

Dual-Fluid Herschel-Bulkley Model for Pumping Flowable Concrete

Dual Product Control of a Binary Distillation Column

Duals by Rotating the Edges of Polyhedra

Dual Slope Analog-to-Digital Converter

Duals of Platonic Solids

Ducado

Duck Cut

Dudeney's Cross-to-Isosceles-Right-Triangle Dissection

Dudeney's Proof of the Pythagorean Theorem

Dudeney's Step Dissection of a Rectangle to a Square

Duffing Oscillator

Duffin's Sequence for Pi

Duff-Porter Alpha-Compositing Operators

Duopoly Competition with Differentiated Products

Duopoly Model in 3D

Dupin Cyclides

Dupin's Indicatrix of a Torus

Du Plantier's Square Root Extractor

Dürer's Impossible Net

Dürer's Solid in a Rhombic Hexecontahedron

Durometer Hardness of Rubber Table Tennis Blades

Dust with Line Shadows in Every Direction

Dutch Drawbridge

Dwarf Planets

Dyadic Cascade Algorithm for Daubechies Wavelets

Dynagraphs

Dynamical Behavior of a Duffing Oscillator

Dynamically Updated Probabilistic Galton Board

Dynamical Network Design for Controlling Virus Spread

Dynamical Systems with Lorenz Attractors

Dynamic Analysis of a Second-Order System with Harmonic Loading

Dynamic Approximation of Static Quantities (Visual Depth Perception 14)

Dynamic Behavior of a Bioreactor

Dynamic Behavior of a Heated Stirred Tank

Dynamic Behavior of an Addition Polymerization in a Batch Reactor

Dynamic Behavior of a Nonisothermal Chemical System

Dynamic Behavior of a Reactive Distillation Column: Mixture of Four Components

Dynamic Behavior of a Reactive Distillation Column Subject to a Reflux Ratio Step

Dynamic Behavior of a Simple Canonical System

Dynamic Behavior of Heated Tanks in Series

Dynamic Behavior of Isothermal Flash Vessel

Dynamic Behavior of Three Tanks in Series

Dynamic Billiards in Ellipse

Dynamic Damping

Dynamic Electricity Prices

Dynamic Equilibrium Example

Dynamic Germination of Seeds and Microbial Spores

Dynamic Model of Pandemic Influenza with Age Structure and Vaccination

Dynamic Profit Maximization for a Monopolist

Dynamic Proximity Networks

Dynamic Simulation of a Binary Distillation Column

Dynamic Simulation of a Gravity-Flow Tank

Dynamics in the Solow-Swan Growth Model

Dynamics of a Binary Distillation Column

Dynamics of a Chain of Coupled Pendulums

Dynamics of a Charged Particle in a Magnetic Field with a Kicked Electric Field

Dynamics of a Continuous Distillation of a Mixture of Benzene, Toluene, and p-Xylene

Dynamics of a Continuous Stirred-Tank Reactor with Consecutive Exothermic and Endothermic Reactions

Dynamics of a Coupled Reactor-Separator System with Time Delay

Dynamics of a Cube-Shaped Mass-Spring Network

Dynamics of a Deterministic Overflow Fluid Network

Dynamics of a Double Spring Mass

Dynamics of a Falling Chain

Dynamics of a Forced Brusselator

Dynamics of a Forced Exothermic Chemical Reaction

Dynamics of a Heated Tank with Proportional Integral Differential (PID) Control and Outlet Flow Time Delay

Dynamics of a Longitudinal Piezoelectric Beam

Dynamics of an Elementary Cellular Automaton

Dynamics of an Enzymatic Aerated Reactor

Dynamics of an Epidemic

Dynamics of a Nonadiabatic Continuously Stirred Tank Reactor

Dynamics of a Spring-Pendulum System

Dynamics of a Susceptible-Exposed-Infected-Recovered (SEIR) Epidemic Model with Time Delay

Dynamics of Automobile Suspension Systems

Dynamics of Counter-Current Cooled CSTRs

Dynamics of Coupled Pendulums

Dynamics of Free Particle and Harmonic Oscillator Using Propagators

Dynamics of Maximal Entropy Random Walk and Generic Random Walk on Cayley Trees

Dynamics of Qubit Lattices

Dynamics of Seasonal Epidemics

Dynamics of Three-Strategy Symmetric Games

Dynamics of Triangle Iterates

Dynamics of Two Continuous Stirred-Tank Reactors Operating in Series

Dynamics of Two Coupled Continuously Stirred Tank Reactors

Dynamics of Two Cylinders with Three Springs

Dynamic Step Distance Transforms

Dynamic Water Absorption by Foods

Dynkin Diagrams

Dzhanibekov Effect

E2 Elimination Reactions of Alkyl Halides

Ear Decomposition of the Petersen Graph

Early Exercise of American Options

Earned Value Management

Earth-Moon Problem

Earthquake Focal Mechanism

Earth's Magnetosphere and the Solar Wind

Earth's Second Moon

Ear Training for Pentatonic Scales

Eccentric Chuck

Eccentric Cylinder and Tappet Drive

Echoes

Eco-evolutionary Game Dynamics with Synergy and Discounting

Ecology of Reef Systems

Economic Trade-Offs in the Operation of a Single Reactor

Ecosystem Dynamics

Ecosystems with Ghost Invasive Species

Ecouter la convergence (French)

E-curve and F-curve for the Tanks-in-Series Model of MacMullin and Weber

Edge Contraction in a Graph

Edge Detection in Images

Edge Enhancement on Multiple Images

Edgeworth Expansion for Near-Normal Data

Edit Distance

Edwards's Solution of Pendulum Oscillation

Efecto Compton (Spanish)

Effective and Inertial Masses of a Photon Near a Black Hole for a Family of Envelope Orbits

Effective Potential of a Black Hole Metric

Effective Resistance between an Arbitrary Pair of Nodes in a Graph

Effective Resistance of Network

Effect of a 3x3 Singular Transformation Matrix on 3D Space

Effect of Altitude on Alveolar Oxygen Pressure

Effect of a Perturbation on the Stable Points of a Dynamical System

Effect of B-Factor on X-Ray Scattering

Effect of Detail on Visual Perception

Effect of Distance in Förster Resonance Energy Transfer

Effect of Extra Payments on an Amortizing Loan

Effect of Friction on Ball Rolling Down a Ramp

Effect of Gravity on a Simple Pendulum

Effect of High Expense Charges on an Investment's Net Return

Effect of Immunity and Susceptibility on Sickness or Mortality Risk

Effect of Keyword Length on the Letter Frequency in Encrypted Messages

Effect of Liquid Murphree Efficiency on the Operation of a Deisobutanizer

Effect of Molar Holdup on the Dynamic Response of a Binary Distillation Column

Effect of Outliers on Fit of Growth Models

Effect of Pressure on Chemical Equilibrium

Effect of Shock on the Stationary and Nonstationary Autoregressive (AR) Process

Effect of Temperature on Chemical Equilibrium

Effect of Temperature on Partial Miscibility in a Binary-Liquid System

Effect of Temperature on Solubility of Aniline-Methylcyclopentane-Hexane System

Effect of Time Delay on a Model of Bone Homeostasis

Effect of Tube Diameter on Plug Flow Reactor

Effect of Viscous Dissipation on Heat Transfer in Laminar Flow

Effect of Volatility and Drift on Random Walks

Effect of Wind Chill on Skin Temperature

Effects of a Force on the Orbit of an Artificial Satellite

Effects of Bin Width and Height in a Histogram

Effects of Cell and Solution Concentrations on Osmosis

Effects of Deformation on Actuated Joints

Effects of DNA Mutations on Protein Sequences

Effects of Temperature Fluctuations on Oscillating Biological Systems

Efficacy of Degenerate Keyboard Maps

Efficiency of Some Machin-Like Formulas

Efficient Single Limit Liability Insurance

Efficient Total Production through Specialization

Efimov Effect in Low-Temperature Trimers

Egg Colored by Gradients

Egg Colored Using Polynomials

Egg Colored Using the Riemann Zeta Function

Egg Colored with Sinusoids

Eggnigmatica

Eggnigmatica II

Egg Shape Construction

Egg-Shaped Orbits of Non-Uniform Oscillators

Eggstravaganza

Eggs using Spherical Coordinates

Egyptian Fractions

Egyptian Multiplication

Ehrenfest's Double-Urn Game

Ehrenstein Contour Illusion

Ehrenstein Illusion

Eigenfunctions and Eigenvalues of the Airy Equation Using Spectral Methods

Eigenfunctions and Energies for Sloped-Bottom Square-Well Potential

Eigenfunctions for a Linear Potential Field

Eigenfunctions of a 1D Quantum System with Adjustable Potential

Eigenfunctions of the Helmholtz Equation in a Right Triangle

Eigenstates for a Hydrogen Atom Confined to an Infinite Spherical Potential Well

Eigenstates for Pöschl-Teller Potentials

Eigenstates for the Hulthen Potential

Eigenstates of the Quantum Harmonic Oscillator Using Spectral Methods

Eigensystems for Special Regions

Eigenvalue Plots of Certain Tridiagonal Matrices

Eigenvalue Problem for 2×2 Hermitian Matrices

Eigenvalues and Eigenfunctions for Angular Double-Well Potential

Eigenvalues and Eigenfunctions for the Harmonic Oscillator with Quartic, Sextic and Octic Perturbations

Eigenvalues and Linear Phase Portraits

Eigenvalues and the Principal Invariants of a Linear Map

Eigenvalues and the Trace-Determinant Plane of a Linear Map

Eigenvalues, Curvature, and Quadratic Forms

Eigenvalues for a Pure Quartic Oscillator

Eigenvalues of Cellular Automaton Matrices

Eigenvalues of Random Symmetric Matrices

Eigenvalue Unfolding in Spacing Distributions of Random Matrices

Eigenvectors by Hand

Eigenvectors in 2D

Eight Dodecahedra

Eight Icosahedra

Eight Queens Puzzle

Eight Spheres

Einstein-de Haas Effect

Einstein Rings from Light Flash at Black Hole

Einstein's Box

Einstein's Formula for Adding Velocities

Einstein's Most Excellent Proof

Einstein Solid

Eisenstein Integer

Eisenstein Snowflakes

Eisenstein Triples

Elapsed Time

Elastic Collision of Two Disks

Elastic Collision of Two Spheres

Elastic Collisions in Galilean Relativity

Elastic Collisions of Two Spheres

Elasticity and Slope with Linear Demand

Elasticity Function

Elasticity of Shear

Elasticity, Total Revenue, and the Linear Demand Curve

Elastic Properties of Diamond-Like Crystals

Elastic Recovery after Plastic Deformation of Metals

Electrical Conductivity of Silicon Semiconductors

Electrical Impedance of Biological Tissues

Electric and Magnetic Fields near a Transmission Line

Electric Current

Electric Dance: A Symmetrical Three-Body Coulombian System

Electric Dipole Potential

Electric Dipoles in a Constant Electric Field

Electric Field around a Charged Ring

Electric Field Generated by a Conducting Spherical Shell Enclosing a Charge

Electric Field Generated by Two Point Charges

Electric Field Lines Due to a Collection of Point Charges

Electric Field of a Dipole

Electric Field of a Line of Charge

Electric Field of a Point Charge

Electric Field of a Set of Random Point Sources

Electric Fields for Pairs of Cylinders or Spheres

Electric Fields for Three Point Charges

Electric Field Transmittance in a 1D Alternating Photonic Crystal

Electric Flux

Electricity Utility over Time

Electric Potential of a Metallic Cylinder Surrounded by a Dielectric in an External Static Electric Field

Electrochemical Impedance

Electrochemical Thin-Film Cyclic Voltammetry

Electrochemical Thin Layer Cells

Electrode-Solution Interface: Distribution of Ions around an Electrode

Electrodiffusion of Ions across a Neural Cell Membrane

Electromagnetic Doorbell

Electromagnetic Energy Density and Poynting Vector of a Relativistic Oscillator

Electromagnetic Field Energies in Capacitors and Inductors

Electromagnetic Fields For Hertzian Dipoles

Electromagnetic Fields in Wireless Power Transmission

Electromagnetic Induction in a Loop of Wire

Electromagnetic Ring Toss

Electromagnetic Wave

Electromagnetic Wave from Dipole over a Perfect Conductor

Electromagnetic Wave Incident on a Dielectric Boundary

Electromagnetic Wave Incident on a Perfect Conductor

Electromagnetic Wave Scattering by Conducting Sphere

Electromagnetic Waves from a Linear Antenna

Electromagnetic Waves in a Cylindrical Waveguide

Electromagnetic Waves in a Parallel-Plate Waveguide

Electromagnetic Waves in Optical Fibers

Electromagnet with Continuous Voltage Source

Electron Collision Model for 2D Spinning Particles

Electron Conductance Models Using Maximal Entropy Random Walks

Electron Configuration Browser

Electron Configurations and Atomic Radii for the Elements

Electronegativity and Bonding Type

Electronic Band Structure of Armchair and Zigzag Graphene Nanoribbons

Electronic Band Structure of a Single-Walled Carbon Nanotube by the Zone-Folding Method

Electronic Structure of 1D and 2D Quasiperiodic Systems

Electronic Structure of a Single-Walled Carbon Nanotube in Tight-Binding Wannier Representation

Electron in a Nanocrystal Modeled by a Quantum Particle in a Sphere

Electron Probability Distribution for the Hydrogen Atom

Electron Waves in Bohr Atom

Electrophilic Addition to Alkenes with Formation of Optical Isomers

Electrophilic Aromatic Substitution Reactions of Benzene

Electrostatic Bonding Forces between Atoms

Electrostatic Fields Using Conformal Mapping

Electrostatic Force between Charged Conducting Spheres

Electrostatic Orbits

Electrostatics of a Linear System of Three Charged Particles

Elementary CA Map Composition Diagram

Elementary CA Mapping Composition Fan

Elementary Cellular Automata Rules with Different Initial Conditions

Elementary Cellular Automata with Short Initial Condition

Elementary Cellular Automaton Dynamics as Wavelets

Elementary Cellular Automaton Egg

Elementary Cellular Automaton Process Visualization

Elementary Cellular Automaton Rules by Gray Code

Elementary Cellular Automaton with Network

Elementary Chess Endings: Mate in One

Elementary Model for Nuclear Fission Reactor

Elementary Nearest Ambidextrous Automata

Elementary Processes in Protein Folding

Elementary Propagation of a Wave

Elementary Transcendental Functions and Their Inverses

Elementary Transformations of a Sine Wave Quiz

Element Density Comparisons

Elements propres interactifs (French)

Elevator System

El Gordo

Eliminating Acetone in Air Using Absorption by Water

Elim Puzzle

Eller Puzzle

Ellipse and Friends

Ellipse by Paper Folding

Ellipse Representing the Confidence Region of a Covariance Matrix

Ellipse Rolling around a Circle

Ellipse Rolling around Another Ellipse

Ellipse Rolling inside a Circle

Ellipses and Hyperbolas with the Same Focal Points

Ellipsograph or Reciprocator

Ellipsoid

Elliptical Conic Section Using Dandelin Spheres

Elliptical Drive

Elliptical Polarization of Light Waves

Elliptical Spheres

Elliptical Torus

Elliptic Chords

Elliptic Curves on a Small Lattice

Elliptic Cylindrical Coordinates

Elliptic Epitrochoid

Elliptic Functions

Elliptic Gears

Elliptic Hyperboloid of One Sheet

Elliptic Hyperboloid of Two Sheets

Elliptic Paraboloid

Embeddings of Graphs in a Torus and in a Moebius Strip

Embroidery I: Honeycomb Lattice

Embryonic Cleavage

Emissive Power for a Blackbody over a Range of Wavelengths

Emoticon

Emotion Tiling

Empirical Characteristic Function

Empirical Graphs

Employer Health Insurance Choices under H.R.3590 and H.R.3962

Empty Focus Approximation to Kepler's Second Law

Emulating Land Use Evolution with a Cellular Automaton

Emulating Other Systems with Cellular Automata

Emulation of a Multicolor Turing Machine by a Two-Color Turing Machine

Emulation of a Register Machine by an Arithmetic System Rule

Emulation of Cellular Automata by Other Systems

Emulation of Elementary Cellular Automata by a Universal Cellular Automaton

Emulation of Turing Machines by Tag Systems and Register Machines

Enantiomorphs of the Truncated Icosahedron

Enclosing the Spectrum by Gershgorin-Type Sets

Encoding Structures into Graphs Using Cayley Graphs

Encrypted Secret Sharing

Encrypting with Double Transposition

Encryption of Messages

Encryption with Irrational Numbers and the One-Time Pad

Encryption with the Enigma Machine

End Behavior of Polynomial Functions

End Effector Trajectory Tracking for Planar Linkage

Endogeneity Bias

Endothermic Reaction in a Heated Batch Reactor

Endpoints Method for Predicting Chemical Degradation in Frozen Foods

Energies for a Heaviside-Lambda Potential Well

Energies for Particle in a Gaussian Potential Well

Energies of Helium Isoelectronic Series Using Perimetric Coordinates

Energy and Position Relationships in Simple Harmonic Motion

Energy and Power of Signals

Energy-Aware M^X/G/1 Queue

Energy Balance Model with Greenhouse Parameterization

Energy Balance on Pressurizing a Tank

Energy Density of a Magnetic Dipole

Energy Density of an Electrostatic Dipole

Energy Density of a Particle Moving at Uniform Speed

Energy Flow in a Negative-Index Material

Energy-Level Diagrams and Molecular Orbitals for Conjugated Polyenes

Energy Levels and Wavefunctions of Two Coupled Atomic Rings

Energy Levels in a Half-Infinite Linear Well

Energy Levels of a Morse Oscillator

Energy Levels of a Quantum Harmonic Oscillator in Second Quantization Formalism

Energy of a Slingshot: David and Goliath

Energy of a Standing Wave on a String

Energy of a Traveling Wave on a String

Energy Spectrum for a Finite Potential Well

Energy Transfer between Two Blackbodies

Engineering Drawings

Engineering Dynamics: Tip or Slip?

Engineering-Style Smith Chart

Enigmatic Comet Holmes

Enlargement in Two Dimensions

Enneper Surface

Enriching Oxygen in Air by Cross-Flow Membrane Permeation

Ensemble Control of Robots with Unicycle Kinematics

Ensemble Statistics for Periodic and Random Level Systems

Entangled Torus Coils

Entanglement between a Two-Level System and a Quantum Harmonic Oscillator

Enteral Nutritional Design

Enthalpy and Entropy Departure Functions for Gases

Enthalpy-Concentration Plot for a Benzene-Toluene Binary Mixture

Enthalpy-Entropy Diagram for Water

Enthalpy versus Composition Diagram for n-Hexane/n-Octane at 101 kPa

Entrainer Selection for Homogeneous Azeotropic Distillation

Entrepreneurial Calculation and the Interest Rate

Entropy Changes in Mixing Ideal Gases

Entropy of a Message Using Random Variables

Entropy of n-Fold Compositions of the Tent Map

Enumerating Cycles of a Directed Graph

Enumerating Pythagorean Triangles

Enumerating the Directed Graphs

Enumerating the Rational Numbers

Enumerating the Rationals

Envelope of Two Families of Plane Curves

Envelope Paradox

Enveloping the Oloid

Enzymatic Reaction in a Batch Reactor

Enzymatic Reactor with Product Inhibition

Enzyme Inhibition Kinetics

Enzyme Inhibition with Time Delay

Epicycles Revisited; Convexity of Lunar Orbit about the Sun

Epicycloid

Epicycloidal Ornaments

Epicycloids from an Envelope of Lines

Epidemic Spread and Transmission Network Dynamics

Epistasis in Genetics

Epitrochoids

EPOXI Spaceflight

Epsilon-Delta Definition of Limit

Equal-Area Parallelograms Using Determinants

Equal Areas

Equal but Opposite Percentage Changes Do Not Cancel

Equal Chords

Equal Cores and Shells in Circles and Spheres

Equal Incircles along a Line

Equality of a Segment and an Arc in Archimedes's Spiral

Equally Distant Chords

Equally Sized Mixed Flow Reactors in Series versus Plug Flow Reactor

Equally Spaced Multipoint Method for Numerical Differentiation

Equation of a Line Game

Equation of a Line in Vector Form 2D

Equation of a Plane

Equation of a Plane in Vector Form

Equation of Continuity

Equations for Valentines

Equations with Fractions

EquationTrekker

Equatorial Telescope Mounts

Equidecomposition of a Rhombohedron, Hexagonal Prism, and a Rhombic Dodecahedron

Equidistance and Betweenness in Euclidean Plane Geometry

Equilateral Triangles in 3D with Integer Coordinates

Equilateral Triangles That Form a Star

Equilateral Triangle to Square

Equilibrio parcial y estática comparativa (Spanish)

Equilibrium Catch in Commercial Fishing

Equilibrium Conversion by Gibbs Minimization

Equilibrium of a Floating Vessel

Equilibrium of a Rigid Bar

Equilibrium of a Suspended Mobile

Equilibrium Water Activity of Binary Dry Mixtures

Equine Motion

Equivalence Classes Modulo m

Equivalence of Linear and Circular Convolutions

Equivalence of Projections in Involutive Rings

Equivalence of Three Catalan Number Interpretations

Equivalence of Two Fibonacci Number Interpretations

Equivalent Forces Due to Hydrostatic Pressure on a Dam

Equivalential Calculus

Equivalential Formula

Equivalent Isothermal Time at a Reference Temperature as a Function of Time

Equivalent Length of a Pipe with Fittings and Valves

Equivalent Products of Integers

Eratosthenes's Measure of the Earth's Circumference

Erdös-Szekeres Tableaux

Erlang B and Telephony

Erosion Index for Particulates

Error-Diffusion Dither Patterns

Escape to Infinity

Escher's Method Applied to Created Celtic Designs

Escher Solid as a Puzzle

Esser's Heart Surface

Estimate Derivative

Estimating a Centered Matérn (1) Process: Three Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers

Estimating a Centered Ornstein-Uhlenbeck Process under Measurement Errors

Estimating a Distribution Function Subject to a Stochastic Order Restriction

Estimating and Diagnostic Checking in Censored Normal Random Samples

Estimating Cohesion and Tensile Strength of Compacted Powders

Estimating Conditional Expectations with Monte Carlo Simulation and Least Squares Regression

Estimating Equilibrium Moisture Content

Estimating Fluid Temperature for Contraction of a Metal Cylinder

Estimating Insurance Premiums Using Exceedance Data and the Method of Moments

Estimating Kinetic Parameters from a Batch Reactor Experiment

Estimating Loss Functions Using Exceedance Data and the Method of Moments

Estimating Percentages

Estimating Perimeter and Area of Simple Polygons

Estimating Planetary Perihelion Precession

Estimating Processing Times in a Row of Storage Tanks

Estimating Relative Volatility from Batch Distillation Data

Estimating the Contraction of a Cooled Cylinder Assuming a Constant Coefficient of Thermal Expansion

Estimating the Feigenbaum Constant from a One-Parameter Scaling Law

Estimating the Local Mean Function

Estimating the Side Length of a Square from Its Area

Estimating the Size of a Population

Estimating the Surface Area and Volume of a Rectangular Prism

Estimating the Thermal Properties of Foods from Their Moisture Contents

Estimating the Time between Mishaps from Quality Control Data

Estimation of Time to Excessive Microbial Count

Estimators of a Noisy Centered Ornstein-Uhlenbeck Process and Its Noise Variance

Ethane Pyrolysis in a Tubular Reactor

Ethylene Glycol Synthesis with a Reactive Distillation Unit

Euclid 1.47 Animated

Euclid, Book 3, Proposition 22

Euclidean Algorithm

Euclidean Algorithm, GCD and LCM

Euclidean Algorithm in the Ring of Algebraic Integers Generated by the Square Root of Five

Euclidean Algorithm Steps

Euclid's Construction of a Regular Dodecahedron (XIII.17)

Euclid's Construction of a Regular Icosahedron (XIII.16)

Euclid's Construction of a Regular Octahedron (XIII.14)

Euclid's Formula and Properties of Pythagorean Triples

Euclid's Proof of the Pythagorean Theorem

Euler Angles

Euler Angles for Space Shuttle

Euler Angles: Precession, Nutation, and Spin

Euler Circles for Categorical Syllogisms

Eulerian Numbers versus Stirling Numbers of the First Kind

Eulerian Tour and Cycle Decomposition

Euler Line

Euler-Maclaurin Summation Formula

Euler Product for the Zeta Function

Euler's Distribution Theorem

Euler's Estimate of Pi

Euler's Generating Function for the Partition Numbers

Euler's Identity

Euler's Method for Solving Linear Diophantine Equations

Euler's Method for the Exponential Function

Euler's Polyhedral Formula

Euler's Rotation Theorem

Euler's Substitutions for the Integral of a Particular Function

Euler's Theorem for Pedal Triangles

Euler's Triangle Formula

Euler Transformation

Euler Zigzag Numbers

European Binomial Option Pricing with Nonconstant Volatility

European Option Greeks

European Option Prices and Greeks in 3D

Europe Vote Exponent

Evaluate Hot Pizza

Evaporation of Water from a Pool or Pond

Evaporation of Water from a Wet T-Shirt

Evaporative Cooling of Water

Evaporative Crystallization with Recycle

Even and Odd Functions

Evens and Odds

Event-by-Event Simulation of Double-Slit Experiments with Single Photons

Event-by-Event Simulation of the Mach-Zehnder Interferometer

Everything about Gell-Mann Matrices (Part 1): Unary Operations

Everything about Gell-Mann Matrices (Part 2): Binary Operations

Evidentiary Uncertainty

Evolutes of Some Basic Curves

Evolutionary Multiobjective Optimization

Evolutionary Prisoner's Dilemma Tournaments

Evolution in a Cellular-Automaton Model of Gray-Scott Reaction-Diffusion System

Evolution of a Gaussian Wave Packet

Evolution of Matter from a Quark-Gluon Plasma

Evolution of Monomer Sequence Distribution in Polymer Analogous Reaction

Evolution of Rotating Substitution Systems in 3D

Evolution of the Fertility, Life Expectancy, and Population in Different Parts of World

Exact and Approximate Calculations of Acid-Base Equilibria

Exact and Approximate Relativistic Corrections to the Orbital Precession of Mercury

Exact and Variational Energies for the Hydrogen Molecular Ion and the Helium Hydride Ion

Exact Confidence Intervals for a Single Proportion

Exact Coordinates of Golden Rhombic Solids

Exact Numerical Solutions for the Stepped-Infinite-Square Well

Exact Recurrent Computations with Integers

Exact Solution for Rectangular Double-Well Potential

Exact Solutions of the Schrödinger Equation for Pseudoharmonic Potential

Exact Solutions of the Schrödinger Equation for the Kratzer Potential

Exact Sphere Representations over Platonic Solids Based on Rational Multisided Bézier Patches

Exact Trilinear Coordinates

Exact Trilinear Coordinates and the Brocard Axis

Exact Trilinear Coordinates and the Euler Line

Exact Trilinear Coordinates and the Pedal Triangle

Exact Values for Sine and Cosine

Exact Values of Trigonometric Functions for Given Angles

Example of a Ring with an Improper Involution

Examples of 1D Three-Color Totalistic Cellular Automata

Examples of 2D Harmonic Functions

Examples of Abelian Groups

Examples of Asymptotes in 2D and 3D

Examples of Finding Asymptotes

Examples of Fourier Series

Examples of Limits of Real Sequences

Examples of Zindler Curves

Excavator

Excavator Operator

Excess Enthalpy and Heat Capacity for an Ethanol-Water Mixture

Exchange Networks

Excising Edges from Cubic Graphs

Exercises in Limits from Above and Below

Exit Times of Brownian Motion in 3D

Exothermic Continuous Stirred-Tank Reactor with Dynamically Varying Cooling Jacket

Expandable Flat Ring

Expanded Fermi Solution for Estimating a Complaint's Probability

Expanded Fermi Solution for Risk Assessment

Expanded Fermi Solutions in Pathogens' Dose-Response Curves

Expanded Fermi Solution to Retrodict the Initial from the Final Number in a Stochastic Process

Expanded Magnitude Estimation Method

Expanding a Rhombic Dodecahedron 5-Compound to a Rhombic Enneacontahedron

Expanding a Set of Possibilities

Expanding Ball of 30 Octahedra

Expanding Cube

Expanding Surface Structure

Expanding Tetrahedral Network

Expanding Triangles Art

Expansion and Divergence

Expansion of a Polynomial

Expatriate Income Tax in China

Expectation Maximization for Gaussian Mixture Distributions

Expectations for Roulette

Expected Dynamics of an Imitation Model in 2x2 Symmetric Games

Expected Dynamics of an Imitation Model in the Hawk-Dove Game

Expected Dynamics of an Intra-Population Imitation Model for Inter-Population 2x2 Symmetric Games

Expected Dynamics of an Intra-Population Imitation Model in the Two-Population Hawk-Dove Game

Expected Motion in 2x2 Symmetric Games Played by Reinforcement Learners

Expected Number in Queue and System for an M/M/S Queue

Expected Returns of the Dow Industrials, Beta Model

Expected Returns of the Dow Industrials, Fama-French Model

Expected Time in System for M/G/1 Queue

Expected Utility: Optimal Asset Investment

Expected Utility: Optimal Insurance

Experimenting with Sums of Primitive Roots of Unity

Experimenting with the Ulam Spiral

Experiment on Heat Conduction

Experiment Verifying Charles's Law

Expert System for Identifying Pedigree Dogs

Explaining Real Estate Price Bubbles

Exploration of Fluid Meandering by Statistical Simulation

Exploration versus Consumption

Exploratory Factor Analysis

Explore Polyhedra

Exploring a Logo by Grignani

Exploring Cylindrical Coordinates

Exploring Measures of Association

Exploring Minimal Models of the Complexity of Security Prices

Exploring Multivariate Data

Exploring Musical Tuning and Temperament

Exploring Polar Graphs

Exploring Relations on Sets

Exploring Robustness of Mean-Difference Confidence Intervals

Exploring Skewness in Box Plots

Exploring Social Choice Theory

Exploring Spherical Coordinates

Exploring Surface Curvature and Differentials

Exploring the Black-Scholes Formula

Exploring the Botany of Waxflowers with Wolfram Language Fancy GUIs

Exploring the Crease Length Problem

Exploring the Event Horizon Shadow of a Black Hole

Exploring the Grand Canyon

Exploring the Mercedes-Benz Logo

Exploring the Reyflex Textilien Logo

Exploring the Tails of the Normal Distribution

Exploring the Tate Logo

Exploring the Times Table

Exploring Unicode Space

Exploring with Inset

Explosion Effects in 3D

Exponential Allowance Riddle

Exponential Congruences

Exponential Decay

Exponential Generating Functions

Exponential Model for Arrhenius Activation Energy

Exponential Model for Population Growth

Exponents

Expression Machine

Expressions Involving the Roots of a Quadratic

Expression Trees for Integrals

Extendable Circular Table

Extendable Fence

Extendable Frame

Extendable Shelter

Extendable Tower

Extend Dodecahedron Edges

Extended Bead-Sort

Extended Discrete Green's Theorem

Extended Euclidean Algorithm

Extended Four-Bug Problem

Extended GCD of Quadratic Integers

Extended Graetz Problem

Extend Icosahedron Edges

Extending Rosser's Theorem

Extending the Rationals with the Square Root of Five

Extending the Square Root Growth Rate Model to Lethal Low Temperatures

Exterior Tangents to Three Circles

External Ballistics of Rifle Bullets

Extra Accuracy Using Diagonal Lines

Extracting a Spherical Sector

Extracting Fixed-Order Degradation Kinetics by the Endpoints Method

Extracting Microbial Inactivation Parameters from Final Isothermal Survival Ratios

Extracting Microbial Inactivation Parameters from Final Survival Ratios

Extracting Pi from Image Data

Extraction of Acetic Acid from Water Using Isopropyl Ether

Extractive Distillation Column to Separate Isopropyl Alcohol from Water

Extractive Distillation of an Azeotropic Mixture of Isopropyl Alcohol and Water: Effect of Entrainer Feed Temperature

Extractive Distillation of an Equimolar Acetone-Methanol Mixture Using Water

Extremal Trigonometric Polynomials

Extreme Value Forecasting

Extreme Value Theorem

Eyeball and Two Muscles

Eyeball Theorem

Eye Parameters (Visual Depth Perception 6)

Eyring-Polanyi versus Exponential Model for Chemical Reactions

Fabry-Perot Interferometer

Fabry-Pérot Interferometer and Rings

Face Recognition Using the Eigenface Algorithm

Faces of the Regular Icosahedron and Five Regular Tetrahedra

Factorial

Factorial Digits

Factorial Number Base

Factoring an Integer

Factoring Binomials

Factoring Gaussian Integers

Factoring Polynomials over Various Rings

Factoring Real Numbers

Factoring the Even Trigonometric Polynomials of A269254

Factoring the Sphenic Numbers

Factoring Time

Factorizing Mersenne Numbers

Factors Affecting Blood Flow

Factor Trees

Factory for Frac-tiles of Order Four

Fagnano's Problem

Failure Probabilities from Quality Control Charts

Fair, Equitable Compensation Arrangements

Faire rouler un verre (French)

Fair Sharing of an Equilateral Triangular Pizza

Falling Body with Zero, Linear, or Quadratic Air Resistance

Falling Cat

Falling Chimney

Falling Cylindrical Magnet in Conducting Tube

Falling Mass Attached to a Rigid Pulley

Falling Stick

False Logarithm Series

Families of Figure-Eight Curves

Families of Four-Point Touching Equilateral Triangles

Families of Four-Point Touching Isosceles Triangles

Families of Four-Point Touching Squares

Families of Newtonian Periodic Planar Three-Body Orbits

Families of Solutions for ODEs

Families of Two-Point Touching Squares

Family of Curves, Tangents, and Intuition

Family of Plane Curves in the Extended Gauss Plane Generated by One Function

Fanning Friction Factor for Smooth and Rough Pipes

Fano Resonance

Faraday Cage

Faraday Disk Dynamo

Farey Sequence

Farey Tree

Farkas's Lemma in Two Dimensions

Farmer Jim's Decision Problem: Growing Wheat or Barley

Farris Wheels

Fastening Mechanism Using a Rocker

Faster on Interstate or Local Roads?

Fate of a Long-Term Index Fund Investment According to the S&P 500

Fate of the Euler Line and the Nine-Point Circle on the Sphere

Fault-Free Tilings

Faustmann's Rule of Optimal Rotation

Feasible Regions for Product Compositions in Ternary Mixtures

Features of a Polar Zonohedron

Fed-Batch Fermentation

Fed-Batch Fermentation and Quasi-steady State

Feedback Control in an Activated Sludge Reactor

Feedback Control in a Stirred-Tank Reactor

Feedback Control of Cellular Concentration in a Continuous Bioreactor (Turbidostat)

Feedback Sensor Design for a Cantilevered Three-Layer Sandwich Beam

Feedforward and Feedback Control in Neural Networks

Feed Stages in a Distillation Column

Feigenbaum's Scaling Law for the Logistic Map

Feigenbaum's Scaling Relation for Superstable Parameter Values: "Bifurcation Diagram Helper"

Feinberg-Horn-Jackson Graph

Fender Tone Circuit

Fenómeno de Difusión-Reacción en una partícula catalítica (Spanish)

Fermat Point

Fermat Point for Many Points

Fermat's 4n+1 Theorem and the n Queens Problem

Fermat's Last Theorem and Lattice Points

Fermat's Little Theorem

Fermat's Magic Cube

Fermat's Principle and Snell's Law

Fermat's Theorem on Stationary Points

Fermat-Weber Point of a Polygonal Chain

Fermi-Dirac Distributions for Free Electrons in Metals

Fern Fractals

Ferrers Diagrams

Feuerbach's Theorem

Feynman Amplitude and Scattering Cross-Section for a Toy Theory

Feynman's Relativistic Electrodynamics Paradox

Feynman's Wobbling Plate

Fibonacci and Padovan Spiral Identities

Fibonacci Determinants

Fibonacci Mountain Matra Meru

Fibonacci Numbers and the Golden Ratio

Fibonacci Numbers Count Domino Tilings

Fibonacci Rabbits

Fibonacci Residues are Periodic

Fibonacci Time

Fibonacci Tree

Fick's Law Applied to Pulmonary Fibrosis

Fields and Poynting Vector around a Transformer

Fields of Magnet Array

Fifteen Great Circles on a Sphere

Fifty-Nine Icosahedra

Filamentation

Filling a Container Defined by a Curve

Filling a Cube Seven Parts at a Time

Filling a Regular Icosahedron with Infinitely Many Golden Octahedra

Filling a Rhombic Hexecontahedron

Filling a Sierpinski Tetrahedron with Octahedra

Filling a Square with Random Disks

Filling a Tetrahedron with Infinitely Many Octahedra

Filling Cone, Hemisphere and Cylinder: Easy as 1:2:3

Filling Space with a Bilinski Dodecahedron and an Acute Golden Rhombohedron

Filling Space with Tetrahedra and Half-Size Octahedra

Filling the Gaps in Mendeleev's Periodic Table

Filtering a White-Noise Sequence

Filtering Images in the Frequency Domain

Filtering Using Common Value

Financial Engineering of a Bond

Find a Formula for Pi

Find a Maximum Matching in a Bipartite Graph

Find a Model for a Set of Propositions

Find a Solid that Matches the Net

Find Bridging Edges in Networks

Finding an Inverse

Finding a Pattern (Linear Equations)

Finding a Tangent Line to a Parabola

Finding Cliques in Networks

Finding Comparative Advantage

Finding Maxima and Minima for the Lorenz Attractor

Finding Probabilities for Intervals of a Normal Distribution

Finding Real-Number Approximants by Direct Methods

Finding Roots Using Binary or Interpolation Search

Finding Segments of an Image by Filtering Its Distance Transform

Finding Strange Attractors of Iterated Maps

Finding Strings of Digits in the Decimal Digits of Famous Numbers

Finding the Area of a 3D Surface with Parallelograms

Finding the Global Minimum of a Function Using Simulated Annealing

Finding the Greatest Common Divisor of Two Numbers by Factoring

Finding the Least Common Multiple of Two Numbers by Factoring

Finding the Linear Function Rule

Finding the Minimum Reflux Ratio Using the Underwood Equations

Finding the Shortest Traveling Salesman Tour

Finding the Vanishing Points of Sample Images

Find the Angle Measure in a Regular Polygon

Find the Angle Measure in a Regular Polygon, Part 2

Find the Angle Whose Sine is the Product of the Sine and Cosine of Two Other Angles

Find the Coefficients of a Partial Fraction Decomposition

Find the Exact Value of an Angle

Find the Fake Coin

Find the Number of Cubes Removed

Find the Opposite Face

Find the Total Variation of a Function

Find Your Name in Pi

Fingerprints of Electronic Files: Performance Tests

Fingerprints of Electronic Files: Precision Tests

Fingerspelling Sign Language Using a Hand Model

Finite Difference Approximations of the First Derivative of a Function

Finite Difference Scheme for the Heat Equation

Finite Difference Schemes of One Variable

Finite-Difference Time-Domain Algorithm for Scattering from Plane-Wave Source

Finite Element Solution of 1D Poisson Equation with Galerkin Spectral Decomposition

Finite Field Tables

Finite Limit at a Finite Point

Finite Limit at Infinity

Finite Lyapunov Exponent for Generalized Logistic Maps with z-Unimodality

Finite Potential Well

Finite-State, Discrete-Time Markov Chains

Finsler-Hadwiger Theorem

Fireworks

Fireworks with Regular Polygon and Circle Points

Firm Costs Optimization Problem in Primal and Dual Form

Firm with Two Plants

First and Second Derivatives of a Periodic Function Using Discrete Fourier Transforms

First- and Second-Order Transfer Functions

First Droz-Farny Circle

First Fermat Point and Isogonic Center of a Triangle

First-Order Logic Test

First-Order Solution to Glass-Ice Stefan Problem

First-Order Transfer Functions in Process Control

First Puzzle

Fiscal Policy Based on Aggregate Demand

Fisher Discriminant Analysis

Fisher-Kolmogoroff Equation

Fisher-Tippett-Gnedenko Theorem: Generalizing Three Types of Extreme Value Distributions

Fishing with Long Line or Gill Net?

Fish-in-Pond Simulation

Fit, Interpolation, or Polynomial Interpolation in Uncertain Calculus

Fitness Model for Gene Frequency in Populations

Fit of First-Order Kinetic Model in Degradation Processes

Fitting a Curve to Five Points

Fitting an Elephant

Fitting an Ellipse to the Orbit of a Star near the Galactic Center

Fitting a Powered Exponential Autocorrelation: Alternatives to Maximum Likelihood via Conjugate Gradient Linear Solvers

Fitting Data to a Lognormal Distribution

Fitting Lifetime Data to a Weibull Model

Fitting Noisy Data

Fitting Primes to a Linear Model

Fitting the Meixner Distribution to S&P 500 Returns

Fitting Times-to-Failure to a Weibull Distribution

Five-Bar Linkage Model of the Bicycle-Rider System

Five Circles and the Golden Ratio

Five Circles Theorem

Five Concyclic Points in a Triangle

Five Definitions of Strain for Large Deformations

Five Famous Fractals

Five-Gear Manual Transmission

Five-Mode Truncation of the Navier-Stokes Equations

Five-Neighbor 2D Totalistic Cellular Automata

Five-Neighbor Two-Color Outer Totalistic 2D Cellular Automaton

Five Points Determine a Conic Section

Five-Speed Transmission: RPM versus MPH

Five-Squares-to-One Dissection

Five Toroidal Polyhedra and Their Nets

Fixation and Distraction (Visual Depth Perception 5)

Fixed Point Elementary Rules

Fixed Point of a 2x2 Linear System of ODEs

Fixing a Fixed Point

Fizeau Wheel

Flash, Bang, Thwack

Flash Calculations Using the Peng Robinson Equation of State

Flash Distillation Cascade for a Benzene-Toluene Mixture

Flash Distillation Cascade for an Acetone-Chloroform Mixture

Flash Distillation Cascade for an Ethyl Acetate-Ethanol Mixture

Flash Distillation Cascade in a Constant Relative Volatility Mixture

Flash Distillation of a Benzene, Toluene, p-Xylene Mixture

Flash Distillation of a Constant Relative Volatility Mixture

Flash Distillation of a Mixture of Four Hydrocarbons

Flash Vaporization of a Heptane-Octane Mixture

Fleeting Random Question Marks

Flett's Theorem

Flexible Frame

Flexible Galton Board

Flexing a Polyhedral Periscope

Flexing Petrie's Honeycombs

Flicker Colors

Flight of a Glider

Flight of a Golf Ball

Flight Profiles of Estes Alpha Model Rocket

Flight through a Star Cluster

Flip Bifurcation in Dynamical Systems

Flipping between Two Elementary Cellular Automaton Rules

Floating Ball

Floating Disk Stereogram

Floating Random Walk Solution to the Dirichlet Problem

Floating Sphere

Floating Wave Energy Converter

Floor, Ceiling, and Round

Floppy Cube

Flor con la función seno (Spanish)

Flory-Huggins Model for Gibbs Free Energy of Mixing in Polymer Solutions

Flow around a Sphere at Finite Reynolds Number by Galerkin Method

Flow Curves of a Herschel-Bulkley Fluid

Flower and Seed Spirals

Flower Around a Limit Point

Flower Fractals

Flower-like Parametric Plots

Flower-Like Polar Plots

Flower Petals Using Parametric Equations

Flow from a Tank at Constant Height

Flow in a Rectangular Channel with Double Orthogonal Collocation

Flow in a Vertical Channel with Walls at Different Temperatures

Flow of a Carreau Fluid in a Circular Tube

Flow of a Vector Field in 2D

Flow of Fluid through a Hole in a Tank

Flow of Liquid through a Hole

Flow of Pi, E, Gamma, and Phi

Flowsnake Q-Function

Flow through an Open Channel

Flow Through a Rectangular Duct

Flow through Chamfered Ducts

Flow Time in an Hourglass

Fluid Flow around a Corner

Fluid Pressure

Fluid Rotating in a Cylinder

Fluids in the Critical Region

Fluid Velocity in Rigid Body Rotation and Irrotational Flow

Fluorescence Analysis Tool for Bio-Imaging

Flux

Fluxes and Energetics of Photosynthesis and Photorespiration

Flying a Box Kite

Flying Saucer Builder

Flying Spaceship Game

Flying to the Moon

Foam Bubbles Simulating Voronoi Diagrams

Focal Attraction with Rotation

Focus and Directrix in a Quadratic Bézier Curve

Focus-Directrix Property of an Ellipse with Dandelin Spheres

Foldable Frame

Foldable Frame on a Telescopic Lift

Foldable Panel

Fold and Twist Algorithm for Some Regular n-Gons

Folding a 2×n Sheet of Labeled Stamps

Folding a Dissection of a 1-by-3 Rectangle into a Cube

Folding a Mitre into a Gnomon

Folding and Unfolding Polar Zonohedra

Folding and Unfolding Polyhedral Nets

Folding an Equilateral Triangle in a Square

Folding a Net into an Octahedron Or Two Tetrahedra

Folding an Octahedron from Squares

Folding a Rectangle into an Envelope

Folding a Strip into a Pentagon

Folding a Strip of Labeled Stamps

Folding a Strip of Paper to Make an n-Gon

Folding a Strip of Unlabeled Stamps

Folding a Strip to Converge to an Equilateral Triangle

Folding a Strip to Form Regular Odd n-Gons

Folding a Tabbed Net into a Cube

Folding a Trapezoid into a Rectangle

Folding a Trapezoid into Two Different Rectangles

Folding a Triangular Net into a Boat

Folding Cosine in the Complex Plane

Folding Cowley's Dodecarhombus Net

Folding Dürer's Partial Net

Folding Hexagons

Folding Ladder

Folding Nets for Some Golden Rhombic Solids

Folding Nets into Polyhedra

Folding Nets of Polyhedra with Subdivided Faces

Folding Polygonal Nets into Polyhedra

Folding Up a Truncated Icosahedron

Following Chaotic Reflections

Fonction de répartition (French)

Fonctions affines (French)

Font Explorer

Font Polygon

Food Calories

Food Color Comparisons

Food Preservation Hurdle Technology

Food Searching Model for Ants

Food Webs

Force Balance on a Moving Cart

Force Balances on a Truss

Forced Convection for Internal Laminar Flow

Forced Nonlinear Oscillator

Forced Oscillations

Forced Oscillations of a Damped Oscillator

Forced Oscillator with Damping

Forced Pendulums with Damping

Force on a Thrust Reverser

Forces Acting on a Ladder

Forces and Drafts in Flat Rolling

Forces Exerted on an Immersed Object

Forces in a Power Tower Truss

Forces on a Bouncing Ball

Forces on a Completely Submerged Gate

Forces on a Partially Submerged Gate

Forces on a Pendulum

Forces on a Roller Coaster

Forces on Massive Parallel Wires Carrying Equal Currents

Force to Overcome Vacuum Pull

Ford Circles

Ford Circles with Variable Radii

Forecasting with Exponential Moving Averages

Foreclosure Regimes

Forest Fire Simulation Using a Randomized Hexagonal Automaton

Forest of Points

Forgetful Burglar

Forming a Klein Bottle

Forming the Efficient Frontier When Returns Are Non-Normal

Forms for Syllogisms

Formula for 3D Rotation

Formula Generator

Formulas and Structures for Some Simple Molecules

Fortescue's Theorem for a Three-Phase Unbalanced System

Fortune's Algorithm for Voronoi Diagrams

Forward and Inverse Kinematics for Two-Link Arm

Forward and Inverse Kinematics of the SCARA Robot

Forward Kinematics

Forward Kinematics of Humanoid Robots

Forward Problem Solved with GeoDestination

Foucault's Pendulum

Four-Bar Linkage

Four Bug Problem

Four Collinear Points Related to the Altitudes

Four-Coloring Planar Graphs

Four-Coloring Real Maps

Four-Color Maps

Four-Color Outer Median Cellular Automata in 1D

Four-Color Outer Median Cellular Automata on Graphs

Four-Color Outer Median Cellular Automata on the Grid

Four Concurrent Lines in a Cyclic Quadrilateral

Four Concyclic Points

Four Dividable Rhombohedra

Four Dragon Curves

Fourfold Triacontahedron

Four General Unfoldings of a Cube

Four Hypergeometric Lattice Walks

Four Icosahedra around a Tetrahedron

Fourier Coefficients of a Square Pulse

Fourier Construction of Regular Polygons and Star Polygons

Fourier Descriptors

Fourier Power Spectrum as a Measure of Line Jaggedness

Fourier-Series Approximation of a Square Wave

Fourier Series Approximations to Roots of Unity

Fourier Series Approximation to Equilateral Triangle

Fourier Series Coefficients of a Rectangular Pulse Signal

Fourier Series for Three Periodic Functions

Fourier Series of Simple Functions

Fourier Sound Synthesis

Fourier Synthesis for Selected Waveforms

Fourier Transform of Radially Symmetric Potential Functions

Fourier Transform Pairs

Fourier Transforms of Cellular Automaton Images

Fourier View of an Outer Totalistic Three-Color Cellular Automaton

Four in a Row

Four Interwoven Triangles

Four Introductory Examples of Two-Dimensional Vector Fields

Four Kinds of Rhombic Polyhedra

Four Lines and Four Circumcircles

Four Nested Archimedean Solids

Four Octahedron-Tetrahedron Compounds around a Tetrahedron

Four-Piece Dissection of Hill's Tetrahedron of Type 2 into a Triangular Prism

Four-Piece Dissection of Juel's Pyramid to a Prism

Four-Point Parabolas

Four Points Determine a Sphere

Four Polyhedra, Each with an Unfolding that Overlaps Itself

Four Rows of Cans

Four-Set Venn Diagram Game

Four Space Curves

Four Theorems on Spherical Triangles

Four-Variable Karnaugh Map

Four Visual Proofs of a Theorem about a Regular Nonagon

Fractal Blades

Fractal Cellular Textures

Fractal Creation with Iterated Function Systems

Fractal Curves

Fractal Curves Generated by Fourier Series

Fractal Curves Generated by the Sum-of-Digits Function

Fractal Dimension versus Time Complexity in Turing Machines

Fractal Ir-rep-tiles of Order Two

Fractalizing Polygons

Fractal Maze

Fractal Octahedra I

Fractal Patterns from a Substitution Blueprint

Fractal Polygon Tiler

Fractal Popcorn

Fractal Reflection of Circle Configurations

Fractal Right Triangle

Fractal Robot Arm

Fractals and Their Hausdorff Dimension

Fractals Generated by Jacobi Theta Functions

Fractals Generated by Multiple Reflections of Circles

Fractals Generated by the Weierstrass P Function

Fractal Tetrahedra (Mitsubishi Logo in 3D)

Fractal Tetrahedron

Fractal Tetrahedron in an Octahedron

Fractal Trees

Fractional Derivative of a Power

Fractional Derivative of Sine

Fractional Differintegrals of Several Functions

Fractional Fourier Transform

Fractional Gaussian Noise

Fractional Graphs and Flowers

Fractional Ornstein-Uhlenbeck Process

Fractional Parts of Powers of Numbers

Fractional Parts of Powers of Rationals

Fractional Rheological Constitutive Equations

Fraction Blocks

Fraction of a Circle Covered by Arcs of a Given Length

Fractions

Fractions and Slopes

Fractions in Different Bases

Fraction Tree and Continued Fractions

Fracture Element in Rheological Models

Frame for a Deployable Shelter

Framing a Rhombic Dodecahedron with Regular Octahedra

Franck-Condon Principle in Vibronic Transitions

Franck-Hertz Experiment

Franklin's Point Inclusion in Polygon (PNPOLY) Algorithm

Fraunhofer Diffraction at a Single Slit

Fraunhofer Diffraction at Multiple Slits

Fraunhofer Diffraction at One Slit

Fraunhofer Diffraction (Double Slit)

Fraunhofer Diffraction through a Rectangular Aperture

Fraunhofer Diffraction Using a Fast Fourier Transform

Frederickson's Dissection of an Octagon to Five Octagons

Frederickson's Dissection of a Regular Dodecagon into Two Congruent Regular Dodecagons

Frederickson's Hinged Dissection of Five Decagons to One

Frederickson's Second Dissection of an Octagon to Five Octagons

Free Convection past an Isothermal Vertical Plate

Free-Electron Model for Linear Polyenes

Free Energy Changes in Homogeneous Nucleation

Free Fall on the Solar System Planets and the Moon

Free Fall with Terminal Velocity

Free-Flow Leakage from Landfill Geomembrane Defects

Free Modules for Balancing Abstract Chemical Equations

Free Precession of a Rotating Rigid Body

Free Response in a Second-Order System

Free Rotation of an Asymmetric Top

Free Rotation of a Rigid Body: Poinsot Constructions

Freese's Dissection of a Dodecagram into a Hexagram

Freese's Dissection of a Hexagram into Four Hexagrams

Freese's Dissection of a Hexagram into Three Congruent Hexagrams

Freese's Dissection of a Regular Decagon into Five

Freese's Dissection of a Regular Dodecagon into 12

Freese's Dissection of a Regular Dodecagon into an Isosceles Right Triangle

Freese's Dissection of a Regular Dodecagon into a Regular Hexagon and the Reverse

Freese's Dissection of a Regular Dodecagon into a Square

Freese's Dissection of a Regular Dodecagon into Four Regular Dodecagons

Freese's Dissection of a Regular Dodecagon into Six Squares

Freese's Dissection of a Regular Dodecagon into Three

Freese's Dissection of a Regular Dodecagon into Three Congruent Squares

Freese's Dissection of a Regular Dodecagon into Two Equilateral Triangles

Freese's Dissection of a Regular Dodecagon into Two Squares

Freese's Dissection of a Regular Hexagon into a Square and an Equilateral Triangle

Freese's Dissection of a Regular Hexagon into Seven Hexagons

Freese's Dissection of a Regular Hexagon into Three

Freese's Dissection of a Regular Hexagon into Two Congruent Regular Hexagons

Freese's Dissection of a Regular Nonagon into Two

Freese's Dissection of a Regular Octagon into Four

Freese's Dissection of a Regular Octagon into Nine

Freese's Dissection of a Regular Octagon to Eight Congruent Regular Octagons

Freese's Dissection of a Regular Pentadecagon into Two

Freese's Dissection of a Regular Pentagon into Two Smaller Ones

Freese's Dissection of a Regular Pentagon to a Square

Freese's Dissection of a Regular Starlike Nonagram into Three Equilateral Triangles

Freese's Dissection of Four Equilateral Triangles into One

Freese's Dissection of Four Regular Dodecagons into a Square

Freese's Dissection of Three Squares into Four Regular Dodecagons

Freese's Dissection of Two Regular Dodecagons into a Square

Freese's Dissection of Two Regular Dodecagons into Three Squares

Freese's Dissection of Two Regular Pentagons into a Square

Freese's Two Dissections of a Regular Pentagon into Five

Freese's Two-Octagons-into-One Dissection

Free Surface next to a Wet Wall

Free Vibrations of a Spring-Mass-Damper System

Freezing of Water around a Heat Sink

Freezing Point Depression: How Much Salt Will Melt Ice?

Frenet Frame

Frenkel-Kontorova-Tomlinson Model for Sliding Friction

Frequencies of Character Pairs

Frequencies of Digits of Square Roots

Frequency and Impulse Response of Linear Filters

Frequency Chord Projection

Frequency Distribution of the Logistic Map

Frequency-Filtered Random Noise

Frequency-Modulated Continuous-Wave (FMCW) Radar

Frequency of Cellular Automata

Frequency Response of an LCR Circuit

Frequency Spectrum of a Noisy Signal

Frequency Spectrum of a Step of a Substitution System

Frequentist versus Bayesian PDF for Binary Decisions Like Coin Tossing, OSHA Compliance, and Jury Trials

Fresnel Coefficients of Metals

Fresnel Diffraction at an Edge

Fresnel Diffraction at a Single Slit

Fresnel Equations

Frictional Force on a Car in a Turn

Frictional Pressure Drop in a Pipe

Frieze Designer for Kindergarten

Frieze Functions

Friezes from Function Graphs

Frobenius Equation in Two Variables

Frog Jumping Problem

From Bohm to Classical Trajectories in a Hydrogen Atom

From Circle to Sine and Cosine Curves with Angle in Degrees

From Continuous- to Discrete-Time Fourier Transform by Sampling Method

From Images to Graphs: Morphological Graphs

From Quadrophony to Octophony

From the Tether Problem to the Involute of a Circle

From Vector to Line

From Vector to Plane

Fry's Geometric Demonstration of the Sum of Cubes

Fuel Break

Fuel Consumption Calculator

Fugacities in a Can of Soda

Fugacities in an Ideal Binary Mixture

Fugacity as a Driving Force for Mass Transfer

Fugacity Dependence on Pressure in an Ideal Binary Mixture

Fugacity from Equation of State for Water

Fuhrmann's Theorem

Fully Random, Five-Rule Interactive Cellular Automata (ICA)

Función seno y el movimiento armónico (Spanish)

Function Explorer 2D

Function Explorer 3D

Function Identification Game

Functions in Two-Dimensional Vector Space or Complex Plane

Functions of Different Parts of the Brain

Functions of Matrices

Functions Related to Primes

Functions That Enumerate Pairs

Functions with Vertical, Horizontal, and Oblique Asymptotes

Function Transformations

Function Transformations and Inverses

Function Transformations Quiz

Fundamental Commutation Relations in Quantum Mechanics

Fundamental Law of Fractions

Fundamental Laws of Random Matrix Theory

Fundamental Theorem of Arithmetic

Fundamental Theorem of Calculus

Fundamental Theorem of Calculus and Initial Value Problems

Fundamental Unit

Fund Drawdown Simulation

Fun with Koch Snowflakes

Futoshiki Generator

Future Value Calculator

G^1 Hermite Interpolation with Pythagorean-Hodograph Cubic Curves

Gabor 3D

Gabriel's Horn

Gailiunas's Spiral Tilings

Gains from Trade

Galactic Coordinate System

Galactohedra

Galileo's Experiment at the Leaning Tower of Pisa

Galileo's Inclined Plane Experiment

Galileo Spaceflight

Galileo's Paradox

Galileo's Thought Experiment on Inertia

Galileo Thermometer

Galton Board

Galvanometer as a DC Multimeter

Game Clock

Game of Bulbs

Game of Dice

Game of Dice 2

Game of Life Configurations

Game of Life in 3D Layers

Game of Life with Random Initial Conditions

Gamma Correction

Gammes pythagoriciennes (French)

Gamow Model for Alpha Decay: The Geiger-Nuttall Law

Gantt Charts and Network Diagrams

Gaps between Consecutive Primes

Gaps between Successive Primes

Gaps in GPS Data

Garage Door Lift Mechanisms

Garbage Collection by Ants

Garden of Eden States

Gardner's Problem

Garfield's Proof of the Pythagorean Theorem

Gas Absorption Computed Using the Gauss-Seidel Method

Gas Absorption Computed Using the Successive Over-Relaxation (SOR) Method

Gas Absorption with a Rapid Chemical Reaction

Gas Absorption with Chemical Reactions

Gas-Driven Piston Undergoing Simple Harmonic Oscillation

Gas Particle Attraction and Repulsion Using Lennard-Jones Potential

Gas-Phase Catalytic Dehydrogenation of 1-Butene to 1,3-Butadiene

Gas-Phase Chemical Equilibrium at Constant Pressure or Constant Volume

Gas-Phase Fugacity Coefficients for Propylene

Gateshead Millennium Bridge

Gauss-Bonnet and Poincaré-Hopf for Graphs

Gauss Code Loops

Gaussian Approximations to 1s Slater-Type Orbitals

Gaussian Beam Propagation through Two Lenses

Gaussian Brackets

Gaussian Divisors of an Integer

Gaussian Filtering for Blurring

Gaussian Laser Modes

Gaussian Matrix Kernels

Gaussian Primes

Gaussian Prime Spirals

Gaussian Quadrature

Gaussian Smoothing

Gaussian Wave Packet in a Linear Potential Field

Gaussiennes, effet des paramčtres (French)

Gauss Law in Electrostatics

Gauss-Legendre Approximation of Pi

Gauss Map

Gauss Map and Curvature

Gauss on Vega's Thesaurus Logarithmorum Completus

Gauss's Circle Problem

Gauss's Line

Gauss Sum Walks

Gavrilov-Shilnikov Model

Gay-Lussac's or Amontons's Law for an Ideal Gas

Gazis-Herman-Rothery (GHR) Car-Following Model

GCD Cube

GC Nucleotide Content Ratio

Gearless Cycloidal Speed Reducer

Gear Shifting

Gedankenexperiment for Three Entangled Electrons: Analog of GHZ Photon Experiments

Geiger Counter with Dead Time

Gematria (Letter Sums)

Genealogy Graphs from XML

Gene Expression and Eye Color

General Additive Cellular Automata

General Assembly Resolution Viewer

General Divisor Methods

General Equilibrium with Production: Robinson Crusoe with and without Trade

Generalized Arrhenius Function

Generalized Cantor Sets and Their Hausdorff Dimensions

Generalized Cassini Curves

Generalized Central Limit Theorem

Generalized Coons Surface

Generalized Digit Parity

Generalized Digit Parity for Integer Sequences

Generalized Extreme Value Distributions: Application in Financial Risk Management

Generalized Fibonacci Sequence and the Golden Ratio

Generalized Gosper Curves and Trisected Variants

Generalized Hyperbolic Distribution

Generalized Inscribed and Escribed Triangles

Generalized Kaprekar Routine

Generalized Logistic (Verhulst) Isothermal Microbial Growth

Generalized Mobile Automata

Generalized Pythagoras Theorem

Generalized Straightedge and Compass Fractal

Generalized Trisection Construction

Generalized Ulam Sets in the Plane

Generalized Unsöld Theorem for Hydrogenic Functions

Generalized Waterman Polyhedra

Generalizing the Crease Length Problem

General Parabola Equation

General Rational Cyclic Polygons

Generate Uniform Spherical 3D Random Vectors

Generating 2D Metallic-Mean Quasiperiodic Tilings with NKS Substitution Rules

Generating 3D Figures with a Given Symmetry Group

Generating 9-Flips

Generating a Bezier Curve by the de Casteljau Algorithm

Generating a B-Spline Curve by the Cox-De Boor Algorithm

Generating a Cardioid III: Circles Passing through a Point

Generating a Cardioid II: Reflecting in Tangents

Generating a Cardioid I: One Circle Rolling around Another

Generating a Cardioid IV: Feet of Perpendiculars

Generating a Cardioid VII: Joining Points on a Circle

Generating a Cardioid VI: Reflected Rays

Generating a Cardioid V: Rolling a Hoop

Generating a Hyperbola Using Steiner's Method

Generating a Hyperboloid by Rotating a Line

Generating a Lemniscate I: Envelope of Circles

Generating a Lemniscate III: Using a Linkage

Generating a Lemniscate II: Rotating Line

Generating a Lemniscate IV: Rotating a Line

Generating All Coprime Pairs

Generating an Ellipse Using Steiner's Method

Generating Arithmetic Expressions

Generating a Rotating Field by Superposition of Three Alternating Fields

Generating Conics by Newton's Method

Generating Cube-Like Structures from 3-Tuples of Equidistant Points on a Circle

Generating Entangled Qubits

Generating Fractals with Regular Expressions

Generating Functions

Generating Functions and Rodrigues's Formulas for Special Functions Used in Quantum Mechanics

Generating Julia Sets

Generating Lissajous Figures

Generating Near-Isosceles Pythagorean Triples

Generating Patterns Similar to Peruvian Textiles

Generating Permutations by a Sequence of Transpositions

Generating Points with Uniform Density in a Triangle, Parallelogram, or Disk

Generating Pseudorandom Numbers with Elementary Cellular Automata

Generating Random DNA Sequences

Generating Realistic Baseball Line Scores

Generating the Surreal Numbers

Generations Cellular Automata

Generator of Pythagorean Triples

Generic Euler's Elastica

Generic Random Walk and Maximal Entropy Random Walk

Genetic Drift of Allele Frequency

Genetic Toggle Switch

Genetic Transformation

Geneva Drive (Maltese Cross)

Geodesate

Geodesic Balls in the Nil-Space

Geodesic Cone in Nil-Geometry

Geodesic Domes with Shell and Frame

Geodesic Precession on a Timelike Circular Orbit around a Schwarzschild Black Hole

Geodesics and Conjugate Loci on a Torus

Geodesics in Schwarzschild Space

Geodesics in the Morris-Thorne Wormhole Spacetime

Geodesics of a Torus Solved with a Method of Lagrange

Geodesics on Some Surfaces

Geometrical Doll

Geometric Analog of Cube of Sum

Geometric and Continued Fraction Expansion of the Golden Ratio

Geometric Art

Geometric Brownian Motion with Nonuniform Time Grid

Geometric Construction of the Square Roots of a Complex Number

Geometric Difference between a Finite Difference and a Differential

Geometric Distribution

Geometric Elements of a Circle

Geometric Illustration of Machin-Like Formulas

Geometric Interpretation of Perrin and Padovan Numbers

Geometric Mean Constructions

Geometric Mean Filtering for Blurring

Geometric Mean of Continued Simple Fraction Terms

Geometric Multiplication

Geometric Problems of Antiquity

Geometric Proof of the Tetrahedral Number Formula

Geometric Properties of an n-Cube

Geometric Properties of Generalized Hermite Polynomials

Geometric Representation of Method of Lagrange Multipliers

Geometric Representation of the Cube of a Sum

GeometricScene Triangle Centers

Geometric Series

Geometric Series Based on Area Ratios of Similar Polygons

Geometric Series Based on Equilateral Triangles

Geometric Series Based on the Areas of Squares

Geometric Solution of a Quadratic Equation

Geometric Solution of a Quadratic Equation Using Carlyle's Circle

Geometric Solution of a Trigonometric Equation

Geometric Square Root Construction

Geometry of Cubic Polynomials

Geometry of Gregorian Telescope

Geometry of Logarithms

Geometry of Quartic Polynomials

Geometry of the Pyramid of Khufu

Geometry of Two-Variable Associated Legendre Polynomials

Geometry of Two-Variable Laguerre Polynomials

Geometry of Two-Variable Legendre Polynomials

Geosynchronous Orbit

Gerling's 12-Piece Dissection of an Irregular Tetrahedron into Its Mirror Image

Gershgorin Circles

Gershgorin Circle Theorem

Gerwien's Simultaneous Dissection of Three Triangles of Same Area

Geske-Johnson Method

Getting e from Randomness

Gettysburg!

Giant Component in Random Graph

Gibbs Free Energy Minimization Applied to the Haber Process

Gibbs Free Energy of Chemical Reaction

Gibbs Phase Rule for One- and Two-Component Systems

Gibbs Phenomena for 1D Fourier Series

Gibbs Phenomenon in Laplace's Equation for Heat Transfer

Gibbs Phenomenon in the Truncated Discrete-Time Fourier Transform of the Sinc Sequence

Gielis's Superformula for Complex Shapes

Gilbreath's Conjecture

Gillespie's Stochastic Simulation Algorithm for Chemical Reactions

Gingerbreadman Trajectories

Ginzburg-Landau Equation

Girder Bridge Model

Girih Tiles

Given a Segment, Construct Its Perpendicular Bisector; Given a Triangle, Construct Its Circumcircle

GL(2,p) and GL(3,3) Acting on Points

GL(3,n) Acting on 3D Points

Glass Cut

Glass Slide Reflectance from Vector Amplitudes

Glissettes and the Orthoptic Curve of the Ellipse

Global and Local Errors in Runge-Kutta Methods

Global and Local Sequence Alignment Algorithms

Global B-Spline Curve Fitting by Least Squares

Global B-Spline Curve Interpolation

Global B-Spline Surface Interpolation

Global Extrema on an Interval

Global Minimum of a Non-Convex Function

Global Minimum of a Surface

Global Optimization Using a Metamodel

Global Recurrence Plot of Cellular Automaton Dynamic

Global Warming Impact in Asti and Other Wine-Producing Locations

Glowing Orb: Lighting Effects on a White Sphere

Glycolysis

Gödelization

Gödel's Universe

Golay Code

Goldbach Comet

Goldbach Conjecture

Goldbach Conjecture Cellular Automaton

Goldbach Partitions

Goldberg's Pentagon-to-Triangle Dissection

Goldberg's Tristable Polyhedron

Golden Integers

Golden Lines in an Equilateral Triangle

Golden Octet Truss

Golden Pair of Cubes

Golden Ratio by Paper Folding

Golden Ratio by the Fibonacci Sequence

Golden Ratio Dividers

Golden Rhombic Solids with Nets

Golden Rhomboidal Dodecahedron

Golden Section

Golden Spiral

Golden Truncated Icosahedron

Goldilocks and the 3 Similar Triangles

Golf Player Handicap Calculation

Golomb Rulers and Fibonacci Sequences

Gomory's Theorem

Goodness of Fit for Random Subsets

Goodstein Function in Terms of Fast-Growing Function Hierarchies

Gordon-Taylor and Fox Equations for Glass Transition Temperature

GPS Simulator

Graceful Graphs

Gradient Bar Illusion

Gradient Echo Pulse Sequence in Magnetic Resonance Imaging

Gradient of Ground Temperature in Response to Cold Winds

Gradients in 2D and 3D

Gradual Transition of States in 2D Cellular Automata

Graham Scan to Find the Convex Hull of a Set of Points in 2D

Graham's Square Root Extractor

Gram-Schmidt Process in Three Dimensions

Gram-Schmidt Process in Two Dimensions

Granger-Orr Running Variance Test

Granular CA Synthesis

Granular Toppling and Piling

Graph and Contour Plots of Functions of Two Variables

Graph Automorphisms

Graph Browser

Graph Connectivity Drawing with Four Simple Graphs

Graph Connectivity Drawing with Some Finite Graphs

Graph Detangling

Graph Embedding Trajectories

Graphene Brillouin Zone and Electronic Energy Dispersion

Graph for Six Degrees of Kevin Bacon

Graphical Application of Horner's Method

Graphical Construction of a 2x2 Matrix and Its Inverse

Graphical Illustration of Bivariate Constrained Optimization

Graphical Linear Programming for Three Variables

Graphical Linear Programming for Two Variables

Graphical L-Systems

Graphical Method for Evaluating the Performance of N Tanks in Series

Graphical Modulo-4 Image Encryption

Graphical Representation of Geometric Series

Graphical Representations of Depleted Zeta Subseries

Graphical Solution for a Multistage Continuous Feed-and-Bleed Ultrafiltration System

Graphical Solution of a Quadratic Equation Using a Result from Optics

Graphical Solution of a Quadratic Equation Using the Arithmetic and Geometric Mean

Graphical Solution of a Quadratic Equation with Complex Coefficients

Graphics Lighting Transformation

Graphic Solution of a First-Order Differential Equation

Graphic Solution of a Second-Order Differential Equation

Graphing Continued Fractions of Quadratic Irrationals

Graphing Derivatives

Graphing Elementary Transformations of Basic Functions

Graphing Functions with Four Parameters

Graphing Systems of Inequalities

Graph of a Relation under a Linear Coordinate Transformation

Graph of a Six-Cube and Skeleton of a Rhombic Triacontahedron

Graph of Inequalities

Graph Products

Graph Puzzles

Graphs and Sections of Some Polynomial, Exponential, and Trigonometric Functions

Graphs and Their Complements

Graph Searching: Breadth First and Depth First

Graphs from Zero-One Matrices

Graphs of Exponential and Logarithmic Functions

Graphs of Exponential Functions

Graphs of Partitions

Graphs of Powers and Their Reciprocals

Graphs of Random Permutations

Graphs of Successive Digits of Pi, e, and Phi

Graphs of Taylor Polynomials

Graphs of the Beta Function

Graphs of the Six Trigonometric Functions

Graphs of the Successive Digits of Rational Numbers

Grating

Grating 3D

Gravestone from Transformation of Bilinski Dodecahedron

Gravestone from Transformation of Bilinski Dodecahedron 2

Gravitational Force between Two Spheres

Gravitational Interaction Simulator

Gravitational Lensing by a Point Mass

Gravitational Lensing of a Point Source

Gravitational Potential of a Cuboid

Gravitational Redshift

Gravitational Slingshot Effect

Gravitational Wave Frequency Distribution for Two Orbiting Point Particles

Gravitational Wave Hodograms

Gravitational Wave Polarization and Test Particles

Gravitational Waves Emitted by Colliding Black Holes

Gravitational Waves from Non-precessing Spinning Binary Black Hole Coalescence

Gravitation versus Curved Spacetime

Gray and Dark Solitons in the de Broglie and Bohm Approaches

Gray Code's Error Reduction with Encoders

Gray Color Meditation

Gray Indexed Minimum Change Permutation

Gray-Scott Reaction-Diffusion Cell with an Applied Electric Field

Great Circles on Mercator's Chart

Greatest Planetary Elongation

Great Rhombic Triacontahedron Sculpture

Greedy Algorithms for a Minimum Spanning Tree

Greek Numerals

Greenberg-Hastings Model

Green's Function

Green's Functions for Diffusion

Green's Functions with Reflection Conditions

Gregory Series

Grid Designs Generated by Langton's Ant

Gridiron Pendulum

Grid Packing at an Angle

Grids of Lines

Groops

Gross Domestic Product (GDP) and GDP per Capita

Ground Fault Interrupter

Group and Phase Velocity

Group Chase and Escape

Group Homomorphisms on the Integers Modulo n

Grouping Country Data

Grouping Images by Color

Grouping the Faces That Belong to the Same Vertex of a Polyhedron

Group of Symmetries of the Square

Group Trends for Elements in the Periodic Table

Grover's Quantum Search Algorithm

Grow an Alexander Horned Sphere

Grow Dahlias

Growth Curve and Life Cycle of Viruses

Growth Curves for a Mixture of Two Subpopulations

Growth in 1D Substitution Systems with Two Colors and Up to One Neighbor

Growth Inhibition and Retardation by Antimicrobials

Growth Model for the Blue-Green Alga Anabaena catenula

Growth of a Rhombic Dodecahedron

Growth Rate of Kolmogorov Flow

Grünbaum's Skeletal Polyhedra

Grünbaum's Venn Diagram

Guessing a Number Using the Chinese Remainder Theorem

Guessing the Frieze Group

Guessing the Symmetry Group

Guess the Age of HM Queen Elizabeth II with Wolfram Artificial Intelligence

Guess the Antisymmetric Frieze Group, Part 1

Guess the Antisymmetric Frieze Group, Part 2

Guess the Color Name

Guess the Wallpaper Group

Guess Who?

Guilloché Outline Rules

Guilloché Patterns

Guitar Chord Diagram

Guitar Chord Maker

Guitar Chords

Guitar String Harmonics: Standing Waves

Guitar Tuner

GUM versus Exact Uncertainty of sin(x) and cos(x) When x Is Normally Distributed

Gyroelongated Dipyramid

Gyroscope

Gyroscopic Joint

Haar Function Interval Points

Haar Functions

Haberdasher's Problem

Hackers Language

Hacker's Symbol: The Glider in the Game of Life

Hadron Decays

Hadwiger-Finsler Inequality

Hair and Relative Humidity

Half-Distance Rules with High Resolution

Half-Distance Rules with Low Resolution

Half-Life of a Radioactive Decay

Half-Life of a Radioactive Element

Halftone Process for Printing Photographic Images

Half-Tone Screens

Halving a Triangle

Halving a Triangle Perimeter

Halving the Perimeter of a Heart-Shaped Curve

Halving the Perimeter of a Zigzag Polygon

Hamilton-Connected Harary Graphs

Hamiltonian Cycles through Polyhedral Skeletons

Hamiltonian Path on a Polyhedral Net

Hamiltonian Tours on Polyhedra

Hammering a Nail into a Board

Hammer Time

Hammond's Postulate and Selectivity in Free Radical Halogenation

Hanbury Brown and Twiss Interference for Bosons and Fermions

Handling Molecular Pathways in Systems Biology

Hand Model

Hand Moving on a Moebius Strip

Hanegraaf's Dissection of a Nonagon into a Triangle

Hanegraaf's Dissection of a Truncated Octahedron into a Hexagonal Prism

Hanegraaf's Rectangular Block of Size 2×1×1 to a Cube Dissection

Hanging a Hollow Sphere with a Leaf Spring

Hangman Word Game for a Computer Player

Hangman Word Game for a Human Player

Hankel Function and Spherical Hankel Functions in the Complex Plane

Happy Pi Day!

Hardy and Ramanujan's Asymptotic Formula for the Partition Numbers

Harmonic Bézier Surfaces

Harmonic Distortion of Nonlinear Transfer Function

Harmonic Electric Field Applied to a Particle in an Infinite Square Well

Harmonic-Gaussian Double-Well Potential

Harmonic Oscillation

Harmonic Oscillator Eigenfunctions

Harmonic Oscillator in a Half-space with a Moving Wall

Harmonic Oscillator Wavefunctions

Harmonograph

Hartl Optical Disks

Hashing Words in Cryptography

Hasse Diagram of Power Sets

Hasse Diagrams of Integer Divisors

Hat Monotile Coronas

Hat Monotile Family

Hawkins Numbers and the Prime Number Theorem

Head Motion of the Wolfram 2,3 Turing Machine

Head-to-Toe Vector Addition

Healthcare Reform and Effective Marginal Tax Rates

Health-Wealth Tradeoffs

Hearing Cellular Automata

Heart Disease Risk

Heart Electrophysiology

Heat Balance in Freezing and Thawing Food

Heat Capacity of Solids in the Debye Approximation

Heat Conduction in a 1D Harmonic Chain with 3D Vibrations

Heat Conduction in a Rod

Heat Conduction in Some Standard Solids

Heat Diffusion in a Semi-Infinite Region

Heat Diffusion through Different Materials

Heat Exchanger Effectiveness

Heat Flow across Circuit Board

Heat Flow between a Human and a Chair

Heat Flow between Two Reservoirs

Heat Flow from a 2D Source

Heat Flow from Lava to Ice

Heat Flow through a Pipe

Heat Generation and Conduction through Composite Walls

Heating of Bodies in a Limited Volume of Well-Stirred Fluid

Heating Water and Air in a Sealed Container

Heating Water in a Closed Vessel

Heat Transfer along a Rod

Heat Transfer and Temperature Distribution in a Fin

Heat Transfer and the Second Law of Thermodynamics

Heat Transfer between a Bar and a Fluid Reservoir: A Coupled PDE-ODE Model

Heat Transfer between Flowing Liquids in Cylindrical Tubes

Heat Transfer between Two Immiscible Liquids in Laminar Flow

Heat Transfer in a Bank of Tubes

Heat Transfer in a Bar with Rectangular Cross Section

Heat Transfer in a Heat Exchanger

Heat Transfer in Fins

Heat Transfer in Fluid Flow

Heat Transfer through a Cylinder

Heat Transport and Chemical Reaction in Tubular Reactor with Laminar Flow

Heavy Spring with Double Pendulum

Hecks Boards

Hedging the Black-Scholes Call Option

Hedging the European Put Option

Hegemonic Zones of Influence

Height of Object from Angle of Elevation Using Sine

Height of Object from Angle of Elevation Using Tangent

Heilbronn Triangles in the Unit Square

Heilbronn Volumes

Heisenberg Group Action on Quintics

Heisenberg-Type Uncertainty Relation for Qubits

Heisenberg Uncertainty Product for Different Photon States

Helical Bevel Gear

Helical Spring

Helical Spring between Two Cylinders

Helical Staircase

Helical Staircases

Helices

Helices Made of Icosahedra and Rhombohedra

Helices of Tetrahedra

Helices on a Rhombic Icosahedron

Helicoid with a Hole

Helicopter Tilt Control

Helium Ionization Fraction as Function of Density and Temperature

Helix Made of Golden Rhombohedra

Helix of Augmented Rhombic Icosahedra

Helix of Tetrahedra

Helix Staircase Plotter

Helix with Polygonal Cross Section

Hello Block World

Helmholtz Coil

Helmholtz-Coil Fields

Hemisphere Volume and Surface Area

Hemodialysis

He-Ne Laser

Henneberg's Minimal Surface

Hénon Map Visualization

Henry's Law for Gases Dissolved in Water

Henry's Law for Oxygen and Carbon Dioxide

Hepatocellular Carcinoma Gene/Protein Networks

Heppes's Two-Tip Tetrahedron

Herd Immunity for Smallpox

Hereditary Representation

Hering Illusion

Hermite Lissajous Figures

Heron's Formula

Hertzian Contact Stress

Heterogeneous Chemical Equilibrium with Calcium Carbonate

Heterogeneous Kinetics by Scanning Electrochemical Microscopy

Hexagonal Close Packing and Triangular Orthobicupola

Hexagonal Insect Vision

Hexagonal Lattice of Polyhedra

Hexagonal Lattice Structure

Hexagonal Outer Totalistic Cellular Automata

Hexagonal Pattern Made of Tetrahedra

Hexagonal Prism Totalistic Cellular Automaton

Hexagonal Raster

Hexagonal Two-Color Four-Neighbor Totalistic Cellular Automata

Hexagons and the Golden Ratio

Hexagrammum Mysticum

Hexecontahedron Net

Hex Life: Hexagonal Cellular Automata

H-Fractal

HH versus HT Pattern Expectations in Sequences of Coin Flips

Hidden Correlation in Regression

Hidden Periodicity in Quality Control Records

Hidden Variables in Quantum Mechanics

Hierarchical Clustering and Heat Maps in Mathematica

Hierarchical Zonotopal Spaces

Higgs Mass and Decay Width

High-Frequency Sonar Performance

Highlight Graph Elements

Highlighting Patterns in Cellular Automata

High-Precision Newton Algorithm for Generalized Logistic Maps with Unimodality z

High-Pressure Chemical Equilibrium

High-Pressure Vapor-Liquid Equilibrium Computations Using the Hayden-O'Connell Method and Wilson Model

High-Pressure Vapor-Liquid Equilibrium Data for a Binary Mixture: the Poynting Factor Correction

High Pressure Vapor-Liquid Equilibrium Data of a Binary Mixture of Chloroform and Acetone

Hilbert and Moore 3D Fractal Curves

Hilbert and Moore Fractal Curves

Hilbert Space Bases for Distinguishing Pure Quantum States in Low Dimensions

Hill Cipher Encryption and Decryption

Hill-Climbing Algorithm

Hindmarsh-Rose Neuron Model

Hinged and Translational Dissection of Two Squares to One

Hinged Dissection of a Cross into a Square

Hinged Dissection of a Decagon into Two Pentagons and Two Pentagrams

Hinged Dissection of a Generalized Greek Cross to a Square

Hinged Dissection of a Hexagram into Seven Smaller Ones

Hinged Dissection of an Equilateral Triangle into a Hexagram

Hinged Dissection of an Equilateral Triangle into Two Hexagons

Hinged Dissection of a Pentagram to a Decagon

Hinged Dissection of a Regular Heptagon into Eight Smaller Ones

Hinged Dissection of a Spherical Triangle into a Spherical Lune

Hinged Dissection of Equilateral Triangles

Hinged Dissection of Four Hexagons into One

Hinged Dissection of One Pentagon to Five Pentagons

Hinged Dissection of One Pentagram into Five Pentagrams

Hinged Dissection of Squares

Hinged Dissections: From Equilateral Triangle to Square

Hinged Dissections: From Three Squares to One

Hinged Dissections of a Hexagram and a Hexagon

Hinged Lining for a Tunnel

Hinged Octahedron

Hinged Tessellations

Hinged Tripod for Holding a Vertical Pole

Hippias Quadratrix

Hippopede of Eudoxus

Hirano's Construction of a Regular Pentagon

Hironaka's Curve

Histogram Equalization

Histogram of Flipping Cellular Automaton

Histograms of Heating and Cooling Degree Days

Histogram Threshold by Max Contour Contrast

HIV Progression

Hjelmslev's Theorem

Hoberman Cube

Hoberman Rings Attached in a Plane

Hoberman Sphere (Cuboctahedron)

Hoberman Sphere (Octahedron)

Hodgkin-Huxley Action Potential Model

Hodographs for Kepler Orbits

Hoehn's Theorem

Hölder Approximations to Popular Means

Hofstadter's MU Riddle

Hofstadter's Quantum-Mechanical Butterfly

Holditch Curves inside an Ellipse

Hold-or-Exercise for an American Put Option

Hole-Free Magic 45-Ominoes

Hole in a Cylinder

Holes in a Spikey

Holes in the Faces of a Dodecahedron

Holiday Greenery with Stars

Holistic Theorem

Homeomorphism of a Disk Mapping the Origin to Another Interior Point

Homogeneous Coordinates and the Projective Plane

Homogeneous Linear System of Coupled Differential Equations

Homogeneous Splines

Homogeneous System of Three Coupled, First-Order, Linear Differential Equations

Honeycomb

Honeycombs with Halves of a Rhombic Dodecahedron of the Second Kind

Hooke's Law

Hoop Dreams

Hopf Bifurcation in a Biased van der Pol Oscillator

Hopf Bifurcation in the Brusselator

Hopf Bifurcation in the Sel'kov Model

Hopf Bifurcations in a Nonlinear Two-Dimensional Autonomous System

Hopf Fibration of the Three-Sphere

Hopfield Network with State-Dependent Threshold

Horgan Minimal Non-Surface

Horizontal and Vertical Line Tests

Horizontal Visibility Graphs for Elementary Cellular Automata

Horner's Method

Horner's Method for Converting an Integer from Base b to Base 10

Horn Growth in 2D

Horosphere Packings of the (3, 3, 6) Coxeter Honeycomb in Three-Dimensional Hyperbolic Space

Hotelling Model of Product Quality Differentiation

Houndstooth Patterns

Hourglass

House-Like Solids from Kindergarten Blocks

House of Representatives Reapportionment by Hill's Method

House Profits in Negative Edge Games

How Area Changes with Diameter

How Continuous Innovation Affects Supply, Producer Surplus, and Consumer Surplus

How Do Confidence Intervals Work?

How Does the Vertex Location of a Parabola Change?

How Doorbells Work

How Far Can One See from a Height?

How Fast Can You Run?

How Five-Petal Flowers Grow on a Rhombic Triacontahedron to Become a Rhombic Hexecontahedron

How Increasing the Money Supply Affects the Economy

How Loess Works

How Long Does It Take a Society to Learn a New Term?

How Long Is the Coast of Britain?

How Many Balloons Does It Take to Lift a Little Girl?

How Many Gallons in My Pool?

How Many Rectangles Are There?

How Many Right Triangles Can You Find?

How Many Socks Do Two Feet Wear Out?

How Many Triangles Are There?

How Many Triangles in a Six-Pointed Star?

How Many Turns?

How Many Words Do You Know?

How Much Should I Reinvest in a Business?

How Normal Is the MRB Constant?

How Old Were Some Famous Mathematicians?

How Old Would You Be on Another Planet (or Pluto)?

How Rare Is that U.S. Coin?

How Receiver Operating Characteristic Curves Work

How Rings Form around a Planet

How Tall Is That Building?

How Text Rotation Works in Mathematica

How the Altitude Divides the Hypotenuse

How the Area of a Disk Grows

How the Primes Are Distributed

How the Proton and Neutron Got Their Masses

How the Roots of a Polynomial Depend on Its Constant Coefficient

How the Superposition of the Periodic Pulsations of +1 and -1 Generates Values of the Mertens Function

How the Trigonometry Functions Are Related

How the Zeros of the Zeta Function Predict the Distribution of Primes

How to Avoid a Collision

How to Catch a Standing Wave

How to Design a Building so It Works Like a Termite Mound

How to Inscribe a Square in a Triangle

How to Torpedo a Ship

How to Use the McCabe-Thiele Method for Fractional Distillation

How Triple Powers of Integers Begin and End

How Valid Is the General Record Examination Really?

How Zippers Work

HSV Colors

HSV Loci in the RGB Color Space

HTML Generator for Basic Layouts

Hubbard Model Interactive Calculator for 1D Systems

Hue, Saturation, and Brightness Image Controls

Hue-Saturation-Brightness (HSB) Explorer

Huffman Coding

Huffman Encoding

Huffman Encoding of the Evolution of a Cellular Automaton

Huffman Tree Encoding

Human Population Densities by Continent

Human Walking Animation

Hunger's Law of Cosines Dissection

Hunter-Nash Method for Liquid-Liquid Extraction (LLE)

Hunveyor-Surveyor Field Work Simulations

Hurricane Risk by State

Hurst Exponent of Stock Price

Hutchinson's Equation

Huygens's Principle

Hybrid Orbitals in Organic Chemistry

Hydrides as Isoelectronic Perturbations of the Neon Atom

Hydrogen and Lithium Orbitals Using a Hartree Eigenvalue Method

Hydrogen Atom: Fine Structure of Energy Levels

Hydrogen Atom in Curved Space

Hydrogen Atom in Varying Dimensions

Hydrogen Atom Radial Functions

Hydrogen Emission Spectrum Using Bohr Model

Hydrogen Fuel Cell

Hydrogenic Radial Functions via Supersymmetry

Hydrogen-Like Continuum Eigenstates

Hydrogen Orbital Densities

Hydrogen Orbitals

Hydrostatic Pressure

Hyperbolas, Lemniscates, and Cassini Ovals Generated by w = Sqrt(z)

Hyperbolic Distribution

Hyperbolic Paraboloid as a Ruled Surface

Hyperbolic Paraboloid Embracing an Elliptic Paraboloid

Hyperbolic Quadrilateral

Hyperbolic Triangle

Hyperbolization of a Dodecahedron

Hyperboloid as a Ruled Surface

Hyperboloid Geodesics

Hyperboloid of One Sheet with Op Art Motifs

Hyperboloids and Ellipsoids

Hypergeometric-Gaussian Modes

Hyperlabyrinth Chaos

Hypocyclic Mechanism

Hypocycloids

Hypocycloids in the Mathematica Icon

Hypothesis Tests about a Population Mean

Hypotrochoid from Collinear Orbiters

Hysteresis in the Flow Curves of Pseudoplastic Semiliquid Foods

Hysteresis Modeled with Cellular Automata

I Am a Regular Polygon

I-Beam Support

IC50 for an RTK Antibody

Ice Cube Melting in Water

I Changed My Tires; Was I Too Speedy?

I Ching 3D

Iconography for Elementary Cellular Automata Based on Radial Convergence Diagrams

Icosahedra along the Edges of Icosahedra

Icosahedral Compositions of Rhombic Dodecahedra of the Second Kind

Icosahedral Group Polyhedra

Icosahedral Rotational Symmetry Types

Icosahedron Ball

Icosahedron Covered with Polyhedra

Icosahedron Decorated with Diamonds

Icosahedron-Dodecahedron Sculpture

Icosahedron Fractal

Icosahedron to Small Rhombicosidodecahedron

Icosahedron Towers

Icosidodecahedron and the Compound of Five Octahedra

Icosidodecahedron as a Common Element

Ideal Gas Law

Ideal Gas Law Solver

Idealized Belousov-Zhabotinsky Reaction

Idealized Cam-Follower Mechanism

Idealized Closed Loop for Processes in Three Continuous Stirred-Tank Reactors

Idealized Controller

Idealized Conventional and Pressure-Assisted Thermal Preservation Processes

Idealized Galton Board

Idealized Gear Mechanism

Idealized Hoppering

Idealized Path of Apollo Missions

Ideal Nth-Band Discrete Filters

Identify Chemical Potential Plots

Identifying Some Inorganic Compounds

Identifying the Target from RNA Structure Ensemble

Identifying Trinomials That Are Perfect Squares

Identify Temperature Profiles for Heat Generation or Conduction through Composite Walls

Identify the Vertices of a Polyhedron

IFS: Rotation, Translation, and Scaling

Ikeda Attractor

Ikeda Delay Differential Equation

Illusion from Rotating Rings

Illustrating Arithmetic with Graphic Arrays

Illustrating Cosecant with the Unit Circle

Illustrating Cosine with the Unit Circle

Illustrating Cosine with the Unit Circle II

Illustrating Cotangent with the Unit Circle

Illustrating Kepler's Conjecture on Sphere Packing

Illustrating Secant with the Unit Circle

Illustrating Sine with the Unit Circle

Illustrating Tangent with the Unit Circle

Illustrating the Central Limit Theorem Using the Quantile Plot for Sums of Unit Exponential Random Variables

Illustrating the Central Limit Theorem with Sums of Bernoulli Random Variables

Illustrating the Central Limit Theorem with Sums of Uniform and Exponential Random Variables

Illustrating the Law of Large Numbers

Illustrating the Locker Problem

Illustrating the Use of Discrete Distributions

Illustrating Trigonometric Curves with the Unit Circle

Illustrative Performance Characteristics of Modern Motorcycles

ImageAdjust Parameters

Image Blurring

Image Color Analyzer

Image Compression via the Fourier Transform

Image Compression via the Singular Value Decomposition

Image Deconvolution

Image Histograms of the Four Seasons

Image Inpainting

Image Jitter Filter

Image Kernels and Convolution (Linear Filtering)

Image Padding

Image Processing of Calligraphy

Image Processing on Partitions

Image Quality Adjustment

Image Restoration for Degraded Images

Image Sharpening

Image Smoothing Using Stationary Wavelet Transform

Image Warping

Image Warping Using Conformal Mapping

Immiscible Liquids on Pressure-Composition Diagram

Impact of Sample Size on Approximating the Normal Distribution

Impact of Sample Size on Approximating the Triangular Distribution

Impact of Sample Size on Approximating the Uniform Distribution

Impact of Trade on Firm Productivity, Revenue, and Profit

Impedance for a Electrochemical Redox-Electroadsorption Reaction (E-EAR) at a Rotating Disk Electrode (RDE)

Impedance of a Micro-Disk Microelectrode

Impedance of a Redox Reaction (E) at a Rotating Disk Electrode (RDE)

Impedance of the Randles Circuit: Redox Reaction (E) at a Rotating Disk Electrode (RDE)

Impedance Spectra of Piezoelectric Rods

Imperfect Cartel

Implicit Function Game

Implicit Function Transformations Quiz

Implied and Local Volatility Dynamics in the SABR Model

Implied Volatility in Merton's Jump Diffusion Model

Implied Volatility in the Variance Gamma Model

Implosion Mechanism for Plutonium Bomb

Impossible Frames

Improper Integrals

Improving Power Factors in an AC Circuit

Improvisation on Chords

Impulse Acting on a Pendulum

Impulse Response of Two and Three Continuous Stirred-Tank Reactors in Series: Exact and Approximate Solutions

Ince Polynomials

Incipient Growth Processes with Competing Mechanisms

Incircles and a Cevian

Incircles in Right Triangles

Income and Substitution Effects

Income and Substitution Effects with Different Utility Functions

Incommensurability of the Base and Leg in an Isosceles Triangle

Incomplete Gamma Function with Continued Fractions

Inconsistent Set of Statements

Inconsistent Sets of Statements from Knights and Knaves

Increasing and Decreasing Functions

Incremental Tax Model

Indestructible Perpendicular Lines

Indicator Colors for pH Ranges

Individual and Cumulative Binomial Probabilities

Individual and Cumulative Negative Binomial Probabilities

Individual and Cumulative Poisson Probabilities

Individual Insurance Decisions under HR 3560 and HR 3962

Individual versus Market Demand

Induced EMF through a Wire

Induced Holonomy Groups for Thomas Precession on a Sphere

Induction in a Coil by a Gaussian Magnetic Field

Induction of a Sinusoidal Magnetic Field within a Coil

Inefficiency Calculations for a Multi-plane Particle Detector

Inelastic Collisions of Two Rough Spheres

Inelastic Collisions of Two Spheres

Inequalities and Equations with Absolute Values

Inequalities and Equations with Nested Absolute Values

Inequalities for a Malfatti Triangle

Inequalities for an Exradius of a Triangle

Inequality for a Cevian Involving the Circumradius

Inertia

Inertial Coordinate Systems

Inertia versus Gravity in 3D

Inferences about the Difference between Two Proportions

Inference with Fuzzy IF-THEN Rules

Infinite Impulse Response (IIR) Digital Low-Pass Filter Design by Butterworth Method

Infinite Limit at a Finite Point

Infinite Limit at Infinity

Infinitely Dividing the Pie

Infinite Magic Elliptic Curves

Infinite Monkey Theorem

Infinite Number of Cubes inside a Cube

Infinite Number of Squares inside a Square

Infinite Series Explorer

Infinitesimally Flexible Octahedron

Infinitesimally Movable Polyhedron with 18 Faces

Inflating a Dragon

Inflating a Koch Snowflake

Inflation-Adjusted Yield

Inflation in 2D de Sitter Spacetime

Influence of a Moving Nodal Point on the "Causal Trajectories" in a Quantum Harmonic Oscillator Potential

Influence of the Relative Phase in the de Broglie-Bohm Theory

Influential Points in Regression

Informal Power Assessment of the Normal Probability Plot

Infrared-Active Vibrational Modes in Water

Infrared and Raman Vibrational Spectra of Methane

Inhibition of Enzyme Reactions in Continuous Stirred-Tank Reactor and Batch Reactor

Initial Force on a Mobile Charge in Field of Fixed-Point Charges

Injecting a Liquid into an Evacuated Tank

Injecting Water into Liquid Nitrogen Tanks

Injective, Surjective, Bijective

Injury in Microbial Inactivation

Inscribe a Scaled Copy of a Triangle in Another Triangle

Inscribed and Central Angles in a Circle

Inscribed and Circumscribed Spheres of a Tetrahedron

Inscribed Angles in a Circle Subtended by the Same Chord

Inscribed Angles That Intercept the Same Arc

Inscribed Triangles in Polygons

Inscribing Four Circles in a Triangle

Inset Plot Magnifier

Inside a Helix of Tetrahedra

Inside a Ring of Ten Rhombic Hexecontahedra

Inside the Rhombic Hexecontahedron

Inside World of the Torus

Insolvency Setoff

Inspecting the Rosetta Stone

Insphere and Four Exspheres of a Tetrahedron

Instability of Laplace's Equation

Instantaneous Rate of Change

Instantaneous Rate of Change: Exploring More Functions

Instantaneous Rate of Change: Exploring More Functions with the First and Second Derivatives

Instantly Periodic General Continued Fraction Representations of Square Roots

Instrumental Polarization of a Beam Scanner

Insulin Molecule

Insurance and Precautions

Insurance Disclosures

Insurer Assessments with Tax Credits

Insurer Ruin

Intarsia Patterns with Modular Graphics

Integer Exponentiation Mappings

Integer Exponents

Integer Names in American English

Integer Polynomial

Integer Rotation Patterns

Integers

Integer-Sided Triangles

Integers Mod n and the Cyclic Subgroups

Integers Relatively Prime to the First n Primes

Integer Torus Maps

Integer Torus Maps Applied to Letterforms

Integer Triangle of the Gergonne Point

Integer Trig Hunt

Integer Trigonometric Patterns

Integer Value Spatial Distance

Integral Error Criteria for Controller Tuning

Integral Evaluation Using the Monte Carlo Method

Integral Grid Triangles with Consecutive Side Lengths

Integral Mean Value Theorem

Integrals of Nested Elementary Functions

Integrals over Dirac Delta Function Representations

Integrated Information in Partitioned Boolean Nets

Integrating across Singularities

Integrating and Differentiating Trigonometric Signals

Integrating a Quadratic Divided by the Square Root of a Quadratic

Integrating a Rational Function with a Cubic Denominator with One Real Root

Integrating a Vector Field along a Curve

Integrating "Beyond Infinity" and Back

Integrating Odd Powers of Sine and Cosine by Substitution

Integrating Some Rational Functions

Integration by Parts

Integration by Riemann Sums

Integration Is a Sum

Integration using Hermite Reduction

Intensity Distribution for Multiple Slit Diffraction

Intensity Distribution from Two Coherent Sources

Intensity of Segregation versus Time in a Semi-Continuous Reactor

Intensity Profiles for Newton's Rings

Interacting Cylindrical Magnets

Interacting Vortices in a Disk

Interaction at a Distance: The Radiation Model

Interaction Energies between Spherical Colloidal Particles in a Symmetric Electrolyte Solution

Interaction in a Two-Factor Regression Model

Interactions between Persistent Structures in CA Code 20

Interactions between Textured Glue Particles and a Ball Based on Idealized Dynamics

Interactive Color Posterization

Interactive Curve Fitting

Interactive Maze

Interactive Rings Tessellation

Interactive Spline

Interactive Venn Diagrams

Interactive White Balance Adjustment for Photographic Images

Intercepting ICBMs in Three Dimensions

Interest Rate Swap

Interference in Diffraction Grating Beams

Interference of Waves from Double Slit (Young's Experiment)

Interference Patterns

Interference Patterns from Sources on a Circle

Interference Patterns from Two Point Sources Projected on Planes

Interior and Exterior Angles of Regular Polygons

Interior Angles of a Triangle

Interleaved Circles

Interleaving Theorems for the Rayleigh-Ritz Method in Quantum Mechanics

Interlocking Disks

Interlocking Rings

Interlocking Tori

Intermediate Value Theorem

Intermolecular Forces for Small Molecules

Internal Combustion Engine

Internal Force Calculation for a Continuous Beam

Internal Rotation in Ethane and Substituted Analogs

Interpolate Smoothly

Interpolating a Set of Data

Interpolating B-Spline Curves with Boundary Conditions

Interpolating Polynomial

Interpolating the Hilbert Curve with a B-Spline

Interpolating the Hilbert Curve with a B-Spline to Create a Surface

Interpolating Vertical Segments

Interpretation of Some Divergent Series via the Zeta and Eta Functions

Interpreting a Square Grid as a Hexagonal Grid

Interpreting Double Integral as a Volume

Interrupted Pendulum

Interrupted Sinusoidal Map Projection

Intersecting 3D Triangles

Intersecting a Rotating Cone with a Plane

Intersecting Chords Theorem

Intersecting Circles

Intersecting Circles and a Right Angle

Intersecting Cylinders

Intersecting Irregular Tetrahedra

Intersecting Line Segments

Intersecting Lines in All Possible Ways

Intersecting Lines Using Slope-Intercept Form

Intersecting Secants Theorem

Intersection and Union of Cylinders

Intersection of a Cone and a Sphere

Intersection of a Convex Polyhedron and a Plane

Intersection of a Generalized Cylinder over a Rose Curve with a Circular Cylinder

Intersection of a Line and a Circle

Intersection of an Altitude and a Line through the Incenter

Intersection of an Ellipsoid and a Hyperboloid

Intersection of a Plane and a Tetrahedron

Intersection of Circular and Polygonal Cylinders

Intersection of Sectors

Intersection of Three Polygonal Cylindrical Surfaces

Intersection of Two Circles

Intersection of Two Cylinders

Intersection of Two Lines Using Vectors

Intersection of Two Polygonal Cylinders

Interval Interpolating Polynomial

Interval Notation

Interval Visibility Graphs

Interwoven Perforated Cubes

Interwoven Spherical Triangles

Interwoven Threads

Intramarginal Rent

Intramolecular Reaction between Neighboring Functional Groups in Random Copolymers

Intricate Patterns from a Simple Complex Function

Intrinsic 3D Curves

Intrinsically Defined Curves

Intrinsically Knotted Graphs

Introducing Higher Derivatives

Introduction to Taylor-Maclaurin Series

Introduction to the Doppler Effect

Introduction to Univariate Regression and Sum of Squared Errors

Intuition for the Fundamental Theorem of Calculus

Intuitive Parameterization of the Bivariate Normal Distribution

Invaders from the Computational Universe

Invariants of an Algebraic Conic Equation

Inverse Composition Rule

Inverse Fourier Sound

Inverse Function of a Trigonometric Function Game

Inverse Gnomonic Projections of Plane Regions

Inverse Hilbert Matrix Coefficients Mod m

Inverse Kinematics

Inverse Kinematics for a Robot Manipulator with Six Degrees of Freedom

Inverse Kinematics in Redundant Robot Manipulator

Inverse Square Laws

Inverse Stereographic Projection of Simple Geometric Shapes

Inverse Stereographic Projection of the Logarithmic Spiral

Inverse Transformation of s-Reflection Coefficient between Oblique and Normal Incidence

Inversion Curve of Joule-Thomson Using the Peng-Robinson Cubic Equation of State

Inversion of an Array of Cubes

Inversion of the Laplace Transform Using the Gaver-Stehfest Algorithm

Inversive Geometry I: Basic Properties of Inversion

Inversive Geometry III: Inverting an Ellipse

Inversive Geometry II: The Peaucellier Inversor Mechanism

Inversive Geometry IV: Inverting a Point with a Compass in Three Steps

Inversive Geometry V: Circle through Three Points

Inversive Geometry VI: Inverting a Polar Grid

Inversive Geometry VII: Spider Eyes

Inverted Pendulum Controls

Inverting a Point in the Osculating Circles of a Curve

Inverting the Regular Dodecahedron to a Rhombic Dodecahedron

Inverting the Rhombic Dodecahedron

Inverting the Truncated Octahedron

Investigating Limits at Infinity Numerically

Investigating Limits Numerically

Investment Leverage Effect

Investment Returns

Investor Perceptions of the Relationship of S&P 500 Stocks

Inviscid Burgers's Equation

Ionization Energies of Elements up to Z=36

Ions with Noble Gas Configurations

Iota-Delta Function for Generating Cellular Automata

Irradiation Illusion

Irrational Digits Walk

Irreducible Gaussian Fractions

Irregular Tilings

Irreptiles

Irreversible and Reversible Temperature Equilibration

Is a Point Inside or Outside a Regular Polygon?

Ising Model

Island Type Liquid-Liquid Equilibrium Diagrams

Isobaric Compression and Expansion of an Ideal Gas

Isobaric Vapor Liquid Equilibrium Computations

Isobaric Vapor-Liquid Equilibrium Data of an Immiscible Mixture

Isobaric Vapor-Liquid Equilibrium Data of a Partially Miscible Mixture

Isobaric Vapor-Liquid Equilibrium Diagram for a Constant Relative Volatility Mixture

Isochrons for a Dubins Car

Isocosts, Isoquants, Isocline Lines, and Scale Lines for Homogeneous (Cobb-Douglas) Functions

Isogonal and Isotomic Conjugates

Isohepta Triangles

Isolated RGB Channels of Images

Isolated Singularities

Isolated Singular Points of a First-Order Differential Equation

Isomer Generator for Organic Molecules

Isomorphic Types on Graphs: 1-Neighborhood Random Graphs

Isomorphic Types on Graphs: 1-Neighborhood Random Grid Graphs

Isomorphic Types on Graphs: 1-Neighborhood Random Tree Graphs

Isomorphic Types on Graphs: One-Neighborhood Gödel Sections

Isonona Triangles

Isonona Triangles for 3D Printing

Iso-n Triangles

Iso-Optic Curve of a Regular Polygon

Iso-Optic Curve of the Ellipse

Iso-Optic Plane of the Regular Tetrahedron

Isopenta Triangles

Isoperimetric Inequality for Polygons

Isoperiodic Potentials via Series Expansion

Isoptic Curves of an Ellipse

Isosceles Trapezoid Area

Isothermal Germination of Seeds and Microbial Spores

Isothermal Plug Flow Reactor

Isothermal Plug Flow Reactor with Recycle

Isothermal Reactor with Complex Reactions

Isothermal Yield of Allyl Chloride versus Conversion of Propylene

Isotherms for Expedited Moisture Sorption

Isotherms of Peng-Robinson Equation of State

Isotope Browser

Isotope Decay

Isovolatility Lines and Equilibrium Vectors

Is the Given Function Injective?

Is the Golden Ratio Really the Most Beautiful Proportion?

Is There a Klein Paradox in Graphene?

Is This Graph Planar?

Is This Number a Prime?

Item Characteristic Curves

Iterated Cyclic Averaging of Points

Iterated Games

Iterated Maps Using Complex, Dual, and Split-Complex Numbers

Iterated Matrix Operations in 3D

Iterated Nonlinear Map

Iterated Random Rotation 3D

Iterated Subdivision of a Triangle

Iterates, Cycles, and Bifurcations of the Logistic Map

Iterates for the Mandelbrot Set

Iterates of Generalized Logistic Maps for Superstable Parameter Values

Iterates of the Logistic Map

Iterates of the Logistic Map in 3D

Iterating Affine Transforms

Iterating a Square-Root Expression

Iterating Linear Functions

Iterating Rational Functions

Iterating the Collatz Map on Real and Complex Numbers

Iteration Methods for Solving Kepler's Equation

Iterations of Kaneko Map

Iterations of Newton's Method for Two Nonlinear Equations

Iterations of Some Algorithms for Nonlinear Fitting

Iterations of Some Algorithms for Unconstrained Local Optimization

Iterations of Strick Map

Iteration versus Recursion in the Fibonacci Sequence

Iteratively Reflected n-gons

Iteratively Reflecting a Point in the Sides of a Triangle

Iterative Polygon Simplification

Jack Lew Signature Function

Jacobi Polynomials in an Orthogonal Collocation Method

Jacobi Theta Functions

Jamie's Function

Jansen Walker

Japanese Kanji

Japanese Theorem for Cyclic Polygons

Japanese Theorem for Three Tangent Circles and a Triangle

Jarvis March to Find the Convex Hull of a Set of Points in 2D

Jazz Voicings

Jeener's Klein Surface

Jefferson National Expansion Memorial

Jeffery's Orbits

Jensen's Disks

Jiles-Atherton Model of Magnetic Hysteresis

Jingle Bell Surface

Johnson Graphs

Johnson's Theorem

John von Neumann's First Pseudorandom Number Generator

Joint Density of Bivariate Gaussian Random Variables

Joint Density of Trivariate Gaussian Random Variables

Joint Space and Tooling Space for Robot Motion Control

Jordan's Lemma Applied to the Evaluation of Some Infinite Integrals

Jorge-Meeks K-Noids

Josef Albers - Homage to the Square

Josephus Problem

Joukowski Airfoil: Aerodynamic Properties

Joukowski Airfoil: Flow Field

Joukowski Airfoil: Geometry

Joule Experiment on Free Expansion

Joule (Free) Expansion Based on a Block Cellular Automaton

Joule's Experiment

Joule's Experiment and the First Law of Thermodynamics

Joule-Thomson Expansion

Joule-Thomson Inversion Curves for Soave-Redlich-Kwong (SRK) and Peng-Robinson (PR) Equations of State

Joule Wire Heater

JPEG Compression Algorithm

Juggling the Cascade Pattern

Jug Problem

Jug-to-Square Dissection

Julia Sets and the Mandelbrot Set

Julia Sets Produced by Cubic Polynomials

Jumping over Row of Parked Cars

Junk Food Molecules

Juno Spaceflight

Kaiser Window Transform

Kakeya Needle Problem

Kakuro Product Puzzle

Kakuro Puzzle

Kakutani's Solution of the Dirichlet Problem

Kaleidocycles

Kaleidoscope

Kaleidoscope with One Horizontal and Two Vertical Mirrors

Kaleidoscopic Polygons

KAM Tori Reforming

Kanizsa Polygon Illusion

Kapitza's Pendulum

Kaprekar Routine

Karhunen-Loeve Directions

Karhunen-Loeve Directions and Regression

Karush-Kuhn-Tucker (KKT) Conditions for Nonlinear Programming with Inequality Constraints

k-Cayley Trees

k-Closure of a Directed n-Cycle Graph

Keccak Cinema Contemplation

Keeling Curve for Atmospheric Carbon Dioxide

Kekulč's Monkey in Anthracene

Kelland's Gnomon-to-Square Dissection

Kelly Portfolio Analysis

Kelvin Ship-Wave Pattern

Kempe's Angle Adder

Kempe's Angle Trisector

Kempe's Multiplicator

Kempe's Translator

Kempe's Universality Theorem: An Example

Ken Burns Effect

Kenmotu Circle

Kenyon Tiling Construction (Boundary)

Kenyon Tiling Construction (Substitution)

Kepler and Oscillator Elliptical Orbits

Keplerian Orbital Elements

Kepler Orbits

Kepler Problem with Classical Spin-Orbit Interaction

Kepler's Harmonices Mundi

Kepler's Mysterium Cosmographicum

Kepler's Rhombic Solids

Kepler's Rhombic Triacontahedron and Rhombic Icosahedron

Kepler's Second Law

Kepler's Third Law

Kermack-McKendrick Epidemic Model with Time Delay

Kermack-McKendrick SIR Model

Kermit's What-Happens-Next-Machine

Kernel Density Estimation

Kernel Density Estimations: Condorcet's Jury Theorem, Part 5

Keyboard and Composer

Keynesian Cross Diagram

Keypad Security Timer

Khatib-Khayat Model for Pumping Flowable Concrete

Kids Cryptography with Key from Leonardo Groups

Kiesswetter's Function

Kim's Method for Pricing American Options

Kim's Method with Nonuniform Time Grid for Pricing American Options

Kinematics of a Moving Point

Kinematics of a Redundant Anthropomorphic Arm with Seven Degrees of Freedom

Kinematics of Biped Legs for Humanoid Robots

Kinematics of Planar Elastic Chains

Kinematics of SCARA Robot in 2D

Kinematics of Traffic Congestion

Kinetic and Thermodynamic Control of Electrophilic Addition Reactions

Kinetic Order of Degradation Reactions

Kinetics of CFC Catalyzed Ozone Destruction

Kinetics of Chemical Reaction with an Intermediate Product

Kinetics of DNA Methylation in Eukaryotes

Kinetics of Elimination Reactions

Kirchhoff Imaging

Kirillov-Reshetikhin Crystals

Kissing Coins

Kite Tiling and a Dodecahedron

Kjeldahl Method for Determining Percent Protein from Percent Nitrogen

Kleene's Three-Valued Logic

Klein-Nishina Formula for Compton Effect

Klein Paradox

k-Nearest Neighbor (kNN) Classifier

Kneser Arrays

Kneser Graphs

Knight Paths

Knights and Knaves Puzzle Generator

Knights and Knaves Puzzle Generator with Not All Statements Determined

Knights, Knaves, and Normals Puzzle Generator

Knitting Charts

Knitting Hyperbolic Pants

Knopp's Osgood Curve Construction

Knot Explorer

Knot Pattern Similar to a Lotus Kolam

Knots

Knots with 10 Crossings

Knots with Fewer than 10 Crossings

Knot Vector Generation for B-Spline Interpolation

Koch Curve Randomization and Crystal Edge Disorder

Koch Curves

Koch-Subdivided Polyhedra

Kolkata Paise Restaurant (KPR) Problem

Kolmogorov Complexity of 3×3 and 4×4 Squares

Koman Surfaces

Koman Variations

Kon-Tiki Expedition

Kosnita's Theorem

Kowalewski's Coloring of the Rhombic Dodecahedron

Kowalewski's Games with Kepler's Solid

Kowalewski's Settlement Problem for the Rhombic Dodecahedron

Kowalewski's Settlement Problem for Triacontahedron

Kraskov (KSG) Estimator of Mutual Information

Kremser Shortcut Method for Absorption and Stripping

Kronig-Penney Model with Dirac Comb

Kronig-Penney Model with Mathieu Functions

Krugman's Cost Benefit Analysis for Austerity Cuts in Government Spending

Krugman's Model of Increasing Returns and Monopolistic Competition

Krypto, or 24-Game

K-Tiling the Plane with a Minkowski Sum of Segments

Kuramoto Model for Phase Locking of Coupled Oscillators

Kuramoto-Sivashinsky Equation

Kürschák's Dodecagon

K-value of Several Hydrocarbons versus Temperature and Pressure

Labeled Die

Labeled Fuss-Catalan Polygon Divisions

Labeled Polygon Triangulations

Labeled Trees of 10 Vertices Using Prüfer Sequences

Labeling the Integer Heptagon

Laboratory Waterbath with Proportional Control

Labyrinth Chaos

Labyrinth Tiling from Quasiperiodic Octonacci Chains

Laceable Knight Graphs

Ladder Operators for the Harmonic Oscillator

Ladybug Counting Game

Lagrange Multipliers in One Dimension

Lagrange Multipliers in Two Dimensions

Lagrange Points

Lagrange Points for Sun-Earth System

Lagrange's Four-Square Theorem Seen Using Polygons and Lines

Lagrange's Milkmaid Problem

Lag Time in Microbial Growth

Laguerre-Gaussian Modes of Paraxial Wave Equation

Lah Numbers

Lambdoma Matrix

Lambdoma of 256 Tones

Lamé's Ellipsoid and Mohr's Circles (Part 1)

Lamé's Ellipsoid and Mohr's Circles (Part 2: Parallels)

Lamé's Ellipsoid and Mohr's Circles (Part 3: Meridians)

Lamé's Ellipsoid and Mohr's Circles (Part 4: Spheres)

Laminar Flow

Laminar Flow between Two Eccentric Tubes

Laminar Flow of a Power-Law Fluid in a Horizontal Pipe

Landau Levels in a Magnetic Field

Land Use Regulation and Municipal Utility

Land Use with Contract

Lane-Emden Equation in Stellar Structure

Langford's Dissection of Five Pentagons into One Pentagon

Langmuir-Hinshelwood Reaction in a Plug Flow Reactor

Langmuir Isotherms for a Binary Mixture

Langton Loops

Languages in South American Countries

Laplace-Dirichlet Eigenstates of an Ellipse

Laplace Distribution in Fluctuating Stock Index Records

Laplace's Equation on a Circle

Laplace's Equation on a Square

Laplacian of Gaussian Filtering

Large Number Names

Largest Disk in a Convex Polygon

Largest Isosceles Triangle Inscribed in a Circle

Largest Square inside a Triangle

Largest Triangle Inscribed in a Circle

Laser Alignment with a Convex-Plane Lens

Laser Alignment with a Plane-Convex Lens

Laser Beam through Two Points by Turning Two Mirrors

Laser Diffraction Pattern

Laser Lineshape and Frequency Fluctuations

Laser Sword

Last Minute Valentine's Graphic

La superposition de deux ondes (French)

Latent Heats of Fusion and Vaporization

Latin Squares Puzzle Generator

Latitude and Longitude of a Point on a Sphere

Lattice Circles

Lattice Effects in Cellular Automata

Lattice Effects in Cellular Automata-Comparisons

Lattice Method Multiplication Grids

Lattice Multiplication

Lattice Multiplication of Polynomials

Lattice of Borromean Rings

Lattice of Factors

Lattice of Subgroups of Permutation Groups

Lattice Path Interpretations

Lattice Points on a Circle

Lattice Points under a Hyperbola

Lattice Random Walk in 2D

Lattice Random Walk in 3D

Lattice Rule

Lattices in Perspective

Lattice Squares of Integer Area

Latticework Design by Runs in Automaton States

Laue Diffractograms in Crystallography

Laue's Method for 2D Lattices Using Ewald's Circle

Launching a Projectile on a Sloped Surface

Launching a Rocket

Lava Lamp

Law of Large Numbers: Comparing Relative versus Absolute Frequency of Coin Flips

Law of Large Numbers: Dice Rolling Example

Law of Mass Action and Chemical Equilibrium

Law of Moments for Lever with Two Weights

Laws of Exponents

Laws of Reflection

Laws of Reflection and Refraction via Huygens's Principle

Lawsuit Settlement Calculator

LCAO Approximation to Bonding Molecular Orbital in Hydrogen

LCM, GCD, and MOD

Leads in Coin Tossing

Leakage Inductance in a Transformer

Leaking Bucket Equation and Reversibility

Learn Butterfly Taxonomy with Wolfram|Alpha

Learning Newton's Method

Learning Place Value by Counting Squares

Learning Some Spanish Words

Learning the Alphabet

Learning the Arabic Alphabet

Learning the Korean Alphabet

Learning Turtle Taxonomy with Wolfram|Alpha

Learn Musical Notes

Learn the Game of Go

Learn the Korean Alphabet

Learn the Radio Code

Learn Your Fretboard

Least Common Multiple and Greatest Common Divisor

Least Squares

Least Squares Criteria for the Least Squares Regression Line

Least Squares Estimate Using a Monte Carlo Method

Least-Squares Estimation of an Ellipse

Lebesgue 3D Curves

Lebesgue Integration

Le Chatelier's Principle in Chemical Equilibrium

Lee-Kesler Generalized Correlations for Gases

Left-Right-Rotating Spiral Array

Legal Incoherence

LEG CA

Legendre Lissajous Figures

Leibniz Criterion for Alternating Series

Lemaire's Dissection of the Maltese Cross to a Square

Lemaire's Second Dissection of the Maltese Cross to a Square

Lemniscate Linkage

Lemniscate Plotting Device

Lemon Batteries

Length Contraction Visualization: Pole and Barn

Length of a Coiled Rope

Length of an Arc of an Ellipse and the Area It Subtends

Length of Line Illusion

Length of the Intersection of a Sphere and a Cylinder over a Cardioid

Length of the Perpendicular from a Point to a Straight Line

Length of the Projection of a Rotating Polygon

Length Scales in the Solar System

Lengths of Permutation Cycles

Lengths of Sides and Angle Bisectors Are Rational Together

Length Units of Measurement

Length, Width, and Height of an Impossible Object

Lens Aberrations

Lens Accommodation in the Human Eye

Lens Doublets

Lens Flares

Lensmaker's Equation

Lenz's Law

Leonardo da Vinci's Helicopter

Leonardo da Vinci's Ornithopter

Leonardo's Dissection of a Motif to a Rectangle

Leontief Production Function

Lester's Theorem

Let's Learn French! An Interactive Learning Game

Letterform Comparison

Letter Highlighting in Text

Letter Products

Level Curves

Levels of a Mathematica Expression

Level Surfaces and Quadratic Surfaces

Level Surfaces for a Polynomial

Leverage Ratios

Lever Rule Applied to Phase Diagram for Partially Miscible Liquids

Lever Rule Applied to the Benzene-Toluene Vapor Pressure Diagram

Lever Rule for the Uranium-Titanium Solid-Liquid Phase Diagram

Leviant's Optical Illusion Enigma

Levich Equation for Rotating Disk Electrode

Lévy Measures

Levy's Conjecture

Lewis Carroll's Bilateral Diagram

Lewis Carroll's Curve

Lewis Carroll's Diagram and Categorical Syllogisms

Lewis Carroll's Diagrams

Lexis Diagram of a Follow-up Study

L'Hospital's Rule for 0/0 Forms

Liability Insurance Desirability under Lognormal Loss Distributions

Liability Insurance Desirability When "Diminution" Is Unlawful

Library of Vertex and Edge Shapes

Liénard-Wiechert Potential for Spiraling Charge

Lie Subgroups of the 2D Torus Group

Life Cycle of a Frog

Life Cycle of a Lytic Phage (T4 Bacteriophage)

Life Cycle of a Star

Life Expectancy in the U.S. Population

Life Insurance Pricing

Life Transitions

Lift Table

Light Beams through Multiple Polarizers

Light Clocks and Time Dilation

Light Cone Causality

Light Dependence and the Calvin Cycle

Light-Dependent Reactions in Photosynthesis

Lighthouses

Light in a Fiber Optic Cable

Lightning

Light on an Impossible Object

Light Polarization and Stokes Parameters

Light Propagation at Soft Interface

Light Ray in a Prism

Light Ray Passing through a Transparent Plate

Light Rays in a Lens

Light Refraction with a Waterdrop

Lights On/Lights Out Game and Solver

Lights Out Puzzle

Likelihood-Based Goodness of Fit in Two-Way Contingency Tables

Lill's Angle Trisection

Lill's Construction for a Depressed Cubic Polynomial

Lill's Graphic Solution of a Quadratic Equation

Lill's Method for Calculating the Value of a Cubic Polynomial

Lily Pond

Limaçons as Envelopes of Circles

Limaçons as Loci and Other Polar Curves

Limited Diagonalization

Limited Mandelbar Sets

Limiting Reagent for the Reaction of Hydrogen and Oxygen to Form Water

Limit Laws

Limit of a Family of Curves

Limit of a Function at a Point

Limit of a Sequence

Limit of sin x/x as x Tends to Zero

Limit of the Sequence a^(1/n)

Limit of the Sum of Two Sequences

Limit-Periodic Tilings

Limit Pricing

Limit Proofs Using Epsilon-Delta

Limits: A Graphical and Numerical Approach

Limit Sets for Schottky Groups

Limits of a Rational Function of Two Variables

Limits of Sequences

Limits of Tree Branching

Lindgren's Dissection of an Octagram into an Octagon

Lindgren's Dissection of a Parallelogram to a Parallelogram

Lindgren's Dissection of a Pentagon to a Hexagon

Lindgren's Dissection of a Pentagram into a Decagon

Lindgren's Dissection of a Quadrilateral to a Triangle

Lindgren's Dissection of One Decagram {10/3} into Two Pentagrams {5/2}

Lindgren's Dissection of One Octagram {8/3} into Two

Lindgren's Dissection of One Octagram into Two

Lindgren's Hexagon-to-Triangle Dissection

Lindgren's Hinged Dissection of Quadrilaterals

Lindgren's Square-to-Dodecagon Dissection

Lindgren's Symmetrical Decompositions of Regular 2n-Gons

Lindgren's Two-Triangles-to-One Dissection

Lindgren's Two-Triangles-to-One Hinged Dissection

Line Angle Histogram

Linear and Quadratic Curve Fitting Practice

Linear Chromatography

Linear Clock and World Time Zones

Linear Collision of Two Disks

Linear Collisions of Two Disks

Linear Combinations of Curves in Complex Plane

Linear Combinations of d Orbitals

Linear Combinations of f Orbitals

Linear Combinations of p Orbitals

Linear Congruential Generators

Linear Congruential Sequences

Linear Dependence between Two Bernoulli Random Variables

Linear Diophantine Equations

Linear Diophantine Equations in Two Variables

Linear Equations: Row and Column View

Linear First-Order Differential Equation

Linear Function Game

Linear Function Quiz

Linear Interpolation between a Square and a Circle

Linear Interpolation between Two Images

Linearized Solution for a Mass Attached to Two Springs

Linear Momentum Balance in Aerodynamic Thrust

Linear Motion

Linear Multistep Methods for First-Order ODEs

Linear Multistep Methods Generator for First-Order ODEs

Linear ODE Forms

Linear Oscillator Perturbed by Plane Electrostatic Waves

Linear-Phase Discrete Filters

Linear Quadratic Regulator Control of an Inverted Pendulum with Friction

Linear Regression

Linear Regression with Gradient Descent

Linear State Estimation Using a Weighted Least-Squares Method

Linear Sweep Voltammetry: Infinite Series Approximation

Line Art

Line Art 2

Line Art 3

Linear Transformation Given by Images of Basis Vectors

Linear Transformations and Basic Computer Graphics

Linear Transformations of a Polygon

Linear Transformation with Given Eigenvectors

Lined Tunnels

Line Etching Effect for Photographic Images

Line Halftones of Photographic Images

Line Jaggedness Visualization with the Mandelbrot-Weierstrass Function

Line Perpendicular to Two Intersecting Lines

Line Plots, Histograms, and Stem-and-Leaf Plots

Line Segments through the Vertices and the Circumcenter of an Acute Triangle

Lines from a Point to All the Points of a Circle

Lines in 3D Space (Parametric, Vector, and Cartesian Forms)

Lines of Force for Two Point Charges

Lines on a Cubic Surface

Lines Parallel to the Sides of a Triangle

Lines: Point-Slope

Lines: Slope-Intercept

Lines through Points in the Poincaré Disk

Lines: Two Points

Line through a Given Point on a Given Plane Perpendicular to the Plane

Line through Two Points

Linkage for the Cissoid

Linkage Inverting Figure-Eight Curves

Linked Electric and Magnetic Fields for Source-Free Maxwell Equations

Linked Sliders

Linked Torus Knots

Linking Two Rings

Lion and Man

Liouville's Theorem Applied to 1D Harmonic Oscillator

Lipschitz Continuity

Liquid Chromatography Simulation

Liquid Chromatography with Linear Adsorption Equilibrium and Plate Model

Liquid in a Rotating Cylinder

Liquid-Liquid Equilibrium Diagram for a Chloroform-Water-Acetic-Acid Mixture at 25°C and 1 atm

Liquid-Liquid Equilibrium Diagrams for Ternary Mixtures

Liquid-Liquid Equilibrium for the 1-Butanol-Water System

Liquid-Liquid Extraction (LLE) on a Right-Triangle Ternary Phase Diagram

Liquid-Liquid Miscibility for Organic Acids with Methanol

Liquid Mirror

Liquids in Containers of Different Shape

LISA Orbits

Lissajous Array

Lissajous Art

Lissajous Figures

Lissajous Figures from Projections of Points on Circles

Lissajous-like Kolam

Lissajous Patterns on a Sphere Surface

Listing's Law

Littlewood-Offord Problem

Lloyd Relaxation of Voronoi Diagrams

Loading Plot of a Principal Component Analysis (PCA)

Loan Payment Calculator

Local Behavior of a Polynomial near a Root

Local Digit Values

Local Growth in an Array of Disks

Local Markov Chains for Elementary Cellular Automata

Local Minimum Using SGD, ADAM, OGR Gradient Descent Optimizers

Local Regression for Country Data

Local Solution of a Nonlinear ODE Using a Power Series Expansion

Locate All the Integer Points between Two Integer Points

Locate a Point on a Map of the World

Locate a Point on the Earth's Surface

Locate Capital Cities of the World

Locate Important Real Numbers

Locating Criminals with Geo-Profiling

Locating the Complex Roots of a Quadratic Equation

Location of Complex Roots of a Real Quadratic

Location of the Zeros of a Polynomial with Positive Ordered Coefficients

Location Theory - 3D Bid Rent Curves Become Urban Form

Location Theory - Is the Bid Rent Curve Linear?

Location Theory - Land Use Determination

Loci in the Argand Diagram

Loculus of Archimedes

Locus of a Pressure-Sensitive Binary Azeotrope

Locus of Binary and Ternary Azeotropes in Chloroform-Methanol-Acetone Mixture

Locus of Centers of Spheres

Locus of Points at Constant Distance from the Edges of a Trihedron

Locus of Points Definition of an Ellipse, Hyperbola, Parabola, and Oval of Cassini

Locus of Points with Constant Angle

Locus of the Center of a Circle Inscribed in a Circular Segment

Loeschian Spheres

Logarithmic Integral on the Critical Line

Logarithmic Mean Temperature of a Heat Exchanger

Logarithmic Potential for a Flat Galaxy Model

Logarithmic Property of the Quadrature of the Hyperbola

Logarithmic Scales in Acoustic Spectra: Decibels and Octaves

Logarithmic Spiral

Logarithmic Spirals and Möbius Transformations

Logarithm Seen as the Size of a Number

Logical Expression for Assumptions on Parameters in Mathematica's Symbolic Distributions

Logical Stochastic Resonance

Logic Metapuzzle Generator

Logic on the Number Line

Logic Problems for Elementary Students

Logic with Complex Numbers

Logic with Letters

Logic with Logicians

Logistic Equation

Logistic Map: Onset of Chaos

Logistic Model for Population Growth

Logistic Sigmoid Market Model

Logit and Probit Models for O-Ring Failure Data

Logos Based on a Dissection of One Pentagon to Five Pentagons

Logos of Tokyo 2020 Olympic and Paralympic Games

Logo Text Rotation

Log Survival Ratio as a Function of Time

London Eye

Long Addition

Long Division

Longitudinal and Transverse Waves

Longitudinal Oscillations and Resonance of a Four-Spring, Three-Mass System

Longitudinal Standing Waves

Long Multiplication

Long-Run Average Total Cost

Long Run of Cellular Automata Class IV

Look and Say Sequence Steps

Look and Say Sequence Substrings

Looking at a Cube

Looking at Polyhedra in 3D

Looney Gears

Looped Curves

Loops around a Cuboctahedron

Loop the Loop

López Minimal Klein Bottle

Lorentz Oscillator Model for Optical Constants

Lorentz Oscillator Model for Refractive Index

Lorentz Transformation for a Rotating Square

Lorentz Transformation for Twin Paradox

Lorenz Attractor

Lorenz Curves and the Gini Coefficient

Lorenz-Emanuel System

Lorenz's Model of Global Atmospheric Circulation

Lorenz's Water Wheel

Los Alamos Chess

Lotka-Volterra Competition Model

Lotka-Volterra Discrete Difference Equations

Lotus Effect

Lower Excited States of Helium Atom

Lower Excited States of the Helium Isoelectronic Series

Low-Pass and High-Pass Filtering of Images

Lowpass Filter Design by Pole Placement

Low-Temperature Heat Capacity of Hydrogen Molecules

Loxodrome

Loxodrome Art

Loxodromic Möbius Mesh inside a Sphere

Loyd's Dissection of a Clipped Rectangle to a Square

Loyd's Dissection of a Square to Five Different Figures

Loyd's Squares for a 3-4-5 Triangle

Loyd's Two-Greek-Crosses-to-a-Square Dissection

Lozi Attractor

Lubricated and Frictional Squeezing Flow

Lucas Circles

Lucas-Gauss Theorem

Lucky Numbers

LU Decomposition

Ludum Dare 24: Procedural Bug Creation

Lukasiewicz's Three-Valued Logic

Luna Landers on the Moon

Lunar Calendar Maker

Lunar Libration

Lunar Libration of Longitude

Lung Model Simulation

Lyapunov Exponents for the Logistic Map

Lyapunov Exponents of Elementary Cellular Automata

Lyapunov Fractals

Macaulay Duration

Macaulay Duration as the Balancing Point of a Seesaw

Macaulay's Triangle and Trapezoid Hinged Dissection

Machine Language Pattern for lsmod Program

Machin's Computation of Pi

Mach-Zehnder Interferometer with Phase Shifts

Mackey-Glass Equation

Mack's Square Root Extractor

Macroeconomic Effects of Interest Rate Cuts

Macrostates and Microstates

Magic Cube

Magic Cube of Order 5

Magic-Eye Computational Solution

Magic Hexagon

Magic-Like Squares

Magic-Like Squares (German)

Magic Multiplications with Digits

Magic Number Bidding

Magic Numbers in the Nuclear Shell Model

Magic Square

Magic Square Puzzle

Magic Squares and Designs

Magic Squares for Odd, Singly Even, and Doubly Even Orders

Magic Squares from Latin Squares

Magic Zero Hexagons

Magnetic Braking

Magnetic Circuits

Magnetic Dipole in a Uniform Magnetic Field

Magnetic Field and Magnetic Induction in a Cylindrical Bar Magnet

Magnetic Field Induced by a Current-Carrying Wire

Magnetic Field of a Current Loop

Magnetic Field of a Cylindrical Bar Magnet

Magnetic Field of a Hollow Cylindrical Magnet

Magnetic Field of a Solenoid

Magnetic Fields for a Pair of Parallel Currents and for a Ring Current

Magnetic Flux through a Loop of Wire

Magnetic Force on a Sliding Bar

Magnetic Hysteresis

Magnetic Monopoles and Free Quarks

Magnetic n-gon Billiards

Magnetic Resonance and Bloch Equations

Magnetic Resonance Imaging (MRI)

Magnetic Shielding Effect of a Spherical Shell

Magnetization Using an Ising Model Based on a Search-Update-Feedback Cellular Automata (SCA) Approach

Magnetization with an Ising Model Based on Q2R Cellular Automata

Magnetizing Current Waveform in an Ideal Saturable Inductor

Magnet Types in Particle Accelerators

Magnified Views of the Mandelbrot Set

Magnifying Glass

Major Multinational Languages

Make a Sphericon

Make Mazes on a Moebius Strip

Make Your Own Ruled Surface

Make Your Own Solar System

Making 2D Art Using 3D Graphics

Making 3D Op Art Motifs

Making a Color Spinner

Making a Hexagon Using a Fold-and-Twist Algorithm

Making a Strip of Isosceles Trapezoids

Making Change for a Purchase

Making Change with U.S. Currency

Making Custom Photo Collages

Making Kaleidoscopes

Making Music!

Making Necklaces

Making Patterns

Making Patterns with Wang Tiles

Making Some Simple Molecules

Making the Three Areas Defined by Congruent Overlapping Circles Equal

Mamikon's Method for the Area of the Cycloid

Mamikon's Method for the Area under a Parabola

Mamikon's Proof of the Pythagorean Theorem

Mandala Creator

Mandala Ornament with Cardioid, Circles and Clover

Mandelbrot's Binomial Measure Multifractal

Mandelbrot Set Doodle

Mandelbrot Set Print

Manganese Oxidation States

Manipulability Ellipsoid of a Robot Arm

Manipulable Complete Graph

Manipulable Petersen Graph

Manometers

Manually Connecting Two Terminals with a Path Made of Copies of a Single Trapezoid

Manufacturer, Maintenance Contractor and Joint Profits

Many Sine Curves

Map Coloring on a Torus

Map-Coloring the Interior Regions Defined by the Diagonals of a Regular Polygon

Map Maker

Mapping a 3D Point to a 2D Triangle

Mapping a Convergent Sequence by a Continuous Function

Mapping an Interval by a Cubic Polynomial

Mapping an Interval to Another

Mapping a Square by Complex Functions

Mapping Circles by a Linear Fractional Transformation

Mapping Contour Integrals

Mapping Displacement between Images

Mapping Letter Frequency to a Keyboard

Mapping Lines and Circles onto the Riemann Sphere

Mapping Photographic Images to 3D Surfaces

Mapping Rectangles by the Elementary Transcendental Functions

Mapping Sierpinski Triangles onto Polyhedra

Mapping the Maxima for a Nonisothermal Chemical System

Maps of a Complex Variable

Marble Probability

Marbles Puzzle

Marcus Theory for Electron Transfer in Photosystem II

Marcus Theory of Electron Transfer 1: Classical versus Semi-classical Models

Marcus Theory of Electron Transfer 2: Semiclassical Marcus Equation in Three Dimensions

Marcus Theory of Electron Transfer 3: Interactive Potential Energy Surfaces for Charge Separation

Marcus Theory of Electron Transfer 4: Classical Marcus Equation in Three Dimensions

Marcus Theory of Electron Transfer 5: Two-Dimensional Bell-Shaped Marcus Curves

Marcus Theory of Electron Transfer 6: Solvent Reorganization Energy

Marcus Theory of Electron-Transfer Reactions

Marden's Theorem

Marginal Normality Does Not Imply Bivariate Normality

Marginal Utility Budget Line

Market Structure and Market Power in Oligopoly

Markov Chain Monte Carlo Simulation Using the Metropolis Algorithm

Markov Volatility Random Walks

Mark-Recapture Investigation

Marquand's Representation of Boolean Functions

Martin Gardner's April Fool's Map

Martin's Map Artwork

Mascheroni's Construction of the Center of a Circle

Mass Balance in a Single-Stage Evaporator

Mass Balance in the Haber Process

Mass Balance of Binary Mixtures

Mass Balances for Binary Vapor-Liquid Equilibrium (VLE)

Mass Balances in Absorption and Stripping Units

Mass Balances in Evaporative Crystallization

Mass between Two Damped Springs

Mass Matrix Computation in the Finite Element Method

Mass Motion under a Variable Force

Mass on a Spring: Simple Harmonic Oscillator

Mass Oscillating between a Spring and a Damper

Mass Oscillating between Two Springs

Mass Sliding Down a Rotating Inclined Tube with Friction

Mass Spectrometer (Sector-Type Analyzer)

Mass Supported by Tension of Two Symmetric Wires

Mass Transfer between Adjacent Fluids in Laminar Flow

Mass Transfer in Binary Star Systems

Mass Transfer with Reaction in a Spherical Drop

Mass Units of Measurement

Mass with a Spring and a Rubber Band

Matching Faces in Two Polyhedron Nets

Matching Faces on a Net Using a Schlegel Diagram

Matching Symmetries of 3D Figures

Matching Symmetries of Friezes

Matching Symmetries of Plane Figures

Matching Temperature Data to a Normal Distribution

Matching the Faces of a Polyhedron Shown as a Map Projection to a Net

Material and Energy Balances in a Reactor with Heat Exchange

Mathematica 7's Discrete Distributions

Mathematica Characters

Mathematica Crossword Puzzle

Mathematical Model of the Immune Response

Mathematica Paint

Mathematics of Tsunamis

Mathematics Subject Classification 2000

Mathematics Subject Classification Graphs

Math Songs

MathSynth

Math Trivia Game

Matrix Addition and Subtraction

Matrix Multiplication

Matrix Norm and Spectral Norm

Matrix Rank of Arrays in Coprimality Tensor

Matrix Representation of the Addition Group

Matrix Representation of the Multiplicative Group of Complex Numbers

Matrix Representation of the Permutation Group

Matrix Solutions to Airy's Eigenvalue Problem

Matrix Transformation

Matrix Transformations: "F"

Matrix Transformations in Crystallography

Matrix Transpose

Maurer Rose Chords

Maurer Roses

Maxima and Minima for the Three-Variable Autocatalator

Maximal Unit Lengths in 3D

Maximize the Number of Vertices in an Equilateral Triangular Lattice

Maximizing a Bermudan Put with a Single Early-Exercise Temporal Point

Maximizing a Bermudan Put with Two Early-Exercise Temporal Points

Maximizing an Intermediate Reactant in a Continuous Stirred-Tank Reactor

Maximizing Apparent Velocity in a Camera's Frame

Maximizing Conversion to an Intermediate Product in a Chain of Three CSTRs in Series

Maximizing Conversion to an Intermediate Product in a Two-Stage CSTR

Maximizing Profit in Ore Mining

Maximizing Profit in Various Market Structures

Maximizing Selectivity in the Trambouze Reactions

Maximizing the Area of a Rectangle with Fixed Perimeter

Maximizing the Area of Some Geometric Figures of Fixed Perimeter

Maximizing the Present Value of Resource Rent in a Gordon-Schaefer Model

Maximizing the Viewing Angle of a Painting

Maximizing the Volume and Surface Area of Geometric Solids Inscribed in a Sphere

Maximizing the Volume of a Box

Maximizing the Volume of a Cup Made from a Square Sheet of Paper

Maximizing the Volume of a Cup Made from a Square Sheet of Paper III

Maximizing the Volume of a Cup Made from a Square Sheet of Paper ll

Maximizing the Volume of a Right Circular Cone with Given Slant Length

Maximum Absolute Column Sum Norm

Maximum Absolute Row Sum Norm

Maximum Area Field with a Corner Wall

Maximum Entropy Probability Density Functions

Maximum Fruit Salad

Maximum Heat Transfer by Liquids at Different Temperatures

Maximum Likelihood Estimation

Maximum Likelihood Estimation for Coin Tosses

Maximum Likelihood Estimation of Ordinary and Finite Mixture Distributions

Maximum Likelihood Estimators for Binary Outcomes

Maximum Likelihood Estimators with Normally Distributed Error

Maximum Rectangle Inscribed in a Circle

Maximum Size of Involute Gear Teeth

Maximum Sum Descent

MAX Puzzle

Maxwell-Bloch Equations for a Laser

Maxwell-Bloch Equations for a Two-Level System

Maxwell's Demon

Maxwell's Displacement Current

Mayan Pyramid

Mayo-Lewis Model for Copolymer Composition

Maze Generator and Solver

Mazes in a Rectangular Solid

Mazes Made with Random Characters

Maze Solving with a 2D Cellular Automaton

Mazes on 2n-Gons

Mazes on a Cone, Including Its Base

Mazes on a Cube Given by Six Views

Mazes on a Cylinder, Including Its Ends

Mazes on a Cylinder or Torus

Mazes on a Polyhedron with Six Views

Mazes on Archimedean Tilings

Mazes on a Torus

Mazes on Nets of Common Solids

Mazes on Nets of Rhombic Dodecahedra

Mazes on Polyhedra

Mazes on Polyhedra Maps

Mazes on Polyhedra Seen from Two Viewpoints

Mazes on Riemann Surfaces

Mazes on Schlegel Diagrams

Mazes on Surfaces

Mazes on the Edges of a Polyhedron

Mazes on Various Map Projections of the Earth

Mazes on Various Surfaces

Mazes Produced by Random Spanning Trees

McCabe & Thiele Graphical Method

McCabe-Thiele Graphical Method for a Non-Ideal Binary Mixture

McCabe-Thiele Method for Methanol/Water Separation

McCay-Griffiths Cubic

McNugget Problem and Frobenius Numbers

Mean and Single Prediction Bands for a Nonlinear Model

Mean and Standard Deviation of a Distribution

Mean Distance of Agents in Diffusion-Limited Aggregation

Meandric Systems

Mean, Fitted-Value, Error, and Residual in Simple Linear Regression

Mean, Median, and Quartiles in Skewed Distributions

Mean, Median, and Standard Deviation for Random Values

Mean, Median, Mode

Mean-Reverting Random Walks

Mean Value Theorem

Mean Value Theorem for Integrals and Monte Carlo Integration

Measurement of Electron e/m Using a Modified Magnetron

Measure of the Angle between Two Straight Lines

Measures of Network Centrality

Measures of Node Prominence on a Network

Measuring Angles Using Diagonal Lines

Measuring Angles with a Protractor

Measuring Distance and Orientation Using Camera and Lasers

Measuring Entangled Qubits

Measuring Flow Rates with a Pitot Tube

Measuring Gravity at the Surface of the Earth

Measuring Pulmonary Capacity

Measuring the Perimeter of a Koch Snowflake

Measuring the Specific Heat of a Substance with a Calorimeter

Measuring the Speed of Light with Marshmallows

Measuring with Two Jugs

Mechanical Involute Gears

Mechanical Sensitivity of Soft Testing Machines

Mechanical Work

Mechanics of the Chameleon Tongue

Mechanism for Constructing Regular Polygons

Mechanism for Drawing a Logarithmic Spiral

Mechanism of a Solar Cell

Mechanism to Generate a Hyperbolic Paraboloid

Medial Division of Triangles

Median Split

Median Theorem for Polygons

Meissner Effect in Superconductors

Meissner Tetrahedra

Melting Tile Illusion

Melvyn Knight's Problem

Membership Function

Members of International Organizations

Membrane Concentration Profile

Membrane Potential Responses to Ion Gradients

Membrane Reactor for an Equilibrium-Limited Reaction

Membrane Reactor to Improve Selectivity in Multiple Reactions

Membrane Separation of a Ternary Mixture

Memristor Based Chaotic System

Mendelian Inheritance Pedigree

Menelaus' and Ceva's Theorem for Spherical Triangle

Menelaus' Theorem

Menger Sponge Slices

Mercator's Instructions: The "Organum Directorium"

Mercury's Perihelion Precession

Mercury Transits

Merger Guidelines

Merging Mountains

Merging Schools of Fish

Mersenne Twister and Friends

Mertens Accumulation of Möbius Values

Mertens Conjecture

Merton's Jump Diffusion Model

Meshing Involute Gear Teeth

Meshless Approximation

Mesmerizing Pendulums

MESSENGER Spaceflight

Metal Compounds In Medicine

Metallicity Condition and Electronic Density of States in Achiral Single-Walled Carbon Nanotubes

Metamorphic Soccer Ball

Metamorphosis of a Cube

Metatron's Cube and the Platonic Solids

Methanol Synthesis Using Gibbs Free Energy Minimization

Method of Image Charges: Point Charge inside a Planar Capacitor

Method of Images in Electrostatics

Method of Integer Measures

Method of Joints to Solve a Truss Problem

Method of Lagrange Multipliers

Method of Sections to Solve a Truss

Method of Support Vector Regression

Method of Variation of Parameters for Second-Order Linear Differential Equations with Constant Coefficients

Methods of Social Choice

Methyl Acetate Synthesis Using a Reactive Distillation Unit

Methylation Index and Analysis of SRB-Mediated Mercury Methylation

Methyl Tert-Butyl Ether (MTBE) Decomposition with a Reactive Distillation Unit

Methyl Tert-Butyl Ether (MTBE) Synthesis with a Reactive Distillation Unit

Método de McCabe-Thiele (Spanish)

Michaelis-Menten Enzyme Kinetics and the Steady-State Approximation

Michaelis-Menten Enzyme Kinetics of Bi-Bi Reactions

Michaelis-Menten Kinetics for Hydrogen Peroxide-Catalase Reaction

Michaelis-Menten Kinetics in a Chemostat

Michael Jackson's Anti-Gravity Illusion

Michelson Interferometer and Haidinger Fringes

Michelson Interferometer with Equally Spaced Fringes

Michelson-Morley Experiment

Microbial Population Growth, Mortality, and Transitions between Them

Microbial Survival Curves with Asymptotic Residual

Microbial Survival Curves with Definite Thermal Death Time

Microbial Survival with Dissipating Disinfectant

Micro-Doppler Sonar Simulation

Microlensing Light Curve for Stellar Objects

Microwave Oven

MIDI Frequency Calculator

MIDI Keyboard Limits

MIDI PPQN Duration Calculator

Midpoint and Centroid Formulas

Midsphere Tetrahedra and the Canonical Tetrahedron

Mid-tone Contrast Enhancement of Photographic Images

Milk Centrifugation to Cream and Skim

Miller Indices for a Simple Cubic Lattice

Millikan Oil-Drop Experiment

Mimicking the Kuramoto-Sivashinsky Equation Using Cellular Automaton

Minimal and Maximal Surfaces Generated by the Holomorphic Function log(z)

Minimal Coloring of Platonic Solids

Minimal Colorings of Archimedean Solids

Minimal Crossings for Complete Graphs

Minimal Disjunctive Normal Form

Minimal Enclosing Circle

Minimal Enclosing Sphere

Minimal Hodgkin-Huxley Model: DC Stimulus

Minimally Squared Rectangles

Minimal Model of Simulating Prices of Financial Securities Using an Iterated Finite Automaton

Minimal ORAC Kinetic System: Mathematical Analysis

Minimized Volume for Reactors in Series

Minimizing the Perimeter of a Sector with Given Area

Minimizing the Rosenbrock Function

Minimizing the Surface Area of a Cylinder with a Fixed Volume

Minimizing the Time for a Dog to Fetch a Ball in Water

Minimum Area between a Semicircle and a Rectangle

Minimum Distance between Two Circles in 3D

Minimum Distance Explorer: Circle to Enclosed Polygon

Minimum Number of Managers

Minimum of a Function Using the Fibonacci Sequence

Minimum Surface Area of a Capped Hexagonal Prism

Minkowski Linear Combinations of Two Line Segments

Minkowski Spacetime

Minkowski's Question Mark Function

Minkowski Sum of Convex Robot and Obstacle

Miquel's Pentagram Theorem

Miquel's Theorem

Mirage

Mirror Flip Transpose

Mirror Symmetries of the Cube

Miscible Displacement of Oil in Heterogenous Porous Media

Missing (or Extra) Square Optical Illusion

Missing Voters

Mitering a Closed 3D Path

Miter Joint and Fold Joint

Mittag-Leffler Expansions of Meromorphic Functions

MIU Explorer

Miura Map Folding and Unfolding

Mixed and Improper Fractions

Mixed Base Gray Codes

Mixed Boundary-Value Problem for the One-Dimensional Heat Equation

Mixed Radix Number Representations

Mixing and Infection in a Two-Group SIS Model

Mixing and Segregation in Chemical Reactors (CSTR versus PFR)

Mixing Cell Model Applied to Transport in Porous Media

Mixing-Cell Model for the Diffusion-Advection Equation

Mixing Colors with Blend

Mixing Entropy for Three Letters

Mixing in Two Connected Tanks

Mixing in Two Tanks

Mixing of Quantum Particles Influenced by Nodal Points in the Causal Interpretation

Mixing Salt in Water in One Tank

Mixtilinear Incircles

Mobile Automaton with Memory

Mobile Robot with Single Manipulator

Mock Theta Functions

Model for a Freezing Food Slab

Model for Crystallization in 2D

Model for Earthquake on a Tall Building

Model for the Formulation of Multilayered Emulsions

Modeling a One-Cycle THz Radiation Waveform Moving through Biological Tissue

Modeling a Pseudosphere with Cones

Modeling a Simple Roller Coaster

Modeling a Staircase

Modeling Asteroid Trajectories in 3D

Modeling Blood Glucose Levels

Modeling Disease Dispersion across Two Cities

Modeling Diurnal Photosynthesis

Modeling Leaf Photosynthesis and Photorespiration in Current and Future Environments

Modeling Light Curves

Modeling of Arm-Z with AnglePath3D

Modeling Parasitoid-Host Dynamics with Delay Differential Equations

Modeling Photosynthetic Responses to Carbon Dioxide

Modeling Photosynthetic Responses to Light

Modeling Photosynthetic Responses to Temperature

Modeling Return Distributions

Modeling Ruled Surfaces with Threads

Modeling the Atomic Structure of an Ice Crystal

Modeling the Hyperboloid of One Sheet

Modeling the Menger Sponge

Modeling Transpiration of Leaves

Modeling World Student Populations

Model Modal Modulo 18

Model of a Firefly Swarm

Model of an Immobilized Biocatalyst Tubular Reactor

Model of an Industrial Robot Arm

Model of Electrical Activity in Human Pancreatic Beta Cells

Model of Immune Response with Time-Dependent Immune Reactivity

Model of Microbial Nutrient Uptake

Model of Shell Growth

Model of Snake Locomotion by Frictional Forces

Model of Temperature Variation inside a Building

Models for Edge States in the Electronic Spectra of Dimer Chains

Modern Portfolio Theory

Modern Thread Lampshade

Modificaciones de la función cuadrátrica (Spanish)

Modificaciones de la función cúbica (Spanish)

Modified Divisor Methods

Modified Lights Out Game and Solver

Modified Logistic Isothermal Microbial Growth Ratio

Modifying Overall Image Brightness

Modify Simple Life

Mod Mod Zoom

Modulaciones AM (Spanish)

Modular Addition, Multiplication, and Exponentiation

Modular Arithmetic

Modular Arithmetic Tables

Modular Interference Diagrams

Modular Inverses

Modular Multiplication on a Circle

Modular Music

Moduli Space of Shapes of a Tetrahedron with Faces of Equal Area

Modulus Counting

Möbius Collar

Möbius Monorail

Möbius Mu Function Walk

Möbius Net Corner

Möbius Star

Möbius Strip as a Half-Twisted Square Torus

Möbius Strip Made from a Rotating Bar

Möbius Strips from the Faces of Polygonal Prisms

Möbius Transformations on the Complex Plane and Riemann Sphere

Möbius Transforms

Möbius Triangles

Mohr's Arbelos and Lamé's Ellipsoids

Mohr's Circle

Mohr's Circle and Failure Criterion for Planar Stress States

Mohr's Circle and Stress Transformations

Moineau Progressing Cavity Pump

Moiré Pattern of Two Equally Spaced Circular Ring Patterns

Moiré Pattern of Two Fresnel Zone Plates

Moiré Pattern of Two Straight Line Patterns

Moiré Patterns

Moiré Patterns and Commensurability in Rotated Graphene Bilayers

Molar and Mass Concentration Conversion for Electrolytes

Molarity of Aqueous Salt Solutions

Molecular Dynamics of Lennard-Jones Particles Using the Velocity Verlet Algorithm

Molecular Electrostatic Potential Maps (MEPs) of Some Polar Molecules

Molecular Graphs

Molecular Graph Theory Applied to Fullerenes

Molecular Motion in Solids, Liquids, and Gases

Molecular Orbitals for First- and Second-Row Diatomic Molecules

Molecular Pie Charts

Molecular Point Groups

Molecular Weight Distribution in Equilibrium Step-Growth Polymerizations

Molecule Construction Set

Molecules Distributed between Two Compartments

Molien Series for a Few Double Groups

Mollow Triplet

Moment of a Force about a Point

Moment of Inertia

Moment of Inertia of a Cylinder about Its Perpendicular Axis

Momentum Eigenstates

Mona Lisa and the Golden Rectangle

Monarch Butterfly Life Cycle

Mondrian Art Problem

Mondrian Four-Coloring

Mondrian Puzzles

Mondrian's Cubes

Monetary Policy in Krugman's Model of a Liquidity Trap

Money Creation in the Banking System

Money Supply Process

Mong

Monge-Kantorovich Transportation Problem

Monge Point of a Tetrahedron

Monodromy of z^n + b z + 1 = 0

Monoliths in Cellular Automaton 146

Monopolistic Competition with a Homogeneous Product

Monopolist's Profit Maximization

Monopoly and Natural Monopoly

Monopoly Model

Monopoly Profit and Loss

Monopoly Profit-Maximization with Quadratic Marginal Cost

Monopoly with Two Plants

Monopsony in the Labor Market

Monte Carlo Clique Search

Monte Carlo Estimate for Pi

Monte Carlo Estimation of Area

Monte Carlo Expectation-Maximization (EM) Algorithm

Monte Carlo Methods to Estimate Area

Monte Carlo Model of Charge Recombination in Feldspars

Monte Carlo Sampling Coverage

Monte Carlo Simulation of Line-of-Sight Distance Measurements

Monte Carlo Simulation of Markov Prisoner

Monte Carlo Simulation of Retirement Savings with Variable Annual Return

Monte Carlo Simulation of Two-Electron Spin Correlations

Monte Carlo Valuation of an Option

Montmort's Problem

Montucla's Rectangle-to-Rectangle Dissection

Monty Hall Paradox

Monty Hall Problem

Moon Lander

Moon Landing Simulation

Moore-Spiegel Attractor

Moral Hazard

Moral Hazard and Least-Cost Contracts: Impact of Changes in Agent Preferences

Moral Hazard and Least-Cost Contracts: Impact of Changes in Conditional Probabilities

More Uniform Polyhedra

Morley's Theorem

Morphed Tetrahedral Bezier Surfaces

Morphing a Möbius Strip into a Torus

Morphing Cartesian to Polar Coordinates

Morphing from Plot to Log Plot

Morphing the Császár Polyhedron

Morphing the Graph of a Function to Its Domain

Morphing Wallpaper Functions

Morphological Euler Number from the Polar Plots of Sine Functions

Morphological Operations in Binary Images

Morphological Processing

Morph Sphere to Disc

Morris-Lescar Model of Membranes with Multiple Ion Channels

Morse Code Emitter

Morse-Smale Flows on a Tilted Torus

Mortal Fibonacci Rabbits

Mortgage Calculator

Mosaic Effect for Photographic Images

Moser Spindles, Golomb Graphs and Root 33

Most Common Angles

Motion Blur

Motion Diagram

Motion Grouping

Motion in a Central Field

Motion in a Gaussian Potential

Motion in a Tunnel through the Earth

Motion in Two Dimensions with Constant Acceleration

Motion of a Bead on a Spoke

Motion of a Charged Particle in an Electromagnetic Field

Motion of a Conical Pendulum

Motion of a Disk Hanging from a Spring on an Inclined Plane

Motion of a Driven Damped Oscillator

Motion of a Dumbbell Acted on by Constant Forces

Motion of an n-Point Dynamical System

Motion of an Object Subject to Forces in One Dimension

Motion of a Parachuter

Motion of a Particle Colliding with Massive Objects

Motion of a Particle in Crossed Electric and Magnetic Fields

Motion of a Pendulum in the Wind

Motion of a Planet around a Star

Motion of a Rolling Disk Driven by a Rod and Spring

Motion of a Simple Pendulum with Damping

Motion of a System Consisting of a Rolling Cart, Pendulum, and Spring

Motion of Atoms in Crystal

Motion of Exploding Projectile

Motion of Particles in Ocean Waves

Motion of Pendulum Interrupted by a Peg

Motion of Pendulum with Varying Length

Motion of Projectile with or without Air Resistance

Motion of Quadruple Pendulum

Motion of Single Ion in a Linear Paul Trap

Motion of the Moon: Eclipses

Motion of the Moon: Phases

Motion of Three Magnetic Vortices

Motion of Two Balls Connected by a Rod

Motion of Two Masses Connected by Springs

Motion on a Surface

Motion on Surface of the Earth: Coriolis Force

Motion Parallax versus Depth, 2D (Visual Depth Perception 12)

Motion Parallax versus Depth, 3D (Visual Depth Perception 13)

Motion Planning for Robot Path around Obstacles

Motion, Pursuit, Fixate, and Distractor (Visual Depth Perception 2)

Motion/Pursuit Law in 1D (Visual Depth Perception 1)

Motion/Pursuit Law in 2D (Visual Depth Perception 3)

Motion/Pursuit Law on Invariant Circles (Visual Depth Perception 4)

Motion/Pursuit Ratio and Depth in 1D (Visual Depth Perception 17)

Motion/Pursuit Ratio and Depth in 2D (Visual Depth Perception 18)

Motions of a Hexapod Robot

Motions of a Simulated Damped Harmonic Oscillator

Motion Traced on the Torus and Klein Bottle

Motorcycle Graphs

Motzkin Number Diagrams

Motzkin Numbers and Their Geometrical Interpretation

Mountainscape

Movable Concentric Color Rings

Movement between Three Populations in a Closed System

Movement of an Edge Dislocation

Movement of an Oloid

Moving a Circle in a Parabola

Moving a Couch around a Corner

Moving-Average Discrete Filters

Moving Eyes

Moving Fingers with Affine Transformations

Moving Pearl Chains in 3D

Moving Stick Figures

Moving the Vertices of the Great Rhombicuboctahedron

Moving Two Particles with Shared Control Inputs Using Wall Friction

Moving Wave Analysis

Mrs. Perkins's Quilts

Müller-Lyer Illusion

Multi-Bug Problem with Variable Speeds and Gaps

Multicolored Turmites

Multicolor Neighbor-Dependent Substitution Systems

Multicolor Random Array of Squares

Multicomponent Batch Distillation

Multicomponent Distillation Column

Multicomponent Distillation Column with a Sidestream

Multicomponent Distillation: The Case of Pentane/Hexane/Heptane System

Multicomponent Simple Batch Distillation

Multidimensional Scaling

Multi-Force Newtonian Particle Simulator

Multilanguage Word Lengths

Multilayer Photonic Bandgap

Multilingual Palindromes

Multi-Particle Evolution Map

Multiple Angle Formulas for Sine and Cosine

Multiple Derivatives

Multiple-Effect Evaporation of Sugar Solution

Multiple Ferris Wheels

Multiple Input Parameters for TRIZ Matrix Application

Multiple-Link Functions

Multiple Multiply Sided Dice Probability

Multiple Nets for a Cube

Multiple Nets of an Octahedron

Multiple Nets of a Triangular Dipyramid

Multiple Planes through Surfaces

Multiple Reactions in a Continuous Stirred-Tank Reactor with Heat Effects

Multiple Reactions in a CSTR with Heat Effects Using Arc-Length Continuation

Multiple Reflections in Two Mirrors

Multiple Reflections of a Regular Polygon in Its Sides

Multiple Reflections of a Rotating Triangle

Multiple Reflections of a Superball

Multiple Signals in Nuclear Magnetic Resonance

Multiple Slit Diffraction Pattern

Multiple States in an Isothermal Continuous Stirred-Tank Reactor

Multiple Steady States in a Continuously Stirred Tank Reactor

Multiple Steady States in a Continuous Stirred-Tank Reactor with Heat Exchange

Multiple Steady States in Continuous Culture with Substrate Inhibition

Multiples with Only the Digits 0 and 1

Multiple Tubular Reactors with Interstage Cooling

Multiplication as Jumping

Multiplication Bingo

Multiplication by Adding Logs

Multiplication Flash Cards

Multiplication Made Easy

Multiplication of Fractions

Multiplication of Hazard in Expo-Power Distributions

Multiplication of Hazard in Gompertz-Makeham Distributions

Multiplication of Integers

Multiplication Table

Multiplication Table Mod m

Multiplication Tables for the Group of Integers Modulo n

Multiplicative Functions

Multiplicative Interactions

Multiplying a Double-Digit Number by a Single-Digit Number

Multiplying a Matrix by a Number

Multiplying a Monomial and a Linear Polynomial

Multiplying Binomials

Multiplying Complex Numbers

Multiplying Fractions

Multiplying Mixed Numbers

Multiplying Probabilities

Multiplying with Lines

Multipoint Padé Approximants

Multipole Expansions of Electric Fields

Multipole Fields

Multipole Shapes

Multipurpose Tool

Multirate Signal Processing: Downsampling

Multirate Signal Processing: Upsampling

Multisecting an Angle Using Archimedes's Spiral

Multiseed 2D Cellular Automata

Multiseed Averaged 2D Cellular Automata

Multiset Partitions

Multistage Batch Distillation

Multistage Batch Distillation with Azeotrope

Multistage Operation with Cold-Shot Cooling

Multiterm Nestedly Recursive Functions

Multi-Time Bifurcations of Wavefronts in 2D and 3D

Multivariable Derivative Test

Multivariable Epsilon-Delta Limit Definitions

Multiwavelet Sets in the Plane

Multiway Systems

Multiway Systems Based on Numbers

MU-MIMO Beamforming by Constructive Interference

Munching Square Thresholds

Munker-White Illusion

Musical Animated Large-Angle Pendulums

Musical Instruments and Colored Surfaces

Musical Interval Recognition

Musical Interval (Relative Pitch) Test

Musical Lines and Curves

Musical Logo Widget

Musical Scales

Musical Scales and Modes in Every Key

Musical Variables: Modes and Instruments

Music Box Toy with Elementary Cellular Automata

Music Box with Rotating Ballerina

Music from the Game of Life

Music from the Rationals

Music Note and Melody Synthesizer

Mutual Information between Boolean Net Regions

Mutualism and Evolutionary Multiplayer Games: Revisiting the Red King Effect

Mysterious Numbers from Gold List Approximants

Nagel's Theorem

Named Binary Cartesian 2D String Rewriting Systems

Named Colors

Nanotube Builder

Napier's Bones

Napier's Inequality (I)

Napier's Inequality (II)

Napkin Chess

Napoleon's and van Aubel's Theorems

Napoleon's Theorem

Narayana Numbers

Nash Equilibria in 3×3 Games

Nash Equilibria with Continuous Strategies

Natatory Bladder of a Fish

National Cardiovascular Data Registry (NCDR) Cath PCI Risk Score System

National Football League In-Game Probability

Natural Convection between Two Vertical Plates

Natural Language Neutral Symbolism in Propositional Logic

Natural Logarithm Approximated by Continued Fractions

Natural Modes of Vibrations for Some Simple Systems

Navier Solution for a Singularly Loaded Kirchhoff Rectangular Plate

N-Body Problem in 2D

n-Digitaddition

Nearest Center Orbit Twins

Nearest Hexagonal Positions

Nearest in a Crowd

Nearest Named RGBColor

Nearest Neighbor Graph Connections

Nearest Neighbor Networks

Near-Miss Johnson Solid with Diamonds

Near-Penrose Shapes

NEAR Shoemaker Spaceflight

Nearsightedness and Farsightedness

Neat Alternating Tilings of the Plane

Necker Cube

Necker Cube: A Variation

Negabinary Numbers to Decimal

Negative Disk Magnifier Illusion

Negative Externality

Negative Pedal Curves of an Ellipse

Negligible Senescence Scenario

Neighbor-Dependent Network Systems

Neighbor-Dependent Substitution System

Neighbor-Dependent Substitution Systems of Two Kinds

Neighborhood Graphs with HITS and SALSA

Neighborhood Ranges

Neighborhoods of Nearby Stars

Nelson Mandela Tribute

Nernst Equation for Cellular Membranes

Nested Gears

Nested Helices

Nested Image Rotations

Nested Perforated Cubes

Nested Polygon Disks

Nested Regular Polygons

Nested Square Root Representation of the Golden Ratio

Nested Structure of the Continued Fraction of Liouville's Constant

Nested Trigonometric Function Plots

Net and Gross Reserve of Life Insurance

Net for Schwarz's Lantern

Net Lease Economics

Net of the Pentagrammic Antiprism

Net Present Value

Nets for a Two-Cube Calendar

Nets for Bilinski's Dodecahedron

Nets for Cowley's Dodecarhombus and Related Solids

Nets for Polyhedral Approximations of the Sphericon

Nets for Regular Spherical Models

Nets for Some Triacontahedron Stellations

Nets for the Császár Polyhedra

Nets for the Rhombic Icosahedron

Nets of Polyhedra

Nets of Polyhedra with Selected Op Art Motif

Nets of Polyhedra with Texture

Nets of Regular Compounds

Nets of Some Icosahedron Stellations

Nets of Some Simple Polyhedron Compounds

Network Centrality Using Eigenvectors

Network Motifs and Graphlets

Network of Musical Instruments for Rhythm Accompaniment

Networks for Basic Number Theoretic Functions

Networks of Space Flights by American Pre-Shuttle Astronauts

Network View of Conway's Game of Life

Neuberg Cubic

Neural Cryptography

Neural Impulses: The Action Potential in Action

Neural Network for a Basic Truth Table

Neuronal Bursting

Neutrino Oscillations

Newcomen Steam Engine

New Horizons Spaceflight

Newton-Cotes Quadrature

Newton-Cotes Quadrature Formulas

Newton Flows of Polynomials

Newtonian Gravitational Wave Chirp Signal from Merger of a Compact Binary

Newtonian Reflecting Telescope

Newtonian Telescope

Newton-Leibniz Formula Test

Newton Polygon and Branching of Algebraic Curves

Newton's Color Wheel

Newton's Ellipse

Newton-Simpson's Formula for the Volume of a Prismatoid

Newton's Integrability Proof

Newton's Law of Cooling

Newton's Method

Newton's Method in p-adic Form

Newton's Method of Drawing the Cissoid of Diocles

Newton's Method on a Mesh of Initial Guesses

Newton's Pi Approximation

Newton's Polynomial Solver

Newton's Projectile

Newton's Rotating Bucket Experiment

Newton's Second Law

New York City Subway Stations

n-Flakes

NFL Quarterback Passer Rating

NFL Teams Map

n-Fountains

n-gon Polynomials

Nicomedes's Geometric Construction of Principal Cube Root

Nicomedes's Mechanism for Constructing a Conchoid

Nilpotent Matrices in Jordan Decompositions

Nine-Point Circle

Nine-Point Circle in the Complex Plane

Nine-Point Cubic

Nine Summits Quiz

n+l Rule for Atomic Electron Configurations

NMR Signal Processing Lab: Two Spins-1/2

Noble's Square Root Calculator

Nodal Domains of Spherical Harmonics

Nodal Points in Bohmian Mechanics

Nodal Surfaces of Degenerate States

Nodes in Optical Fibers

No-Four-In-Plane Problem

Noise Cancellation in Headphones

Noise Retrieval from Averaged Sequences

Noise Temperature of a Radar System

Nomogram for the Geometric Mean

Nomogram of p and s Reflectances for an Ambient-Film-Substrate System

Nomography for Beginners

Nonadiabatic Tubular Reactor with Negligible Mass Dispersion

Nonadiabatic Tubular Reactor with Recycle

Noncircular Planetary Drive

Noncircular Roller Drive

Noncoplanar Lines

Noncrossing Partitions

Non-Crossing Rule for Energy Curves in Diatomic Molecules

Nondiscriminating Monopolist with Two Independent Markets

Non-Euclidean Triangle Continuum

Nonexistence of a Multivariable Limit

Non-Ideal Vapor-Liquid Equilibrium (VLE) Modeled by the Margules Equation

Nonisothermal Degradation Kinetics

Nonisothermal Effectiveness Factor (The Weisz and Hicks Problem)

Nonlinear Chemical Dynamics: The Peroxidase-Oxidase Reaction

Nonlinear Coupled Oscillator

Nonlinear Image Filtering

Nonlinear Impedance of Tafelian Electrochemical Systems

Nonlinearized Motion of a Simple Pendulum

Nonlinear Warping

Nonlinear Wave Equation Explorer

Nonlinear Wave Equations

Nonlinear Wave Resonances

Nonlocal Cellular Automata

Nonlocality in the de Broglie-Bohm Interpretation of Quantum Mechanics

Non-logarithmic Slide Rule

Nonogram from Photo

Nonograms from Invaders

Nonparametric Additive Modeling by Smoothing Splines: Robust Unbiased-Risk-Estimate Selector and a Nonisotropic-Smoothing Improvement

Nonparametric Curve Estimation by Kernel Smoothers: Efficiency of Unbiased Risk Estimate and GCV Selectors

Nonparametric Curve Estimation by Kernel Smoothers under Correlated Errors

Nonparametric Curve Estimation by Smoothing Splines: Unbiased-Risk-Estimate Selector and its Robust Version via Randomized Choices

Nonparametric Density Estimation: Robust Cross-Validation Bandwidth Selection via Randomized Choices

Nonparametric Regression and Kernel Smoothing: Confidence Regions for the L2-Optimal Curve Estimate

Nonparametric Simulation

Nonperiodic Substitution Tiling of the Plane

Non Placet Net of a Dodecahedron

Nonplanar Rectangular Heptagons

Non-Renewable Resource Economics

Nonsense Sentence Generator

Non-Sinusoidal Oscillation: A Balloon on a String

Non-Spherical Geodesic Structures

Nonstationary Heat and Mass Transfer in a Porous Catalyst Particle

Nonsteady-State Heat Conduction in a Cylinder

Non-Terminating Reversal-Addition

Nonuniqueness of Option Pricing Under the Meixner Model

Nordstrand's Weird Surface

No Repeated Distances

Normal and Log-Normal Probability Density Functions with Identical Mean and Standard Deviation

Normal and Shear Coupling for Unidirectional Angle Ply

Normal Approximation to a Binomial Random Variable

Normal Approximation to a Poisson Random Variable

Normal Curvature at a Regular Point of a Surface

Normal Distribution with Continued Fractions

Normal Forces Can Do Work

Normal Forms for Logic Problems

Normalized B-Bases for Trigonometric Polynomial Curves

Normalized C-Basis and C-Curves

Normalizing Vectors

Normal Lines to a Parabola

Normal Modes in a Periodic Monatomic Linear Chain

Normal Modes in a Periodic Square Lattice

Normal Modes of a Beaded String

Normal Modes of a Circular Drum Head

Normal Modes of a Double Pendulum

Normal Mode Vibrations of Buckminsterfullerene (C60)

Normal Oscillatory Modes of Rotating Orthotropic Disks

Normal Sections and Gauss Map for the Hyperbolic Paraboloid

Normed Line

Nosquare Puzzle

No Supply Curve in a Monopolistic Market

Note Frequencies on Musical Scale

Note Placement on the Four Common Musical Clefs

Note Positions on a Violin

No-Three-in-Line Problem

November 7, 2012

Nowhere-Neat Squaring the Rectangle

Nowhere-Neat Squaring the Square

Nowhere-Neat Tilings

Nowhere-Neat Tilings of the Plane

Nowhere-Neat Tilings of the Plane, Part 2

n-Player Chessboards

NPV and its Contributions

n-Sectors of the Angles of a Triangle

N-Step Transition Matrices for Markov Chains

nth Roots of a Complex Number

Nuclear Fission

Nuclear Liquid-Drop Model Applied to Radioactive Decay Modes

Nuclear Magnetic Resonance Spectrum of Ethanol

Nuclear Meltdown on Mars

Nucleation Rates for Cd-Se Nanoparticles

Nucleophilic Substitution (SN1) Reactions

Nucleophilic Substitution (SN2) Reactions

Nullcline Plot

Null Distribution of the Correlation Coefficient

Numbered Cube

Number Guessing with Binary Numbers

Number Guessing with Ternary Numbers

Numbering the Vertices of Polyhedra

Number Lines

Number Line Solutions to Absolute Value Equations and Inequalities

Number Magic with Squares

Number of Cannonballs in Piles of Different Shapes

Number of Cubes Removed

Number of Cubes Stacked in a Corner

Number of Digits in Base k Expansion of Fractions

Number of Finite Groups

Number of Handshakes

Number of Horizontal Rhombuses

Number of Normals to a Curve

Number of Repeating Digits in Base b Expansion of Fractions

Number of Squares in a Square

Number of Ways to Complete a True/False Test

Numbers as Sets

Numbers in Various Bases

Number Systems in 3D

Number Systems Using a Complex Base

Number-Theoretic Construction of Digital Circles

Number Theory Tables

Numerical Approximation of the Fourier Transform by the Fast Fourier Transform (FFT) Algorithm

Numerical Calculation of Eigenfunctions for Finite Square-Well Potential

Numerical Evaluation of Some Definite Integrals

Numerical Example of One-Way ANOVA

Numerical Flowers

Numerical Instability in the Gram-Schmidt Algorithm

Numerical Integration by Simpson's 1/3 and 3/8 Rules

Numerical Integration Examples

Numerical Integration of the Logistic Equation Using Runge-Kutta Methods

Numerical Integration: Romberg's Method

Numerical Integration using Rectangles, the Trapezoidal Rule, or Simpson's Rule

Numerical Inversion of the Laplace Transform: The Fourier Series Approximation

Numerical Inversion of the Laplace Transform: The Zakian Method

Numerical Iso-Optic Curve of the Ellipse

Numerical Methods for Differential Equations

Numerical Range for Some Complex Upper Triangular Matrices

Numerical Solution of Some Fractional Diffusion Equations

Numerical Solution of the Advection Partial Differential Equation: Finite Differences, Fixed Step Methods

Numerical Solution of the Dispersion Equation for a First-Order Reaction

Numerical Solution of the Falkner-Skan Equation for Various Wedge Angles

Numerov Solutions for Single- and Double-Well Potentials

Nuremberg Scissors

Nutation of a Symmetric Top

Nutts Puzzle

Observed Distribution of Random Chord Lengths in a Circle

Observing Magnetic Fields with Iron Filings

Obtuse Angle Shadowing Networks and Distance-Based Interpolation

Obtuse Random Triangles from Three Parts of the Unit Interval

Obtuse Random Triangles from Three Points in a Rectangle

Occurrence versus Claims-Made Insurance Policies

Octagram-to-Square Dissection

Octahedra Constructed from Eight Identical Triangles

Octahedral Ring

Octahedral Rotational Symmetry Types

Octahedral Vase

Octahedron Decorated with Polygons

Octahedron Fractal

Octahedron Frame Made of Rhombic Dodecahedra

Octahedron in a Sphere

Octahedron Stars

Octahedron to Small Rhombicuboctahedron

Octonion Algebra Multiplication Tables

Octonions and the Fano Plane Mnemonic

Odd-4 Graph, Fano Planes, and the Coxeter Graph

Odd and Even Values of Divisor Functions

Odd Disk Overlap

Odd Number Theorem

Odd One Out

Odd One Out 3

Odd One Out 4

Odd Ones Puzzle

Odd or Even

Offset Slider-Crank Mechanism

Offspring of Adam and Eve

Ohmic Drop and Uncompensated Electrolyte Resistance in an Electrochemical Cell

Ohm's Law

Ohm's Law for Alternating Currents

Oil-Drop Experiment

Oil Mallee Farming Optimization Problem

Oil Well Decline Modeling Using Hyperbolic-Exponential Forecasting

Olbers's Paradox

Oldham Coupling

Oloid

Olympic Logos Based on Hanegraaf's Dissection of a Dodecagon to Five Dodecagons

Olympic Medal Times in the Men's 100 Meter

Olympic Pole Vaulting

Omitted Variable Bias

Omitted Variable Bias in 3D

One- and Two-Word Palindromes

One-Dimensional Cellular Automata on the Regular Tessellations

One-Dimensional Cellular Automata with Memory

One-Dimensional Fractional Brownian Motion

One-Dimensional Heat Conduction with Temperature-Dependent Conductivity

One Disk Per Diagonal

One-Half the Apothem Times the Perimeter

One Interpretation of a Catalan Number Recurrence Relation

One Point Perspective

One-Sample t-Test and Confidence Interval with Dot Chart in Small Samples

One-Sided Fourier Transform: Application to Linear Absorption and Emission Spectra

One-Sided Polyominoes

One-Slit Diffraction Pattern

One-Soliton Nonlinear Schrödinger Equation with Arbitrary Linear Time-Dependent Potential

One Step of Runge-Kutta

One-Term Nestedly Recursive Functions

One to Zero Cellular Automaton Function

One-Vertex Origami Folding

One-Wheeled Robot-Gyrostat

One World Trade Center Antiprism

Onion Polyhedra

On the Areas of Triangles Associated with an Excircle

On the Ewing Model of Magnetism

On the Ewing Model of Magnetism 2

On the Fundamental Theorem of Phyllotaxis

On the Stability Limit of Leapfrog Methods

Ontology of the One-Dimensional Wavefunction in Bohmian Mechanics

On Which Side of a Directed Line Is a Point?

Opacity Explorer 2D

Opacity Explorer 3D

Op-Art

Op Art Block in Three-Point Perspective

Op Art Dominoes

Op Art Motifs on Quadrilaterals

Op Art on 2D Regions and 3D Surfaces

Op Art on a Sphere

Op Art on a Sphere and a Cylinder

Op Art on Golden Rhombic Solids

Op Art on Golden Rhombic Solids (II)

Op Art on Platonic Solids

Op Art on Polyhedra

Op Art on Surfaces

Op Art on the Poincaré Disk

Op Art with an Open, Flexible Four-Cube

Op Art with Block in Perspective

Op Art with Polygon Spirals

Op Art with Two Blocks in Perspective

Openable Cosine Dome

Openable Zonohedral Dome

Open a Cube

Open and Closed Belt Drive

Open and Closed Kaleidoscopes

Open Circuit Voltage Coupled into a Semi-Infinite Transmission Line by an Exponential, Plane Waveform

Open Dice Rolls

Open Flexible Frame Based on a Rhombic Dodecahedron

Opening a Door

Opening an Umbrella

Opening a Sphere

Open Meanders

Operating a Chemostat (CSTR Bioreactor)

Operating an AC Three-Phase Induction Motor

Operational Amplifier Gain-Bandwidth Characteristics

Operation of a Debutanizer

Operation of a Depropanizer

Operation of a Dividing Wall Column and a Petlyuk Column

Operation of a Knife Switch

Operation of a Memristor

Operation of an Absorption Column

Operation of an Air Conditioner

Operation of an Ethane Steam Cracker

Operation of an Ideal Belt Conveyor

Operation of a Partial Condenser

Operation of a Rectifying Column

Operation of a Stripping Column

Operation of a Throttling Valve

Operation of Heat Exchangers

Operations of C3v Symmetry Group Applied to Ammonia

Operations on a Rhombic Dodecahedron

Operations on Graphs

Operations on Sets

Opposite Coefficients Method for Solving Two Equations in Two Unknowns

Opposite Rotations of Frame Segments

Optical Activity of Tartaric Acid Stereoisomers

Optical Depth of Field Calculator for Cameras

Optical Filter with Sinusoidally Varying Permittivity Using Mathieu's Equation

Optical Illusion of the Extra Piece

Optical Illusions with Changing Colors

Optical Matrix Elements of Single-Walled Carbon Nanotubes for Longitudinal Polarization of Light

Optical Model of the Human Eye

Optical Properties of Biological Tissue in the THz Radiation Regime

Optical Properties of Graphene

Optical Pumping: Population Dynamics

Optical Pumping: Visualization of Steady State Populations and Polarizations

Optical Rogue Waves (Rogons)

Optical Rotation and Ellipticity

Optical Selection Rules for Zigzag Graphene Nanoribbons

Optics: Law of Reflection

Optimal Bin Packing with Random Lengths

Optimal Conditions for CO2/n-Hexane Flash Separation

Optimal Consumption Paths

Optimal Control of a Continuous Stirred-Tank Reactor

Optimal Economic Strategy for the Operation of a Batch Reactor with Dead Time

Optimal Induction of Foreign Protein Synthesis

Optimality of Greedy Change-Making

Optimal Joint Measurements of Qubit Observables

Optimal Magnification in X-Ray Imaging System

Optimal Operation of a Batch Reactor with Dead Time

Optimal Parameterization of Rational Quadratic Curves

Optimal Patch Exploitation

Optimal Queue of Cars

Optimal Rectangles for Circles

Optimal Setup of Two Continuous Stirred-Tank Reactors (CSTRs) in Series

Optimal Temperature Policy for a Reversible Reaction

Optimal Temperature Policy for First-Order Reversible Reactions

Optimal Transport Scheduling

Optimal Volleyball Spikes and Blocks

Optimization of Cobb-Douglas Function

Optimization of the Rosenbrock Banana Function

Optimized Preferential Pairings for Groups of Four

Optimize the Length of the Crease of a Folded Piece of Paper

Optimizing a Chain of Continuous Stirred-Tank Reactors

Optimizing a Gauss Gun

Optimizing Diffusion-Weighted MRI Using Electrostatic Repulsion

Optimizing Maleic Anhydride Production

Optimizing Temperatures and Volumes for Maximum Conversion to an Intermediate Reactant in a Chain of Two Continuous Stirred-Tank Reactors

Optimizing the Counterweight Trebuchet

Optimizing Tone Separation of Photographic Images

Optimum Cycle Period for Batch Reactor with Downtime

Optimum Temperature for Lactose Hydrolysis in Batch Reactors

Option Prices in Merton's Jump Diffusion Model

Option Prices in the Kou Jump Diffusion Model

Option Prices in the Variance Gamma Model

Option Prices under the Fractional Black-Scholes Model

Options Board Using Black-Scholes Prices

Options: Time Value

Orbison's Illusion

Orbital Dynamics in Field of Two Planets

Orbital Elements

Orbital Parameters

Orbital Resonance in the Asteroid Belt

Orbital Speed and Period of a Satellite

Orbital Transformations in Diels-Alder Reaction

Orbital Wobble

Orbit Diagram of the Hénon Map

Orbit Diagram of the Logistic Map

Orbit Diagram of Two Coupled Logistic Maps

Orbit Diagram of Two Coupled Logistic Maps with Delay

Orbit of a Launched Satellite

Orbit of a Test Charge in the Field of a Charged Ring

Orbits and Stabilizers of Groups Acting on Colorings of 4x4 Chessboards

Orbits around and through a Sphere

Orbits around a Spinning Black Hole

Orbits around Schwarzschild Black Holes

Orbits around the Lagrange Point L4

Orbits of a Triple Pendulum

Orbits of Martin's Map

Orbits of the Chirikov Standard Map

Orbits of the Gingerbreadman Map

Orbits of the Hopalong Map

Orbits of the Tent Function's Iterates

Orbit Spectral Density in Olfactory Signal Processing

Orbits with Epicycles on a Deferent

Orchard-Planting Problem

Order, Chaos, and the Formation of a Cantor Set Attractor in Elementary Cellular Automata

Ordered Dither Patterns

Order of Operations Tree

Ordinary and Extraordinary Refractive Indices in a 2D Anisotropic Crystal

Ordinary Regression and Orthogonal Regression in the Plane

Ordinary Vapor Compression (OVC) Cycle for Refrigerant R-134a

Oregonator with Time Delay

Organic Molecule Explorer

Organometallic Compounds of Transition Metals

Oriented Run-Length Compression

Oriented Triangle Angles

Orienting a Compass

Orienting a Spin with a Magnetic Field

Origami Bases

Origami Flanged Pots

Origami: Paper Planes

Ornamental Holiday Decoration

Ornamental Parametric Figures

Ornamental Snails

Orthocentre d'un triangle inscrit dans une hyperbole (French)

Orthogonal Circle Inversion

Orthogonal Grids

Orthogonality as well as Equidistance Can Be Used as the Sole Primitive Notion for Euclidean Geometry

Orthogonality of Associated Legendre Functions for Noninteger Order and Index

Orthogonality of Sines and Cosines

Orthogonality of Two Functions with Weighted Inner Products

Orthogonal Projection of a Rectangular Solid

Orthogonal Projection of a Solid of Constant Width

Orthogonal Projections of the Edges of a Cube

Orthogonal Systems of Circles on the Sphere

Orthogonal Views of Named RGB Colors

Orthographic Projection of Parallelepipeds

Orthologic Triangles

Orthonormality of Standing Waves

Orthonormal Polynomials under Different Inner Product Measures

Orthonormal Scales in a Nyquist Diagram

Orthopolar Lines for a Quadrilateral

Oscillation of a Mass-Spring System as a Model for Lattice Vibration

Oscillation of Two Masses Connected by Springs

Oscillations of a Mass-Spring System on an Inclined Plane

Oscillations of an Elastic Pendulum

Oscillations of a Pogo Stick

Oscillator with Generalized Power-Law Damping

Oscillatory Shear Flows of Two Hydrodynamically Interacting Spheres at Low Reynolds Numbers

Oscilloscope with Two Signal Inputs

Osculating Circles

Osculating Circles 3D

Osmotic Pressure

Other Formulations of the Collatz Problem

Otto Cycle

Oulipo: Wordshift + 7

Outer Billiards on Regular Polygons

Outer-Totalist Hexagons Between Past and Future

Outer Totalistic 2D Cellular Automata with Memory

Outer-Totalistic 3-Color Cellular Automaton 50010

Outgoing Waves Generated by a Pulsating Source

Outlet Stream Temperature of an Adiabatic Mixer

Overhanging Cards

Overlapping Circles

Overlapping Go Games

Overlapping Intervals

Overlapping Lattices of Figures

Overlapping Light Colors

Overlapping Patterns

Overlapping Rings

Overlapping Volcano Unfolding of a Prismoid

Overtones

Oxidation Number of Carbon

Oxidation of Ammonia by Air

Oxidation of Naphthalene in a Tubular Flow Reactor

Oxidation States of Carbon

Oxygen Diffusion for Survival of Freshwater Fish

Oxygen Dynamics in a Chemostat with Substrate Inhibition

Oxygen Transport by Hemoglobin and Myoglobin

Pack Disconnected Components

Packed Bed Reactor Design for a Gas Phase Catalytic Reaction

Packed Bed Reactor with Longitudinal Mixing

Packed Bed Reactor with Three Chemical Species: Alternative Computational Methods

Packing a Circle with Circles

Packing Disks with Consecutive Integer Radii in a Circle

Packing Equal Spheres in a Sphere

Packing of Rhombic Dodecahedra Expanding and Contracting in Two Directions

Packing Spheres into a Thin Cylinder

Packing Squares with Side 1/n

Packing Squares with Triangles

Packing the Slothouber-Graatsma Cube

Padé Approximants

p-Adic Continued Fractions

Padovan's Spiral Numbers

Painting with Wavelets

Paint Mondrian Style

Paint Your Own Rothko!

Pairwise Axes Rotations in Factor Analysis

Pairwise Tangent Circles Centered at the Vertices of a Triangle

Palindrome Primes

Pál Joints

Pancake-Cutting Problem

Pandiagonal Magic Squares of Order Five

Pandigital Olympic Circles Puzzle

Pantograph Linkage

Paper Clip

Paper Folding

Paper-Folding an Ellipse

Paperfolding Dragon Curve

Paper Folding Using Two Points

Paper Model of Conic Sections

Paper Size Series A

Pappus Chain

Pappus's Hexagons

Pappus's Hexagon Theorem

Parabola as a Locus of Centers of Circles

Parabolas from Rays

Parabolic Cylindrical Coordinates

Parabolic Envelope from Congruent Triangles

Parabolic Function Game

Parabolic Projectile Motion: Shooting a Harmless Tranquilizer Dart at a Falling Monkey

Parabolic Trough Solar Concentrator

Parabolograph

Paradoxical Triangular Braid

Parallax

Parallel and Counterflow Heat Exchangers

Parallel Axis Theorem for a Solid Cylinder

Parallelepiped with Edges on Three Skew Lines

Parallel Lines: Angles with a Transversal

Parallel Lines Have the Same Slope

Parallel Lines Optical Illusion

Parallel Nonisothermal Reactions in Batch and Semibatch Reactors

Parallelogram Dissection Paradox

Parallelogram Slide

Parallel-Plate Capacitors

Parallel Plate Capacitors and RC Circuits

Parallel Plate Heat Exchanger

Parallel Tangents to an Ellipse

Parallel Transport on a 2-Sphere

Parameter Estimation for a Packed Bed Reactor

Parameterized Families of Elliptic Curves with Large Rational Torsion Subgroups

Parameterized Families of Graphs

Parameterized Offset Surfaces

Parameterizing Mathews versus Eldridge

Parameterizing Temperature-Viscosity Relations

Parameters for Plotting a Cubic Polynomial

Parameters for Plotting a Quartic

Parameters of Uniform Circular Motion

Parametric Analysis of Plasma States

Parametric Curves in 2D

Parametric Curves in 3D

Parametric Density Estimation Using Polynomials and Fourier Series

Parametric Equation of a Circle in 3D

Parametric Equations for a Hyperbola

Parametric Linear Programming

Parametric Movement of a Rubber Band

Parametric Necklace

Parametric Plots from Rectangular Plots

Parametric Representations of Four Surfaces

Parametric Sensitivity of Plug Flow Reactor With Heat Exchange

Parametric Snowflake Design

Parametric Trace

Parametrization of a Fractal Curve

Parametrized Cosine Surfaces

Parametrized Families of Circles

Parametrized Goldberg's Tristable Polyhedron with 12 Faces

Parametrized Toroid with 42 Faces

Paraxial Approximation and the Mirror

Pareto Efficiency in the Edgeworth Box

Pareto?Nash Equilibria in Bicriterial Dyadic Games with Mixed Strategies

Parity Entangled Links

Parity Entangled Rings

Parity Recurrence in Thue-Morse Sequence

Parker Spiral Polygons for Solar Magnetic Fields

Parking a Car

Parliamentary Seat Allocation by the Sainte-Laguë Method

Partial Derivative Functions and Their Plots

Partial Derivatives in 3D

Partial Diversion of a Stream through a Slot

Partial Fraction Decomposition

Partial Fractions in the Set of Rationals

Partially Filled Capacitor

Partially Loaded Rectangular Plate

Partially Miscible Liquids

Partial Molar Enthalpy

Partial Molar Enthalpy and Entropy Quiz

Partial Standing Waves

Partial Sums of a Lambert Series

Particle Generator Based on the E8 Lie Algebra

Particle in a Box: Probability Density and Positional Variance

Particle-in-a-Box Spectra for Delta-Function Perturbation

Particle in an Infinite Circular Well

Particle in an Infinite Spherical Well

Particle in an Infinite Vee Potential

Particle in a Standing Wave Field

Particle Motion in a Nonlinear Force Field

Particle Motion in a Penning Trap

Particle Motion Simulation Using A Priori Collision Detection

Particle Moving around Two Extreme Black Holes

Particle Moving on a Rotating Disk

Particle Position Distribution Using a Brownian Dynamic Simulation

Particles in 1D and 3D Boxes

Particles Thrown from a Rotating Bar

Particle Swarm Optimization Applied to the van de Vusse Mechanism

Particle Swarm Optimization for 1D Problems

Particle Swarm Optimization for 2D Problems

Particle System: Fountain

Particle Trajectories in a Wien Filter

Particular Solution of a Nonhomogeneous Linear Second-Order Differential Equation with Constant Coefficients

Partitioning a List

Partitions of Integers

Parts of a Bassoon

Part-Whole Relations

Pascal-like Triangle Made from a Card Game

Pascal-like Triangles Made from a Game

Pascal-like Triangles Mod k

Pascal's Angle Trisection

Pascal's Barrel

Pascal's Mystic Hexagon

Pascal's Principle

Pascal's Syringe

Pascal's Tetrahedron Mod k

Pascal's Triangle

Pascal's Triangle and the Binomial Theorem

Pascal's Triangle Mod k

Pascal's Triangle Row Digits

Pasch's Axiom in Euclidean Geometry

Passages for Two Players

Passages Puzzle

Passing a Cube through a Cube of the Same Size

Passive Sonar

Pasta: Shapes, Designs, Colors, Origins, and Nutritional Data for Various Types

Patch Reentry of Elementary Cellular Automata

Pathfinding with A* Algorithm

Path Integrals on Causal Sets

Path Nets for Dodecahedron and Icosahedron

Path of an Ant on the Diameter of a Circle Rotating on the Unit Circle

Path of an Ant on the Diameter of a Rolling Circle

Path of a Projectile in a Rotating Frame

Path of Blood Flow in Circulatory System

Path of Light through an Acoustic Wave

Pathogen Dose-Response Curves with the Beta Poisson and Lognormal Models

Pathogen Spillover Effects on Coexistence of Competing Host Species

Pathological Derivatives

Path Rewriting Cellular Automata

Paths inside a Polygon

Paths of Balls Bouncing Off Pegs

Paths of Two-Dimensional Oscillators

Paths Through a Cubic Lattice

Paths through a Grid

Pattern Formation in the Kuramoto Model

Pattern Generator with Fourier Transforms

Pattern Recognition Primer

Pattern Recognition Primer II

Patterns Based on a Hexagonal Lattice

Patterns Based on Pentagonal Assemblies of Polygons

Patterns Based on Whirling Triangles, Squares and Hexagons

Patterns for Functions on the Gaussian Integers

Patterns from All Possible Elementary Cellular Automata

Patterns from a Simple Math Function I

Patterns from a Simple Math Function II

Patterns from de Bruijn Sequences

Patterns from Elliptic Integrals

Patterns from Math Rules Using Complex Numbers

Patterns from the Mean of Two-Color Totalistic 2D Cellular Automata

Patterns in Partitions of Integers

Patterns Produced by Hamming Distance

Pauling Electronegativity and Dipole Moment

Pauli Spin Matrices

Payoff Gradients in Two-Player Games

Pay the Points?

Peak Retention Time Using Discrete Fourier Transform

Peano Curve Explorer

Peano Curve in 3D

Pearl Necklace

Peaucellier's and Hart's Inversor

Peaucellier's Inversor

Peculiar Behavior of the Newton Method

Pedal Curves

Pedal Curves of Conics

Pedal Triangles of Isogonal Conjugates

Peking Opera Egg

Pell Equation

Pendule simple (French)

Pendulum Dangling from a Slider-Crank

Pendulum Dangling from a Spring

Pendulum Hanging from Rolling Disk

Pendulum on a Moving Support

Pendulums Coupled by a Torsion Spring

Pendulum Towing a Rolling Disk

Pendulum Waves

Pendulum with an Oscillating Support

Pendulum with Counterweight

Pendulum with Rotating Pivot

Pendulum with Several Links

Pendulum with Three Magnets

Pendulum with Varying Length or How to Improve Your Next Swing Ride

Penetration of Potential in a Semi-Infinite Region

Penetration of THz Radiation in Biological Tissue

Pen Falling Off a Finger

Peng-Robinson Equation of State for Mixtures

Penicillin Production in a Fed-Batch Bioreactor

Penrose Diagram

Penrose Rhombus Tilings by Projecting Golden Rhombi 2

Penrose's Railway Mazes

Penrose's Train Challenge

Penrose Tiles

Penrose Tilings and Wieringa Roofs

Penrose Triangle

Pentagonal Art Template

Pentagonal Pyramid

Pentagonal Tiling

Pentagonal Tiling around a Decagon

Pentagonal Tiling around a Pentagon

Pentagon Spirals

Pentagon Tilings

Pentagon-to-Near-Equilateral-Triangle Dissection

Pentagon-to-Near-Square Dissection

Pentahex Puzzles

Pentaprism

Percentage Change

Percentage Errors in Approximating the Volumes of a Wine Barrel and a Goblet

Percentages are Reversible

Percentiles of Certain Probability Distributions

Percentiles of Continuous Probability Distributions

Percent of a Number

Percents as Fractions or Decimals

Perceptron Algorithm in Machine Learning

Percolation on a Square Grid

Peregrine Soliton with Controllable Center in the Causal Interpretation of Quantum Mechanics

Perfect 1-Factorizations of Graphs

Perfect Number Generator

Perfect Parallelepipeds

Perfect Pitch Test

Perfect Riffle Shuffling

Perfect Tilings

Perforating the Faces of a Polyhedron

Perforating the Faces of Polyhedra

Performance Characteristics for Step Response of an Underdamped Process

Performance of a Batch Reactive Distillation System versus a Plug Flow Reactor

Performance of a Plug Flow Reactor with Recycle

Performance of CSTR and Plug Flow Reactors versus Temperature

Performance of Reactive Acoustic Mufflers

Perigal's Three-Squares-to-One Dissection

Period and Frequency

Periodic and Damped-Oscillatory Behavior of the Oregonator

Periodic Boundary

Periodic Boundary Condition

Periodic Box-Ball System

Periodic Finite-Difference Time-Domain (FDTD) Algorithm Using Field Transformation

Periodic Functions with m-Fold Symmetry of Type k

Periodic Heat Kernel

Periodicity of Euler Numbers in Modular Arithmetic

Periodic Orbit for Acute Triangles

Periodic Planar Collisionless Three-Body Orbits with Unequal Masses

Periodic Quantum Motion of Two Particles in a 3D Harmonic Oscillator Potential

Periodic Sum of Two Independent Logistic Maps

Periodic Table in 3D

Periodic Wave Generated by a Pendulum Sandglass

Periscope

Permafrost

Permutation Grid Classes

Permutation Lattice

Permutation Notations

Permutations

Permutations, Derangements, and Other Forbidden Position Problems Using Non-Attacking Rooks

Permutations in Lexicographic Order

Permutations, k-Permutations and Combinations

Permutations, Lehmer Code, and Lexicographic Index

Permutation Tree

Permuted Projections of Nested Arrays

Permuted Tabulation of Vanishing Determinants

Perpendicular Bisector Trace of a Parametric Function

Perpendicular Lines Generated by a Quadrilateral

Perpendiculars from a Point on the Line between the Endpoints of the Angle Bisectors

Perpendiculars from the Midpoints of the Orthic Triangle

Perpendiculars to a Chord

Perpetuum Mobile I

Perpetuum Mobile II

Perpetuum Mobile III: Drinking Duck

Person Walking Away from Spotlight

Perspective Anamorphosis of Photographic Images

Perspective Drawing of Billiards Table

Perspective Projection of a Cube onto a Plane

Perturbation Theory Applied to the Quantum Harmonic Oscillator

Perturbation Theory in the de Broglie-Bohm Interpretation of Quantum Mechanics

Perturbed Elementary Cellular Automata

Perturbed Infinite Square Well

Perturbing the Constant Coefficient of a Complex Polynomial

Per Unit Subsidy

Per Unit Tax

Peter de Jong Attractors

P&F Charts

Pharmacokinetic Model for Oral Bioavailability of Aspirin

Pharmacokinetic Modeling

Pharmacokinetics of Drug Clearance

Pharmacokinetic Two-Compartment Model

Phase Behavior on a Pressure-Volume Diagram

Phase Curve and Vector Field for Piecewise Linear Liénard Systems

Phase Matching of SHG in Nonlinear Optics

Phase Mismatch in SHG in Nonlinear Optics

Phase of a Complex Polynomial

Phase Percentage and Carbon Content Estimation in Hypoeutectoid Steels by Image Processing

Phase-Plane Analysis of a Biochemical Reactor

Phase Plane Dynamics of FitzHugh-Nagumo Model of Neuronal Excitation

Phase Plane Plot of the Van der Pol Differential Equation

Phase Plane Trajectories of the Unforced Duffing Oscillator

Phase Plots of Trigonometric Functions

Phase Portrait and Field Directions of Two-Dimensional Linear Systems of ODEs

Phase Portrait of Lotka-Volterra Equation

Phase Portraits, Eigenvectors, and Eigenvalues

Phases of Planets

Phase Space of an Intermittently Driven Oscillator

Phase Space of a Simple Pendulum

Phase-Space Orbits for the Kepler Problem on Constant Energy Surfaces

Phase Space Trajectories of a 1D Anharmonic Oscillator

Phase Transitions in 2D Cellular Automata

Phase Transitions in 2D Cellular Automata--A 3D View

Phase Transitions in Cellular Automata

Phase Transitions in ECA Rule 184

Phasor and Temporal Diagrams in Electrical Power-System Fault Analysis

Phasor Diagram for Series RLC Circuits

Phasor Model for RC Filter Electronic Circuit

Phasor Representation and Time-Domain Plot of Distorted Waveforms

Phasor Representation for Three-Phase Power Transmission

pH Buffering in Human Blood

Phénomčne de contraction des volumes des solutions hydro-alcooliques (French)

Phenomenological Approximation to Newton's Cradle

Phi Space

pH of Monoprotic Acid and Base Solutions

Phone Numbers by Fibonacci Methods

Phone Numbers to Words

Phones Puzzle

Phonon Dispersion Relation in Brillouin Zone

Phonon Modes for 2D Lattice Vibrations

Phosphorene Quantum Dots

Photographic Contrast Masks Using Cellular Automata

Photographic Orton Effect

Photon Number Distributions

Photon World

Photosynthesis

Photosynthetic Common Intercept Measurements

Phyllotaxis Explained

Phyllotaxis of Plant Shoots

Phyllotaxis Spiral Pattern on a Sphere

Phyllotaxis Spirals

Phyllotaxis Spirals in 3D

Physics of a Rear-End Collision

Physics of a Sliding Ladder

Pi = 4?

Piano-Hinged Dissection of an Ellipse to a Heart

Piano Keys

Picard Numbers of Quintic Surfaces

Picard's Method for Ordinary Differential Equations

Picking Up Coins in a Grid

Pickover's Mygalomorph Patterns

Pick's Theorem

Pictorial Bar Charts

Picture Frame

Picture Inspector

Picture Puzzle

PID Control of a Tank Level

Pi Digits Bar Chart

Pi Digits Pie

Piecewise Functions

Pie Charts

Pie Chart with Fractions

Pieri's Ternary Relation and Euclidean Geometry

Piezoelectricity in Barium Titanate

Pi Filter

Pi-Like Ratios for Circular Lakes

Piling of Bars along Dodecahedron Axes

Pinch Composition versus Reflux Ratio for a Benzene-Ethylenediamine Mixture at 1 atm

Pine Cone

Pins, Fins and Staggered Fins on Heat-Transfer Panels

Pinwheel Tiling

Pioneer 10 and 11 Spaceflight

Pipe Flange

Pipe Flow for Power-Law and Carreau Fluids

Pipeline Expansion Loop

Pisot, Salem and Cyclotomic Polynomials

Piston Linkage

Pitch-Class Set Orders and Forms

Pitchfork Bifurcation in Dynamical Systems

Pitot Tube

Pivoting Polymer

Pixel Inspector

Pixelization of a Font

Pixel Painter

Place Value

Placing Dominoes on a Checkerboard

Placing Objects at Predetermined Sets of Points

Plain Bob Bell Ringing

Planar Chromatography

Planar Density of Crystallographic Planes in SC, BCC and FCC Crystals

Planar Graph Embeddings

Planarity

Planar Stress Rotation

Planar Three-Body Problem

Planar Three-Body Problem in Phase Space

Planar Three-Connected Trivalent Network Mobile Automaton

Planar Trivalent Network Growth Using Two Rewrite Rules

Plane Cross Sections of the Surface of a Cone

Plane Cubic Curves

Plane Nets for Pyramids

Plane Poiseuille Flow of Two Superposed Fluids

Plane Sections of a Cone

Plane Sections of Surfaces

Plane Seismic Waves

Planes, Solutions, and Gaussian Elimination of a 3×3 Linear System

Planetary Gear Train

Planetary Trenberth Diagrams

Planetary Tunnels with Coriolis Effect

Plant Pathogen and Hyperparasite Annual Cycle

Plateau-Rayleigh Instability in Water Stream

Platonic Solids

Platonic Solids with an Op Art Motif

Platonic Spline Radiolari

Plato's Shadow Problem

Playable Sudoku Game

Play Hangman

Playing and Solving Peg Solitaire

Playing Blackjack

Playing Cards

Playing with Dots

Playing with Image Channels

Playing with Stellations of the Icosahedron

Playing with the Hénon Map Starting with a Circle or a Square

Plot a Quadratic Inequality

Plot a Quadratic Polynomial

Plot a Quintic Polynomial

Plot, Log Plot, and Beyond

Plot of a Geometric Sequence and Its Partial Sums

Plots of Compositions of Bitwise Operations

Plots of Functions and Their Iterates

Plots of Legendre Polynomials

Plots of Quantum Probability Density Functions in the Hydrogen Atom

Plots of the Fermi-Dirac Distribution

Plots of the Solutions of Three Partial Differential Equations

Plots of Various Number Theory Functions

Plots of Zernike Polynomials

Plotting a Long Time Series

Plotting a Parabola

Plotting a Sine or Cosine Wave

Plotting Closed Curves with a Four Bar Linkage

Plotting Collatz Sequences

Plotting Digits of Irrational Numbers

Plotting Electric Fields with Line Integral Convolution

Plotting Extrusion Profiles

Plotting Julia Sets

Plotting Price Divergences

Plotting Pythagorean Triples

Plotting Rational Functions of a Complex Variable

Plotting the Trivial and Critical Zeros of the Riemann Zeta Function

Plotting Vector-Valued Functions

Plug Flow Reactor with Heat Transfer Jacket

Pocket Calculator

Poem Maker

Poggendorff Illusion

Poincaré Hyperbolic Disk

Poincaré Sphere Visualization of n-Paddle Fiber Polarization Controller

Poincaré's Recurrence Theorem for Two States

Point Horopter

Point in Triangle

Point of Intersection of an Ellipse with a Line

Points and Lines on Folded Paper

Points around an Ellipse

Points on a 3D Spiral

Points on a Spiral

Point Spread and Modulation Transfer Functions for Seidel Aberrations

Point Spread and Modulation Transfer Functions of Zernike Wavefronts

Points Symmetric to the Orthocenter with Respect to the Sides of a Triangle

Pointwise Properties of Real Functions of a Single Real Variable

Poisson Distribution

Poisson Equation on a Circular Membrane

Poisson Spot

Poker

Polar and Rectangular Coordinates

Polar Angles and Points on the Unit Circle

Polar Area Sweep

Polar Coordinates

Polar Curve Generator with Five-Bar Linkage

Polar Fourier Transform

Polar Graph of a Variable Trig Ratio

Polar Graph with Rectangular Graph

Polariton and Jaynes-Cummings Blockade

Polaritons in Semiconducting Organic Films

Polarizability of Hydrogen Atom

Polarization of an Electromagnetic Wave

Polarization of an Optical Wave through Polarizers and Wave Plates

Polarization of Light through a Wave Plate

Polarization State Generator

Polarized Atoms Visualized by Multipole Moments

Polarized Polariton Fields on the Poincaré Sphere

Polarizer-Compensator Combination as a Controlled Polarization Filter

Polar Maze

Polar Plot of a Year's Hourly Temperatures

Polar Plots Drawn by a Mechanical Linkage

Polar Plots for Rose Curves and Limaçons

Polar Plots of Conic Sections

Polar Plots of Legendre Polynomials

Polar Plots of Wavelets

Polar Prime Spiral

Polar Trace

Polar versus Axial Vectors

Polar Zonohedra

Polar Zonohedron around an Icosahedron

Polar Zonohedron Built on a Dodecahedron

Polar Zonohedron Stacked with Rings of Rhombohedra

Polar Zonohedron with 18 Zones

Pole and Barn Paradox

Pole Figures in Crystallography

Poles and Zeros of Time-Domain Response Functions

Polinomios de Taylor de las Funciones Elementales (Spanish)

Polya Conjecture

Pólya Plots

Pólya's Mechanical Model for the Fermat Point

Pólya's Space-Filling Curve

Pólya's Urn

Pólya Urn Simulation

Pólya Vector Fields and Complex Integration along Closed Curves

Polycube Snakes

Polyform Explorer

Polygonal Holes in Polygonal Bars

Polygonal Numbers

Polygonal Sudoku

Polygonal Tori

Polygonal Virtual Grids for CA Computing: Pentagonal, Hexagonal, and Octagonal Samplers

Polygon Diagonals

Polygons Arranged in a Circle

Polygons at the Vertices of Polyhedra

Polygons on n Vertices

Polygon Spirals

Polygons within Polygons

Polygon Triangulations

Polyhedra and Their Graphs

Polyhedra Assembled from 20 Parts

Polyhedra Copied to the Vertices of the Same Kind of Polyhedron

Polyhedral Blooms

Polyhedral Blooms that Retain Symmetry

Polyhedral Compounds

Polyhedral Koalas

Polyhedral Lamps

Polyhedral Maps

Polyhedral Model of a Space Station

Polyhedral Playground

Polyhedrane

Polyhedra Perspective Problems

Polyhedra, Spheres, and Cylinders

Polyhedra with Prismatic Symmetry

Polyhedron Dual

Polyhedron Faces Identification

Polyhedron with a Maze Projected onto a Sphere

Polyline Simplification

PolyLog Function

Polymerization in a Batch Reactor

Polymorphic Type Checking and Monadic Evaluation

Polynomial and Derivative

Polynomial Approximation of the Exponential Function

Polynomial Atomic Functions for Fourier Analysis

Polynomial Fits of Random Walks

Polynomial Fitter

Polynomial Graph Generator

Polynomial Interpolation Using Equispaced versus Chebyshev-Lobatto Points

Polynomial Long Division

Polynomial Long Multiplication

Polynomial Roots

Polynomial Roots in the Complex Plane

Polynomials and Derivatives

Polynomials in the Complex Plane

Polypath Iterations

Polyrhythyms

Pompeďu's Theorem

Poncelet's Porism for Quadrilaterals

Ponchon-Savarit Diagram for an Ethanol-Water Binary Mixture

Ponchon-Savarit Diagram for Methanol-Water Mixture

Ponchon-Savarit Graphical Equilibrium Stage Method

Ponchon-Savarit Graphical Method at Total Reflux

Ponting Square Packing

Ponzo's Illusion

Pool Circles

Pool Shot

Pool Shot 3D

Poor Statistical Qualities for the RANDU Random Number Generator

Population Cube

Population Donut Chart

Population Dynamics with Two Competing Species

Population Evolution of Strontium Atom under Multi-frequency Laser Fields

Population Genetics: Hardy-Weinberg Equilibrium with Two Loci

Population Selector

Population Sizes and Interactions during the Zombie Apocalypse

Populations of Cities

Portfolio Diversification Benefit from Subadditive VaR

Portraits of Cell Division

Position-Dependent Opacity

Position on a Map from Two Azimuth Bearings

Positive-Contact Claw Clutch

Positive Frobenius Numbers of Three Arguments

Positive Integer Explorer

Positive Wigner Function Transformation by Quantum Operations

Possible Calculation of Logarithms of Cosines in Vlacq's Trigonometria Artificialis

Possible Counterexamples to the Minimal Squaring Conjecture

Posterization of Grayscale Images

Post-Event Bonding

Potential and Current Distributions over a Disk Electrode with Vibrating Probe

Potential and Kinetic Energies of a Falling Object

Potential and Lines of Force for Two Parallel Infinite Line Charges

Potential Differences in a Circuit with an EMF Source

Potential Energy of Objects from Daily Life

Potential Field of Two Charges

Potential Flow over a NACA Four-Digit Airfoil

Potential Flow over an Airfoil Specified by Numerical Data File

Potential Flows

Potential Flows through Channels

Potential of a Charged Spheroid

Potentiometric and Colorimetric Titration

Potentiometric Titration of Fe (II)

Potter's Wheel

Power Analysis for a Two-Sample t-Test

Power Content of Frequency Modulation and Phase Modulation

Power Curve of a Mean Test

Powered Clique Polyhedra

Power Efficiency of Amplitude Modulation

Power Hacksaw Linkage

Power in Weighted Voting Systems

Power Law Behavior in Elementary Cellular Automata

Power-Law Cascade to Model Growth of Teeth, Horns and Claws

Power Law Tails in Log Normal Data

PowerMod Is Eventually Periodic

Power of a Point Theorem

Power of a Test about a Binomial Parameter

Power Series Interval of Convergence

Powers in Modular Arithmetic

Powers Modulo m

Powers of Complex Numbers

Powers of Complex Points

Powers of Complex Roots

Powers of Numbers

Power Spectra for Analytic and Numerical Data

Power Spectrum of Cellular Automaton Dynamics

Power Spectrum of the Logistic Map

Power versus Work

Power Voting Systems Like the United Nations Security Council

pq-System Explorer

PR4 Coding of a Magnetic Hard Drive

Practice Identifying Surfaces of Degree at Most Two

Practicing Aircraft Holding Pattern Entries

Pratt Certificates of Primality

Precedence in Some Mathematica Functions

Precession of the Earth's Axis

Precession of the Equinoxes

Precision Error

Predator-Prey Dynamics with Type-Two Functional Response

Predator-Prey Ecosystem: A Real-Time Agent-Based Simulation

Predator-Prey Equations

Predator-Prey Equations Simulating an Immune Response

Predator-Prey Model

Predicting Maximum Sea Levels

Prediction and Entropy of Languages

Prediction of Isothermal Degradation by the Endpoints Method

Predictive Scores and Ultimate Test Passage

Preference Weights from Pairwise Comparisons

Preferred Values of Collatz Paths

Prefixes of Multiples

Prefix, Infix, and Postfix Notation

Prefix Unit Converter

Premium Assistance Calculator for HR 3590 and HR 3962

Premium Ratios with Capital Costs Included

Preorder and Postorder Traversal of Rooted Trees

P-Representation of Laser Light

Present Value Calculator

Pressure

Pressure Drop in a Packed Bed Reactor (PBR) Using the Ergun Equation

Pressure-Enthalpy Diagram for Water

Pressure of a High-Heeled Shoe

Pressure of a Rotating Fluid

Pressure Profile for Column of Multiple Fluids

Pressure-Temperature Diagram for a Binary Mixture

Pressure-Temperature Phase Diagram for Water

Pressure-Volume Diagram for a Vapor-Liquid Mixture

Pressure-Volume Diagram for Heating a Vapor-Liquid Mixture at a Constant Volume

Pressure-Volume-Temperature Diagram

Pressure within an Accelerating Container

Price Competition

Price Controls

Price-Yield Curve

Pricing a Bermudan Option with the Longstaff-Schwartz Monte Carlo Method

Pricing a Diamond

Pricing a European-Style Arithmetic Asian Option: Comparing Bootstrapping and Simulation Approaches

Pricing American Options with the Lower-Upper Bound Approximation (LUBA) Method

Pricing American Options with the Two- and Three-Point Maximum Methods

Pricing Power Options in the Black-Scholes Model

Pricing Put Options with the Binomial Method

Pricing Put Options with the Crank-Nicolson Method

Pricing Put Options with the Explicit Finite-Difference Method

Pricing Put Options with the Implicit Finite-Difference Method

Pricing Put Options with the Trinomial Method

Primality Bit Spiral

Primality Formal System Explorer

Primary and Secondary Shelf Life

Prime Beat

Prime Factorization Graph

Prime Factorization Table

Prime Gaps

Prime-Generating Cellular Automaton

Prime-Generating Recurrence

Prime Number Patterns

Prime Number Races

Prime Numbers in Various Bases

Prime Plaid

Primer on Bipolar Junction Transistors

Primes in the Heegner Fields

Prime Walk

Primitive Elements in the Free Group of Rank Two

Primitive Pythagorean Triples 1: Scatter Plot

Primitive Pythagorean Triples 2: Ordered Pairs

Primitive Pythagorean Triples 3: Ordered Tree Graph

Primitive Pythagorean Triples 4: Ordered Tree Matrices

Primitive Pythagorean Triples on a Curvilinear Grid Defined by Euclid's Formula

Primitive Relation for Elliptic Geometry

Prince Rupert's Cube

Princess and Witch Puzzle

Principal Axes of Inertia

Principal Becomes an Agent

Principal Components

Principal Components Analysis: Application in Value at Risk and Expected Shortfall

Principal Major and Minor Scales on a Piano

Principal Stresses and Mohr's Circle for Plane Stress

Principal Stresses in Compacted Cohesive Powders

Principle of the Lever

Prismatic Dominoes for the Blind

Prism Dissections for the Rhombic Dodecahedron of the Second Kind

Prisoner's Dilemma and Some Analogs in Game Theory

Probabilistic Dartboard

Probabilistic Interpretation of a Fractional Derivative

Probabilistic Model for Microbial Mortality

Probabilistic Models for Robot Motion

Probabilistic Model Showing Sigmoid Semilogarithmic Survival

Probabilistic Roadmap Method

Probabilistic Roadmap Method for Robot Arm

Probabilistic Roadmap Method in 3D

Probabilistic Roadmap Method with Seven-Link Articulated Robot

Probabilité pour que X soit dans un intervalle (French)

Probabilities of Combinations

Probabilities of Matching Colors

Probabilities of Permutations

Probabilities of Winning in Texas Hold'Em

Probability Densities, Expectation Values, and Uncertainties for Gaussian Wavepackets

Probability Density Distribution for Electron Scattering

Probability Density for a Classical Harmonic Oscillator

Probability Density for an Electron Passing through Two Narrow Slits

Probability Density in an Infinite Square Well

Probability Distribution for the kth Greatest of a Sequence of n Random Numbers

Probability in a Communication Channel

Probability in a Geometric Distribution

Probability Logic Test

Probability of a Union by the Principle of Inclusion-Exclusion

Probability of Being Sick After Having Tested Positive for a Disease (Bayes's Rule)

Probability of Being Strange According to Paulos

Probability of Election in a Vote

Probability of Long Leads

Probability of Zero in a System for an M/M/S Queue

Probing Macroscopic Quantum States with Gravitational-Wave Detectors

Probit and Logit Models with Normal Errors

Problem 11340 of The American Mathematical Monthly

Problems in Peg Solitaire

Problems on Circles I: Dissecting a Circle

Problems on Circles II: Halving a Set of Points

Problems on Circles III: Apollonius's Problem

Problems on Circles IV: Circles Tangent to Two Others with a Given Radius

Problems on Circles IX: Circumcircles and Incircles of a Triangle

Problems on Circles V: External and Internal Common Tangents

Problems on Circles VII: Circles of a Given Size Tangent to Other Two

Problems on Circles VIII: A Spiral of Circles

Problems on Circles VI: Poncelet Transversals

Problems on Circles XII: Bouncing a Circle inside Another Circle

Problems on Circles XIII: Common Area of Two Circles

Problems on Circles XI: Perpendicular Tangents to an Ellipse

Problems on Circles XIV: Bisecting the Circumference of Three Circles with a Circle

Problems on Circles X: Tangent Circles Generate Ellipses

Problems on Circles XV: Bar Fixed to Two Rotating Circles

Process-Based Cost Model for a Print and Copy Firm

Process-Based Cost Model for Sand-Casting Bronze Bells

Processing a Neurological Multiunit-Activity Signal

Processing CT Images with Morphologic Algorithms

Processing Various Parts of an Image Differently

Producing Extra-Dry Asti Spumante

Product Distribution Curves for Laminar, Plug, and Mixed Flows

Production of Anhydrous Ethanol Using an Extractive Distillation Column

Production of Cis2-Butene and Cis2-Hexene by Cis2-Pentene Disproportionation

Production of Syngas Using Coal-Steam Reactions

Product of Two Gaussians

Product of Two Levi-Civita Tensors

Product of Two Levi-Civita Tensors with Contractions

Product of Two Primes

Products Determined by a Point on the Circumcircle

Products of Diagonal Lengths in the Regular Polygon

Products of Lines

Products of Segments of Altitudes

Profit Maximization in Perfect Competition

Progression of COVID in the United States

Projected Area of a Cuboid

Projected Areas of Cylinder and Cone

Projected Rates of World Population Increase

Projectile Launched around the Earth

Projectile Motion

Projectile with Air Drag

Projecting a Circle on a Sphere to an Enclosing Cylinder

Projecting a Lattice of Points

Projecting a Polyhedron onto a Plane through Two Holes

Projecting a Triangle

Projecting Graphs of Real-Valued Functions of a Real Variable to the Riemann Sphere

Projecting Images from a Point Cloud

Projecting Points on Spheres to Lower Dimensions

Projecting the Tangent Point of an Ellipse

Projection into Spaces Generated by Haar and Daubechies Scaling Functions

Projection of Earth on Polyhedra

Projection of One 2D Vector to Another

Projection of Polytopes into Three Dimensions

Projection of Three Orthogonal Planes

Projections, an Altitude, and the Orthocenter

Projections of a 4D Hilbert Curve

Projections of Cubes and Half-Cubes

Projections of Midpoints onto Circumradii

Projections of Polyhedra Stellation

Projections of the 16-Cell

Projections of the Four-Cube

Projective Planes of Low Order

Project Projectile

Project Scheduling under Uncertainty

Proof by Induction

Proof of a Goal from a Hypothesis

Proof of Proposition 28, Book XI, Euclid's Elements

Proof of the Difference Formula for Sine and of the Addition Formula for Cosine

Proofs in Multiway Systems

Proofs Using a Quadrature Method of Archimedes

Proof without Words: 1+2+...+(n-1)=n Choose 2

Propagating Waves

Propagation in an Anisotropic Medium Using Huygens's Principle

Propagation of a Plane Electromagnetic Wave

Propagation of Gaussian and Non-Gaussian Laser Beams through Thin Lenses

Propagation of Reflected and Refracted Waves at an Interface

Properties of Acoustic Plane Waves

Properties of a Simple Random Walk with Boundaries

Properties of Chemical Elements

Properties of Fresnel's Interface Reflection Coefficients

Properties of Isosceles Tetrahedra

Properties of Isotopes

Properties of Kerr Spacetime

Properties of Rosette Functions

Properties of the Elements

Property Coinsurance

Proportional-Integral Control of a Reactive Distillation Column

Proportional-Integral Control of Batch Rectification Process

Proportional-Integral-Derivative (PID) Control of a Tank Level with Anti-Windup

Proportional Quantities

Proportional Temperature Control

Proportional Triangle Nesting

Proportions of a Box

Proposals for Medals for the Tokyo 2020 Olympic Games

Proposals for the Ceremony Platform for the Tokyo 2020 Olympic Games

Proposition 1, Book X, Euclid's Elements

Proposition 29, Book XI, Euclid's Elements

Proposition 30, Book XI, Euclid's Elements

Proposition 3, Book XII, Euclid's Elements

Proposition 7, Book XII, Euclid's Elements

Propositional Logic Puzzle Generator

Propositional Logic Test

Propp Circles

Prospecting for Complexity in k=3, r=1 Cellular Automata

Prospect Theory as a Piecewise Quadratic Value Function

Prospect Theory: Shape of the Utility Function

Protein Alignment Wheel

Protein Dot Plot

Protein Synthesis Induction

Proton Moving along the Axis of a Charged Ring

Protothetic

Prototype of a Virtual 2D Orrery

Protractor Practice

Proving Euler's Polyhedral Formula by Deleting Edges

Prüfer Codes of Labeled Trees

Prüfer Encoding of Labeled Trees

Prüfer p-Group

Pseudocolor

Pseudo-Forces in a Rotating Reference Frame

Pseudoprime

Pseudorandom Password Generator

Pseudorandom Walks with Generalized Gauss Sums

Pseudorhombicuboctahedron

Pseudosphere Built with Cones or Cylinders

Pseudosphere Geodesics

Psychrometric Chart

Psychrometric Data Calculator in English Engineering Units

Psychrometric Data Calculator in SI Units

Ptolemaic to Copernican World System Continuum

Ptolemy's Spheres

Ptolemy's Table of Chords

Ptolemy's Theorem

PT-symmetric Quantum Walks and Centrality Testing on Directed Graphs

Pulsars

Pulsatile Flow in a Circular Tube

Pulsating Starfish

Pulse Fourier Approximation

Pulse Traveling on an Elastic String

Pulse Width Modulation Principle

Pum-Num Puzzle

Pump Jack

Pum-Pum Puzzle

Punched Sphere

Puppet

Purchasing Power Calculator

Pure Tones

Pure Tones with Sample Rate

Purity and Yield in Chromatography on Antibodies

Pursuit Curves

Putting a Box Together without Gluing

p-Values Are Random Variables

P-x-y and T-x-y Diagrams for Vapor-Liquid Equilibrium (VLE)

Pyramid Builder

Pyramid Built from Decreasing Polygonal Slabs

Pythagoras Tree

Pythagorean Analogs for Similar Triangles

Pythagorean Dissection

Pythagorean Graphs

Pythagorean-Hodograph (PH) Cubic Curves

Pythagorean-Hodograph Quintic Curves

Pythagorean Means

Pythagorean, Meantone, and Equal Temperament Musical Scales

Pythagorean Periodic Table with Quantum Numbers

Pythagorean Primitive Triples Using Primes

Pythagorean Quadruples Projected on a Sphere

Pythagorean Theorem

Pythagorean Theorem 3D

Pythagorean Theorem for Regular Polygons

Pythagorean Triangles with Consecutive Values

Pythagorean Triangles with the Same Area

Pythagorean Triples

Pythagorean Triples Star

q-Bézier Curves

q-Cosine and q-Sine Functions over the Extended Complex q-Plane

q-Pascal Triangle

QR Decomposition

Q-Representation of Number States

q-Trigonometric Functions

Quacquarelli Symonds (QS) World University Rankings

Quadratic Equation

Quadratic Equation with Factored Form

Quadratic in Vertex Form (or Turning Point Form)

Quadratic Julia Sets

Quadratic Practice

Quadratic Residues

Quadratics Tangent to a Cubic

Quadratic Surface Cross-Sections

Quadratic Surfaces

Quadrics

Quadrilateral Slide

Quadrilateral Tiling with Textures

Quadrotor

Quad Tree Image Decomposition

Quadtree Subdivision

Qualitative and Quantitative Aspects of Phase Transitions in Water

Quality of Approximation by Geometric Series

Quantitative Approach to Law of Mass Action

Quantized Solutions of the 1D Schrödinger Equation for a Harmonic Oscillator

Quantum Alchemy

Quantum Angular Momentum Matrices

Quantum Circuit Implementing Grover's Search Algorithm

Quantum/Classical Correspondence for the Harmonic Oscillator

Quantum Computational Basis Vectors

Quantum Computer Search Algorithms

Quantum Computer Simulation of GHZ Experiment

Quantum Dynamics in 1D

Quantum Effects in Atom-Field Interaction

Quantum Electrodynamics of Electron-Positron Annihilation to Muons

Quantum Entanglement versus Classical Correlation

Quantum Fourier Transform Circuit

Quantum Harmonic Oscillator Tunneling into Classically Forbidden Regions

Quantum Logic Gates: Roots, Exponents, and Eigensystems

Quantum-Mechanical Particle in a Cylinder

Quantum-Mechanical Particle in an Equilateral Triangle

Quantum Mechanics of a Bouncing Ball

Quantum Motion in an Infinite Spherical Well

Quantum Motion of Two Particles in a 3D Trigonometric Pöschl-Teller Potential

Quantum Octahedral Fractal via Random Spin-State Jumps

Quantum Orbits of a Particle in Spherical Coordinates in a Three-Dimensional Harmonic Oscillator Potential

Quantum Particle in a Multi-step Potential Well

Quantum Particle in a Regular Polygon by Finite Element Method

Quantum Particles in an Infinite Square Potential Well

Quantum Pendulum

Quantum Probability as Area on Bloch Sphere

Quantum Random Walk

Quantum Revivals

Quantum Scattering by a Rigid Sphere

Quantum State Discrimination with Two Qubits

Quantum Teleportation

Quantum Theory of Coupled Two-Dimensional Oscillator

Quantum Theory of Rutherford Scattering

Quantum Theory of the Damped Harmonic Oscillator

Quantum Well Explorer

Quarter-Car Suspension Model with Double Spring

Quasicrystals

Quasicrystal Sampling of a Picture

Quasi-exact Solution for a Double-Well Potential

Quasi-Exact Solutions of Schrödinger Equation: Sextic Anharmonic Oscillator

Quasi-Rent in Open Access Fisheries

Quasi-Reversible and Irreversible Voltammograms at Microelectrodes

Quaternion Addition and Multiplication

Quaternion Julia Set

Qubits on the Poincaré (Bloch) Sphere

Quelques polyčdres (French)

Quick Release Linkage

Quick Return Mechanism

Quicksort versus Selection Sort

Quotients and Remainders Wheel

Qutrit States as Probability Vectors

Rabi and Josephson Oscillations

Rabinovich-Fabrikant Equations

Racing Disks

Radial and Axial Variations in a Nonisothermal Tubular Reactor

Radial Cam Design

Radial Distribution Function for Hard Spheres

Radial Distribution Function for One-Dimensional Square-Well and Square-Shoulder Fluids

Radial Distribution Function for One-Dimensional Triangle Well and Ramp Fluids

Radial Distribution Function for Sticky Hard Rods

Radial Distribution Functions for Nonadditive Hard-Rod Mixtures

Radial Engine

Radial Fractal Tree

Radial Gradient

Radially Polarized Laser Beam Intensity Distributions

Radial Metric

Radial Temperature and Concentration Gradients in a Packed Bed Reactor

Radial Tiling

Radial Velocity Curve Fitting

Radians as Percentages

Radians on the Circle of a Ferris Wheel

Radiated Power from a Point Charge in Uniform Circular Motion

Radiation by an Accelerated Charge

Radiation Heat Transfer Coefficient for a Gray Surface

Radiation Pattern for Double-Couple Earthquake Sources

Radiation Pattern from Accelerated Point Charge

Radiation Pattern of a Dipole Antenna with Arbitrary Orientation

Radiation Pattern of a Point Charge in Uniform Circular Motion

Radiation Pulse from an Accelerated Point Charge

Radiation Shielding of a Spherical Black Body

Radiative Transitions in a Hydrogen Atom

Radical Axis and Radical Center

Radical Circle of Three Circles

Radioactive Decay as a Probability Distribution

Radioactive Decay in the Causal Interpretation of Quantum Theory

Radioactive Decay of Five Elements: Time Dependence of Remaining Mass

Radioactive Decay or Drug Degradation

Radio Propagation and Multipath with Diversity Antennas

Radius-1/2 Cellular Automata

Radius and Temperature of Main Sequence Stars

Radius of Curvature of Catenary

Radius of Rolled-Up Trilayer

Ra Expeditions

Ragged Automaton Disk

Rainbow Art

Rainbows of Different Order in Water Droplets and Glass Beads

Rainbows of Multiple Orders

Rainbow String Figures

Raindrop Art

Raising the Degree for Bézier Curves

Ramachandran Analysis of Protein Backbone Dihedral Angles

Ramanujan Primes

Ramanujan R and S

Ramanujan's Strange Formula for Pi

Ramsey(3,3,3)>16

Ramsey(3,3) = 6

Random 2D Nearest Neighbor Networks

Random 3D Nearest Neighbor Networks

Random Acyclic Networks

Random Binary Differences

Random Branching Process

Random Branching Process in 3D

Random B-Spline Surfaces

Random Character Sequences Do Not Follow Zipf's Law

Random Chord Paradox

Random Circles with Power-Law Sizes

Random Closed Meanders

Random Cuboid-by-Cuboid Construction of 3D Cellular Automata

Random Domino Tilings

Random Graph Models

Random Harmonic Series

Random Ink Blot

Randomized Evolutions of Continuous Cellular Automata Generalizing Rules 30 and 90

Randomize Motion for Six Degrees of Freedom

Random Key Graph

Randomly Filling an Array

Randomly Reducing Objects to Spheres

Random-Matrix Eigenvalue Statistics for Quantum Billiards

Random Matrix Theory and Gaussian Noise Thresholding

Random Matrix Theory Applied to Small-World Networks

Random Natural 3D tree

Randomness in the Digits of Pi

Randomness in the Digits of Square Roots

Randomness Test in Coupon Collecting

Random Number Exploration

Random Number Generation

Random Partitioning of a List

Random Permutations of a Given Length

Random Point Construction of 2D Cellular Automata

Random Points on a Sphere

Random Polygon to Ellipse

Random Samples and Random Permutations

Random Simulation of a Financial Portfolio

Random Song Writer

Random Spheres

Random Spheres with Power-Law Sizes

Random Spline Polygon

Random Subdivision of a Square

Random Subgraph of a Complete Graph

Random Tree Aggregation

Random Triangle Path Finder

Random Values from Distributions

Random Walk and Diffusion of Many Independent Particles: An Agent-Based Simulation

Random Walk Generated by the Digits of Pi

Random Walks and the Heat Equation

Random Walks Based on Continued Fraction Expansions of Real Numbers

Random Walks in Elementary Cellular Automata

Random Walks in Platonic and Archimedean Polyhedra

Random Walk Solutions to the Dirichlet Problem for the Laplace Equation

Random Walks on Various Topologies

Random Word

Random Word Generation for Fictional Languages

Random Word Generator

Range-Zero Binary Cellular Automata

Rankine Cycle

Rankine Vortex: A Simple Hurricane Model

Rank Plots for Countries

Rank Transform in Harmonic Regression Time Series

Ranque-Hilsch Vortex Tube

Raoult's Law for Ideal Solutions

Rapidly Exploring Random Tree (RRT) and RRT*

Rare Event Analysis by Flow Cytometry

Rasa Puzzle

Raster Bubble

Rasterization of a Data Plot

Rate Constant Calculation from Four Temperature and Moisture Combinations

Rate Equations for a Three-Level Model in Low-Dimensional Exciton Systems

Rate of Cellular Respiration as a Function of Temperature and Cell Type

Rate of Change of the Distance between Two Point Masses

Ratings of NFL Teams from 1985 to 2012

Ratio-Based Modified Logistic Isothermal Microbial Growth

Ratio Match

Rational Cubic Bézier Curves

Rational Cyclic Orthodiagonal Quadrilateral

Rational Cyclic Polygons

Rational Distance Problem

Rational Function Graphs

Rational Functions of Small Degree

Rational Functions Quiz

Rational Functions with Complex Coefficients

Rational Harmonics

Rational Isogonal Conjugates

Rational Linear Combinations of Pure Geodetic Angles

Rational Linear Combinations of Pure Geodetic Angles, Part 2

Rational Number Explorer

Rational Pedal-Antipedal Triangles

Rational Points on an Elliptic Curve

Rational Rectangles

Rational Refinancing of a Residential Mortgage

Rational Roots of a Polynomial

Rational Tangential Complete Quadrilateral

Rational Triangles with Area Less than 102

Ratio Notation

Ratio of Areas in a Square

Ratio of the Areas of a Circular Segment and a Curvilinear Triangle

Ratio of the Surface Area of a Sphere to a Cylinder

Ratios Involving Six Radii

Ratios of the Areas of an Internal Hexagon to Its Star to the External Hexagon

Ratkowski's Square Root Growth Rate Model for High Temperatures

RATS Sequences

Rauzy Fractals as Stepped Surfaces

Rauzy Fractals of Order Four

Ray Absorber

Ray Diagrams for Lenses

Ray Diagrams for Microscope and Telescope

Ray Diagrams for Spherical Mirrors

Ray in a Square

Rayleigh Waves

Ray Tracing for Points in a Polygon

Ray Tracing With Lenses

RC Flashing Bulb Circuit

RC Oscilloscope

Reachable Set for a Drone

Reaction-Diffusion Equations for an Autocatalytic Reaction

Reaction-Diffusion in a Drop Using Orthogonal Collocation

Reaction-Diffusion in a Two-Dimensional Catalyst Pellet

Reaction Factor for Second-Order Gas-Liquid Reactions

Reaction Force on a Lever

Reaction in an Adiabatic Continuous Stirred-Tank Reactor

Reaction in an Isothermal Continuous Stirred-Tank Reactor (CSTR)

Reaction Paths of Wei-Prater Complex Reaction Networks

Reaction Rate Dependence on Temperature and Moisture During Storage

Reactive Batch Rectification for Quaternary Mixture

Reactive Collision Dynamics in Two Dimensions

Reactive Distillation Computations Including Heat Effects

Reactive Distillation Using Arc Length Continuation

Reactive Scattering on a LEPS Surface

Reactor Design Economics

Reactor Rate and Conversion versus Space Velocity

Reactor Showing Two Attractive Stable Points

Reactor Steady States

Reactor with Recycle Stream

Readable Mess between First and Last Letters

Reading a Function Value with Extra Precision

Reading a Psychrometric Chart

Reading Electric Meters

Reading Hertz's Own Dipole Theory

Real Addition on the Number Line

Real Digits Carpet

Real Elliptic Curves

Real Estate Recessions

Realization of Heawood's Map on a Toroidal Polyhedron

Real Number Walks versus Algorithmic Random Walks

Real Options

Real Roots of Sparse Polynomials

Real-Time Simulation of the Game of Life

Rearranging Color Channels in an Image

Rearranging Dissections of Six Rhombic Dodecahedrons of the Second Kind

Rearranging the Alternating Harmonic Series

Rearranging the Cayley Table of the Dihedral Group by Cosets

Receiver Operating Characteristic Curves and Uncertainty of Measurement

Receiver Operating Characteristic (ROC) Kurve bei Quantitativen Diagnosetests (German)

Recently Discovered Periodic Solutions of the Three-Body Problem

Reciprocal Lattice 2D

Reciprocals of Diagonal Lengths in the Regular Polygon of Unit Side

Reciprocating Compressor with an Intercooler

Recognizing Chords

Recognizing Musical Cadences

Recognizing Notes in the Context of a Key

Reconstructing a Sampled Signal Using Interpolation

Reconstruction of de Decker-Vlacq's 1628 Table of Common Logarithms

Reconstruction of the Great Wall

Reconstruction of Vega's First Calculation of Pi

Reconstruction of Vega's Prime Number Table

Records in Sequences of Random Variables

Recovering the Fourier Coefficients

Recovering the Purchase Price of Hybrid Vehicles in Fuel Savings

Rectangles: Perimeter and Area

Rectangles Reasonably Close to a Given Area

Rectangular Prisms

Rectangular Pulse and Its Fourier Transform

Rectangular Screw Thread

Rectangular Slice Twist

Rectifying an Alcohol-Water Mixture with Variable Enthalpies

Rectifying and Stripping Profiles for the Reactive Cascade

Rectilinear Motion

Recurrence-Based Representations of the Logistic Map

Recurrence Network Measures for the Logistic Map

Recurrence Plot of Mathematical Functions and Constants

Recurrence Table Attractors

Recurring States in Cellular Automaton Evolution

Recursion in the Ackermann Function

Recursive Dungeon Generation

Recursive Exercises I

Recursive Exercises II: A paradox

Recursive Exercises III: Fire Patterns

Recursive Exercises IV: Rep-Tiles

Recursive Exercises IX: Gothic Windows

Recursive Exercises VIII: Kites and Darts

Recursive Exercises VII: Stacks of Cubes

Recursive Exercises VI: Tori

Recursive Exercises V: Nested Triangles

Recursive Exercises XI: Homage to Escher

Recursive Exercises XII: Circles inside Triangles

Recursive Exercises XIII: Nested Pentagons

Recursive Exercises X: Nested Squares

Recursive Extended Euclidean Algorithm

Recursively Defined Partial Tilings of the Plane

Recursive Partitioning for Supervised Learning

Recursive Pythagorean Tree

Recursive Rewriting of Expressions

Recursive Similar Triangles

Recursive Visual Cryptography Scheme

Recycling Robot in Reinforcement Learning

Red Giant Stars and the Death of the Sun

Redox-Electroadsorption Reaction (E-EAR) at a Rotating Disk Electrode (RDE)

Redox Equation Balancer

Redox Reaction (E) at a Rotating Disk Electrode (RDE)

Redox Reaction (EE) at a Rotating Disk Electrode (RDE)

Reduce, Replicate, Rebuild

Reducing a 3×4 Matrix to Row-Echelon Form

Reducing a Differential Equation of a Special Form to a Homogeneous Equation

Reducing Fatalities from Coronavirus Epidemic

Reduction Formulas for Integrals

Reed-Frost SEIR Model

Reference Angles

Reflected and Transmitted Newton's Rings

Reflecting a Lattice of Points

Reflecting a Point through the Midpoints of a Triangle's Sides

Reflecting a Regular Polygon across Its Sides in the Hyperbolic Plane

Reflecting in a Moving Mirror

Reflecting in a Rotating Mirror

Reflecting in Intersecting Lines

Reflecting in Intersecting Planes

Reflecting in Parallel Lines

Reflecting in Parallel Planes

Reflecting inside a Spherical Mirror and a Catacaustic

Reflection and Refraction on a Flat Surface between Two Different Materials

Reflection and Transmission Coefficients of an Optical Cavity

Reflection and Transmission of Acoustic Waves

Reflection from a Freehand Polynomial Mirror

Reflection from a Polynomial Mirror

Reflection in a Circle

Reflection in a Parabolic Mirror

Reflection in Two Dimensions

Reflection Matrix in 2D

Reflection of Parallel Rays by a Sphere

Reflection of Parallel Rays by a Two-Dimensional Body of Nearly Maximal Resistance

Reflections in a Mirrored Corner

Reflections in an Elliptical Region

Reflections of a Line through the Orthocenter in the Sides of an Acute Triangle

Reflections of a Point in the Midpoints of a Triangle's Sides

Reflections of Polycubes in the Three Coordinate Planes

Reflective Properties of Conic Sections

Reflectivity and Induced Polarization by Mirrors

Reflux Policy for a Batch Distillation Operation with a Constant Distillate Composition

Refraction by a Semicylindrical Prism

Refraction from a Submerged Light Source

Refraction in a Biconvex Spherical Lens

Refraction in a Triangular Prism

Refraction of Light Rays by Material with Negative Refractive Index

Refraction through a Ball

Refraction through a Rotating Glass Slab

Refraction through a Semicylindrical Prism

Refraction through Parallel Faces

Refrigeration Cycle Coefficient of Performance

Refrigerator Poetry

Regelation

Regions of Feasible Distillate and Bottom Product Composition for an Ideal Ternary Mixture at 1 atm

Register Machines

Regression Analysis of USA Inflation

Regression Model with Transformations

Regression toward the Mean

Regressive Recursion

Regular 2n-Gon to Rectangles Dissection

Regular Clusters of Polyhedra

Regular Cone Nets

Regularized Logistic Regression

Regular k-ary Trees

Regular n-Gons as Polygons and Stars

Regular Paperfolding Sequence

Regular Polygon Maker

Regular Polygon Rolling on a Catenary

Regular Polygons

Regular Polygons of Edge Length Two

Regular Prism Volume and Surface Area

Regular Right Prism between Two Points

Regular Spherical Polygons

Regular Tetrahedon Rolling on a Plane

Regular Tetrahedra Formed by Lattice Points Equidistant from the Origin

Regular Tilings

Reindeer Linear Transformation

Reinsurance Cut-Through

Related Rates: A Boat Approaching a Dock

Related Rates Clock

Related Rates: Triangle Angle and Area

Relating a Rhombic Triacontahedron and a Rhombic Dodecahedron

Relating the Great Rhombicosidodecahedron to Several Other Polyhedra

Relating the Rhombic Triacontahedron to the Rhombic Enneacontahedron

Relating the Rhombic Triacontahedron to the Rhombic Icosahedron

Relating Trilinear and Tripolar Coordinates for a Triangle

Relation of Diagnostic Accuracy Measures

Relation of Radius, Surface Area, and Volume of a Sphere

Relations and Functions between Small Sets

Relations and Graphs

Relations between Golden Rhombic Solids and Some Archimedean Solids

Relations between Plane Angles and Solid Angles in a Trihedron

Relations between Some Triangles Associated with Excircles

Relations between the Platonic and Archimedean Solids

Relationship between Sine and Tangent

Relationship between the Tone Curve and the Histogram of a Photographic Image

Relationship of Sine and Cosine to the Unit Circle

Relative Circular Motion

Relatively Prime Numbers and Zeta(2)

Relative Motion for Two Ions in a Penning Trap

Relative Motion in a Subway Station

Relative Motion of Two Cars

Relative Primality

Relative Primes and GCDs

Relative Transverse Strain in Materials with Different Poisson Ratios

Relativistic Aberration and Doppler Shift

Relativistic Addition of Velocities

Relativistic Car

Relativistic Effects on Satellite Clock as Seen from Earth

Relativistic Energy Levels for Hydrogen Atom

Relativistic Ground State of Hydrogen-Like Atoms

Relativistic Headlight Effect

Relativistic Mass

Relativistic Particles in Electric and Magnetic Fields

Relativistic Quantum Dynamics in 1D and the Klein Paradox

Relativistic Time Dilation

Relativistic Time Dilation in Muon Decay

Relativistic Traffic

Relativity of Simultaneity

Relaxation Method for Electrostatic Problems

Relaxation Methods for Solving the Laplace Equation

Relaxation of a Discrete Maxwell Model

Relaxation of a Maxwell Element

Reliability Analysis and Failure Probability Using First-Order Reliability Method

Reliability Distributions

Relief-Shaded Elevation Map

Remainder Graphs

Renormalization of Curlicue Fractals

Re-Orient a Sphere with Two Straight Rolls

Repeated Addition and Doubling

Repeatedly Subdividing Triangles through Special Points

Repeated Mediants Lead to Iterative Brackets

Repeating Continued Fractions

Repeating Decimals

Replay 10 Great Chess Games

Replicating Patterns in 2D Binary Cellular Automata with the Parity Rule

Replicator-Mutator Dynamics with Three Strategies

Réponse d'un filtre ŕ un signal carré (French)

Réponse d'un filtre ŕ un triangle (French)

Representation of Boolean Functions Using Binary Trees

Representation of Diffraction by Vector Summation

Representation of Qubit States by Probability Vectors

Representation of Spinors by Two-Dimensional Complex Rotations

Representation of Three-Valued Boolean Functions

Representations by a Sum of Squares

Representations of the Dirac Deltafunction

Representations of Trigonometric and Hyperbolic Functions in Terms of Sector Areas

Representing an Integer by a Sum of Like Powers

Representing an Integer with an Elementary Automaton

Representing Elementary Cellular Automaton Rules

Repressilator

Rep-Tile

Rep-Tiles

Rep-tiles and Fractals of Order Five

Repulsion between Charged Pellets in a Box

Repulsionhedra and the Thomson Problem

Repulsion of Charged Pith Balls

Reshetov's Unistable Polyhedra with 14, 15, 16, and 17 Faces

Residence Time Distribution for Continuous Stirred-Tank Reactors in Series Using the First Four Moments

Residence Time Distribution Function of a Stirred-Tank Cascade (E-Curve)

Residence Time Distribution of Single Continuous Stirred-Tank Reactors Subject to a Square Pulse Input

Residual-Fit Spread Plot

Residual Functions for the SRK and PR Equations of State

Residue Curve and Bubble Temperature Distribution for a Ternary Mixture

Residue Curve and Bubble Temperature Distribution for Methyl Tert-Butyl Ether Chemistry at 8 atm

Residue Curve and Temperature Distribution for Ethyl Acetate Chemistry

Residue Curve Computation for Methyl Tert-Butyl Ether (MTBE) Chemistry

Residue Curve in a Ternary Equilateral Diagram

Residue Curve Map for a Benzene-Toluene-p-Xylene Mixture

Residue Curve Map for a Mixture of Three Alcohols; Nature of the Singular Points

Residue Curve Map for a Mixture of Water, Ethanol, and Ethylene Glycol

Residue Curve Map for a Non-Ideal Ternary Mixture with a Distillation Boundary

Residue Curve Map for Methyl Acetate and Isopropyl Acetate Chemistry at 1 atm

Residue Curve Map Presenting Four Distillation Regions

Residue Curve Maps in a Triangular Ternary Diagram

Residue Curves at High Total Pressures

Residue Curves for a Reactive Ternary System

Residue Curves for Different Activity Coefficient Models

Residue Curves for Methyl Formate Chemistry

Resistors in Parallel

Resistors in Series

Resizable Number Theory Tables

Resizing Images

Resonance and Beats

Resonance in Open and Closed Pipes

Resonance Lineshapes of a Driven Damped Harmonic Oscillator

Response of a Confined Aquifer to Pumping: Nonleaky and Leaky Cases

Response of a Jacketed Exothermic Continuous Stirred-Tank Reactor to a Perturbation

Response of a Reactor with Axial Dispersion to a Pulse Input Tracer (E-Curve)

Response of Low-Pass RC Filter to Periodic Waveforms

Restricted Three-Body Problem

Restricted Three-Body Problem in 3D

Restricted Three-Body Problem in a Plane

Resultant of a Sum of Forces

Resultant of a Vector

Reticular Planes in a Cubic Lattice of Parallel Wires

Retina and LGN: Early Vision Using Gaussian Filters

Retiree Stop-Loss Reinsurance

Retrocausality: A Toy Model

Retrograde Motion

Retrograde Motion Illusion for an Electric Fan

Retroreflective Sphere

Returns to Scale in One-Factor Production Functions

Reuleaux-Like Polygon Shafts

Revenue and Costs Curves Analysis

Revenue and Elasticity

Reverberations in Acoustic Layers

Reversal-Addition Related Systems

Reversal-Addition Systems

Reverse Collatz Paths

Reversed-Out Letterforms

Reverse Engineering GPA Distributions from Honors Data

Reverse Osmosis

Reverse-Then-Add Sequences

Reversi

Reversible and Irreversible Expansion and Compression Processes

Reversible and Irreversible Expansion or Compression Work

Reversible and Irreversible Isothermal Expansion of an Ideal Gas

Reversible Multiplex of Totalistic Cellular Automata

Reversible Reaction in an Adiabatic Plug-Flow Reactor

Reversible Steady-State Voltammograms at Microelectrodes

Reversible Two-Color Cellular Automaton Rules

Revolutionary Cup

Revolving Billboard

Reye's Configuration

RF Attenuator T or Pi Values in 5% Resistors

RGB and CMYK Colors

RGBColor Gradients

RGB Color Space

RGB Explorer

RGB Gamma Controls

RGB Match Up

RGB Spheres

Rhamses Puzzle

Rheological Behavior of FENE Dumbbell Suspension under Elongational Flow

Rhombi at the Incenter of a Triangle

Rhombic 210-hedron

Rhombic Dodecahedra and Escher's Solid

Rhombic Dodecahedra Totalistic Cellular Automaton

Rhombic Dodecahedron 5-Compound

Rhombic Dodecahedron and Polar Zonohedron

Rhombic Dodecahedron Made of Four Rhombohedra

Rhombic Drive for Speed Governor

Rhombic Drive for Stirling Engine

Rhombic Enneacontahedron Sandwich

Rhombic Enneacontahedron with 30 Icosahedra

Rhombic Hexecontahedron Frame

Rhombic Hexecontahedron in a Rhombohedron

Rhombic Hexecontahedron Tower

Rhombic Icosahedron Helices

Rhombic Spirallohedra

Rhombic Triacontahedron Built on a Cube

Rhombic Triacontahedron Measures

Rhombic Triacosiohedron

Rhombicuboctahedron Star

Rhombicuboctahedron Star on a Sphere

Rhombohedra

Rhombohedral Rings around Polar Zonohedron

Rhombohedron with Variable Faces

Rhomboidal Stars

Rhombus Puzzle to Create Logos for Tokyo 2020 Olympic and Paralympic Games

Rhyme Finder

Riccati Differential Equation with Continued Fractions

Richards Growth Curve

Richardson Extrapolation Applied Twice to Accelerate the Convergence of an Estimate

Ridged Pip Die

Riemann Hypothesis

Riemann's Almost Nowhere Differentiable Function

Riemann's Example of a Continuous but Nowhere Differentiable Function

Riemann's Minimal Surface

Riemann's Theorem on Rearranging Conditionally Convergent Series

Riemann Sums

Riemann Sums: A Simple Illustration

Riemann Sums for Functions of Two Variables

Riemann Surface of the Logarithm

Riemann Surfaces of Inverses of Sums of Two Trigonometric Functions

Riemann Surfaces of Inverse Trigonometric Functions

Riemann Surface Transition

Riemann versus Lebesgue

Riemann Zeta Function

Riemann Zeta Function near the Critical Line

Riesz's Rising Sun Lemma

Right and Equilateral Triangle Ternary Phase Diagrams

Right-Angled Tetrahedron

Right Cone Volume and Area

Right Pyramid Volume and Surface Area

Right Tetrahedron: de Gua Theorem

Righty Tighty; Lefty Loosy

Rigid Body Pendulum on a Flywheel

Rigidity Testing of Frameworks

Rigorous Simulation for Distillation of Non-Ideal Binary Mixture

Rigorous Steady-State Simulation of a Multicomponent Distillation Column

Rikitake Model of Geomagnetic Reversal

Rimless Wheel Locomotion

Ring Fractal

Ring of 10 Tetrahedra

Ring of 190 Golden Rhombohedra

Ring of 25 Spikeys

Ring of 2n Rhombohedra

Ring of 90 Rhombohedra

Ring of Hoberman Rings

Ring of Pendulums

Ring of Ten Icosahedra

Rings around the Vertices of a Polyhedron

Rings of 20 Icosahedra

Rings of 5 and 10 Rhombic Triacontahedra

Rings of Dodecahedra

Rings of Five and Ten Polyhedra

Rings of Small Order

Ring Structures Made of Square Pyramids and Matching Tetrahedra

Ripple Art

Risk Aversion, Load, and Optimal Insurance

Risk Guesstimation from Factor Ranges

Risk, Ownership, and Control

Risk Premiums

Risk Regulation Relying on Historical Standard Deviation

River Crossing Puzzle

RLC Series Circuit

RLC Tank Circuit Bandpass Filter: Triangle Waveform Input

RL Series Circuit

Roads and Wheels

Robinson Tiling

RoboSnarf

Robot Builder

Robotics Application of Lissajous Curves

Robot Manipulator Workspaces

Robot Motion with Obstacles

Robot Singularities in Three-Link Manipulators

Robustness of Student t in the One-Sample Problem

Robustness of the Longstaff-Schwartz LSM Method of Pricing American Derivatives

Rock Bed Heat Storage System

Rocket Fire

Rocking Roly Poly Toy

Rock, Paper, Scissors with AI Player

Rock-Scissors-Paper

Roget's Palisade

Rogue Ocean Waves

Roll Any Point on the Sphere to Any Desired Latitude-Longitude Coordinates with One Straight-Line Roll

Roll a Sphere without Changing Orientation to a New Location in Two Straight Rolls

Roller Bearing

Roller Coasters

Roller Crushing Machine

Rolle's Theorem

Rolling a Circle on a Parabola

Rolling a Coin around a Coin

Rolling a Coin inside a Circle

Rolling a Cube on a Chessboard

Rolling a Cube on a Small Rhombicuboctahedron

Rolling a Disk on a Curve

Rolling a Half-Weighted Disk

Rolling a Polygon on a Circle

Rolling a Polygon on Another Polygon

Rolling a Regular Dodecahedron on a Congruent Dodecahedron

Rolling a Regular Polygon on the Unit Circle

Rolling a Regular Tetrahedron on a Regular Icosahedron

Rolling a Sphere around a Circle without Slipping

Rolling Ball inside a Cylinder

Rolling Bridge

Rolling Circles

Rolling Circles with Attached Points and Lines

Rolling Circles with Points and Lines

Rolling Cycloidal Curves

Rolling Cylinder with a Hole

Rolling Direction of a Cylinder

Rolling Disk

Rolling Mill

Rolling Multiple Dice

Rolling One Parabola on Another

Rolling Polygons

Rolling Polygons in a Circle

Rolling Polyhedron and Center of Gravity Plot

Rolling Two Dice with Weighted History

Rolling Up a Sheet of Graphene

Rolling Wheel with Spoke

Roman Numeral Calculator

Roman Numeral Graph

Roman Numerals

Romeo and Juliet

Rřmer's Measurement of the Speed of Light

Roofing a Cube to Produce a Dodecahedron

Roofs with Curves

Root Finder

Root-Finding Fractals

Root Plot of a Polynomial Class

Root Routes

Roots Blower

Roots of a Complex Number

Roots of a Polynomial with Complex Coefficients

Roots of Complex Numbers

Roots of Holomorphic Functions in the Unit Disk

Roots of the Bernoulli Polynomials

Roots of the Derivatives of a Certain Real Polynomial in the Complex Plane

Roots of Unity

Ropes as Nested Helices

Rorschach Test

Roses from Rolling Circles

Rosetta Spaceflight

Rosettes and Baskets Made of Tori

Rosettes from Op Art Patterns

Rosettes from Photos

Rotary to Linear Motion

Rotate and Fold Back

Rotated and Scaled Text in Graphics

Rotating a Cube in Perspective

Rotating a Cube in Space

Rotating a Cube Using Quaternions

Rotating a Cuboid to Form Four Möbius Bands

Rotating a Hypercube

Rotating a Hypercube in 4D

Rotating a Hypercube in Four Dimensions with Eight Spaced Cubes

Rotating a Lattice of Points

Rotating a Mask over a Tone Scale

Rotating a Tesseract in Perspective

Rotating a Unit Vector in 3D Using Quaternions

Rotating Beam Fatigue Tester

Rotating by Powers of i

Rotating Crystal Method for 2D Lattices Using Ewald's Circle

Rotating Cubes about Axes of Symmetry; 3D Rotation Is Non-Abelian

Rotating Disk Electrode: Distribution of Centers with Spillover Effect

Rotating Laser Sword in 3D

Rotating Lines around an Axis or a Circle

Rotating Magnetic Field

Rotating Michelson-Morley Interferometer

Rotating Plane with Intersecting Sphere and Circle

Rotating Points on Two Circles

Rotating Polygon Illusion

Rotating Polygons

Rotating Polyhedra in Space

Rotating Pythagoras

Rotating Regular Polygonal Rings

Rotating Space Station

Rotating Squares, Cubes, and Higher-Dimensional Hypercubes

Rotating Square Tilings

Rotating Substitution Systems

Rotating Text

Rotating the Faces of the Icosahedron

Rotating the Hopf Fibration

Rotating the Sides of a Right Regular Prism

Rotating Wheel Illusion

Rotation about a Point in the Plane

Rotation about Carbon-Carbon Bonds

Rotational and Translational Motion

Rotational Kinetic Energy of a System of Masses

Rotational Symmetries of Colored Platonic Solids

Rotational Symmetries of Platonic Solids

Rotational Symmetry of Multivariate Uncorrelated Standard Normal Distribution

Rotational-Vibrational Spectrum of a Diatomic Molecule

Rotation and Translation of a Rigid Body

Rotation as Product of Two Reflections

Rotation Illusion for Radial Wave Motion of Discrete Points

Rotation Index of Evolutes

Rotation in Two Dimensions

Rotation Matrix Entries

Rotation of Feynman Diagrams around an Electron-Photon Vertex

Rotation of Spinors

Rotation of the Euler Line of a Triangle

Rotation Point Mandala

Rotation Symmetries of Antiprisms

Rotation Symmetries of Prisms

Rotation through Radial Translations

Rotation-Vibration Energy Level Transitions of a Diatomic Rotor

Rotation-Vibration Transitions for a Perpendicular Band of a Symmetric Rotor

Rotation-Vibration Transitions of a Parallel Band of a Symmetric Rotor

Rotation with Zero Angular Momentum (The Square Cat)

Roulette: A Comfortable Ride on an n-gon Bicycle

Roulette (Epitrochogon) of a Disk Rolling around a Regular Polygon

Roulette (Epitrochogon) of a Regular Polygon Rolling around Another Regular Polygon

Roulette (Hypotrochogon) of a Circle Rolling inside a Regular Polygon

Roulette (Hypotrochogon) of a Polygon Rolling inside a Circle

Roulette (Hypotrochogon) of a Polygon Rolling inside Another Polygon

Roulette Plotter Device

Rounding Large Integers

Rounding p-adic Rationals

Rounding Rectangle Corners with the RoundingRadius Option

Route, Speed, and Acceleration of Your Mouse

Routh's Theorem

Rovibronic Infrared Spectrum of a Rigid Diatomic Rotor

Rovibronic Spectrum of a Parallel Band of a Symmetric Rotor

Rovibronic Spectrum of a Perpendicular Band of a Symmetric Rotor

Rowing to Shore and Then Running Away

Row Profiles in Color Images

Rows, Columns and the Main Diagonal of a Matrix

RSA Encryption and Decryption

R-Trees for Indexing Multidimensional Data

Rubik's Cube

Rubik's Cube Mechanism

Rubik's Snake Puzzle

Rudin-Shapiro Curve

Ruffini-Horner Algorithm for Complex Arguments

Ruffini-Horner Method for a Polynomial in Powers of x-h

Ruffini-Horner Method for Polynomials with Rational Roots

Rule 54

Rule Case Fractions in the Wolfram 2,3 Turing Machine

Rule Case Transition Diagrams for the Wolfram 2,3 Turing Machine

Rule Cycling

Rule of 72

Rule of Product Applied to Decks of Cards

Rule of Sum and the Inclusion-Exclusion Principle

Ruler and Compass Construction of a Square with Doubled Area

Rules for Logarithms

Rule Shaped Zonohedron

Run Expectancy Matrix in Baseball

Runge-Kutta versus Velocity-Verlet Solutions for the Classical Harmonic Oscillator

Runge's Phenomenon

Running Circles around Circles

Running in the Rain

Running Objects along a Path

Running Track Math

Russell's Thought Experiment in Special Relativity

Russian Multiplication

Rutherford Scattering

Saari Triangles for a Three-Candidate Election

Saddle-Node Bifurcation

Saddle Points and Inflection Points

Safe Operation of a Semibatch Reactor

Safety Pin

Sagitta, Apothem, and Chord

Sagnac Interferometer

Sagnac Interferometer with Three Mirrors

Sailing against the Wind

Sailplane Altimeter Tools to Show Flight Levels

Sale Price Calculator

Sales Tax and Discounts

Salinon

Sallen-Key Band-Pass Filter

Sallen-Key Low-Pass Unity-Gain Filter Response

Salt Packs for Heating or Cooling

Saltwater Puzzle

Salzer's Method for Numerical Evaluation of Inverse Laplace Transform Involving a Bessel Function

Same but Different

Sample Size Calculation - Means

Sample Size Calculation - Proportions

Sample Size Formula

Samples of Random Graphs

Sample versus Theoretical Distribution

Sampling a Digital Signal

Sampling a Uniformly Random Rotation

Sampling Distribution of a Positively Skewed Population

Sampling Distribution of the Mean and Standard Deviation in Various Populations

Sampling Distribution of the Sample Mean

Sampling of Boolean Functions

Sampling Statistics and Statistical Estimation

Sampling Theorem

Sanderson Engine

Sandpile Model

Sangaku for Incircles

SARIMA Process Forecasting Model

Sarrus Linkage

Saturation Binding of Ligands to Proteins

Saturday Morning Breakfast Cereal Fourier Transform

Saturn's Disappearing Rings

Saturn's Rings and the Cantor Set

Saturn's Seasonal Sundial

Saunders Digit Graphics

Saving for Retirement

Sawing an Eighth from a Bilinski Dodecahedron

Scalar Delay Logistic Equation

Scalar Feynman Diagrams and Symanzik Polynomials

Scalar Multiple of a Vector

Scalar Retarded Potential of a Point Charge Moving on a Circle with Constant Velocity

Scalenohedron

Scale-Up of a Batch Reactor

Scalings of a GI/G/1 Queue Realization

Scalogram of Gravitational Wave from a Binary Black Hole Inspiral

Scanning Electrochemical Microscopy: Diffusion on a Microdisk Electrode

Scanning Electrochemical Microscopy: Feedback Approach Curve

Scanning Electrochemical Microscopy: Fitting Rg with Negative Feedback Curve

Scanning Electrochemical Microscopy in Substrate Generator/Tip Collector Mode

Scanning Electrochemical Microscopy: Negative Feedback Approach Curve

Scanning Reference Electrode Technique (SRET)

Scattering by a Dirac Bubble Potential

Scattering by a Square-Well Potential

Scattering by a Symmetrical Eckart Potential

Scattering of a Gaussian Wave Packet on an Infinite Wall

Scattering over a Square Potential Well

Scattering over Potential Step

Schelling's Model of Residential Segregation

Scherk Minimal Surfaces

Schinzel's Theorem

Schlegel Diagrams

Schoenberg Matrix Player

Schoenberg Plane-Filling Curve

School Addition

School Multiplication

School Subtraction

Schrandt-Ulam Cellular Automata

Schröder Number Diagrams

Schröder Rectangulations

Schrödinger Equation for a Dirac Bubble Potential

Schrödinger Equation for a One-Dimensional Delta Function Potential

Schrödinger Representations in Function Theory

Schrödinger's Cat on Catnip

Schrödinger Wavefunctions in a Continuously Varying Potential

Schwarzschild Space-Time Embedding Diagram

Schwinger's Oscillator Model for Angular Momentum

Scientific Notation

Scissors Lift with Constant Diameter

Scrambled Sentences Builder

Scrambler Ride

Scrap Metal Price of Coins

Screw with Sharp V-Thread

Scuderi Split Cycle Engine

Seader's Method for Real Roots of a Nonlinear Equation

Sea Level

Sea Level Rise

Seam Curves on Sports Balls

Search for Soma Cube Solutions

Seasonal Variations of Day and Night

Seasons

Seating Friends around a Table

Secant and Tangent Lines

Secant Approximations

Secant Intersection with Two Internally Tangent Circles

Secant Root Finding Method

Second Droz-Farny Circle

Second Hardy-Littlewood Conjecture

Second Harmonic Generation and Absorption Spectra

Second-Order Partial Derivatives

Second-Order Reaction with Diffusion in a Liquid Film

Second Virial Coefficients for the Lennard-Jones (2n-n) Potential

Second Virial Coefficients Using the Lennard-Jones Potential

Sections of the 16-Cell

Sections of the Four-Cube

SectorChart

SectorChart Applied to GDP

Sedimentation of Four or Six Spheres in a Newtonian Fluid at Low Reynolds Numbers

Seebeck Effect in a Thermocouple

Seeing the Chinese Remainder Theorem

Seepage under a Dam by Flow Nets

Segmenting a Medical Image

Segment Intersection

Segment Theorem

Seidel Optical Aberrations

SEIRD Model for Analyzing Coronavirus (COVID-19) Pandemic

Seismicity of Germany

Seismoscope

Selected Reflections in the Sides of a Regular Polygon

Selecting from ImageData Using Rows and Columns

Selective Fractalization of Chevron-Type Polygons Edges

Selective Resizing of Images

Selectivity for Adsorption of Ethylene Relative to Ethane in NaX Zeolite at 20 °C

Selectivity in a Semibatch Reactor

Select, View, and Compare Named Colors

Self-Affine Variants of the Sierpinski Carpet

Self-Avoiding Hexagonal Branching

Self-Avoiding Paths through a Lattice

Self-Avoiding Random Walks

Self-Avoiding Random Walks in 3D

Self-Delimiting Binary Representation of a Ternary List

Self-Descriptive Strings

Self-Intersecting Polygons

Self-Intersections in a Polygon

Selfish Binary Halfrange Automaton Cycles 2D

Selfish Elementary Cellular Automata

Self-Replicating Graphs

Self-Similarity in Random Walk

Self-Similar Qubistic Plot of the S_z=0 Half-Filled Hubbard Model Basis States

Semantic Networks

Semenov's Algorithm for Solving Systems of Nonlinear Equations

Semi-Annular Spiral Billiard with Periodic Orbits

Semiclassical Approximation for Quantum Harmonic Oscillator Wavefunctions

Semiclassical Quantization for Asymmetric Rigid Rotors

Semiclassical Simulation of Photon Echoes for Atomic Frequency Comb

Semi-Fibonacci Partitions

Semigraceful Eulerian Graphs

Semi-Rotation Automaton Plot

Semisolid Polyhedra

Semitones in Pythagorean Tuning and 12 Tone Equal Temperament

Semitotalistic Triangular Cellular Automata on a Geodesic Sphere

Sendov's Conjecture

Sensitive Dependence in Iterated Maps

Sensitive Dependence on Initial Conditions in a Simple Three-Body Problem

Sensitivity Analysis of Transition Phases of Perturbed Gene Pathways with a Neural Network

Sensitivity of a Plug Flow Reactor to Model Parameters

Sensitivity of Elementary Cellular Automata to Their Inputs

Sensitivity, Specificity, and Incidence

Sensitivity to Initial Conditions for the Logistic Map

Sensitivity to Initial Conditions in Chaos

Sensitivity To Peturbation in Elementary Cellular Automata

Sensor Fusion with Normally Distributed Noise

Separable and Nonseparable 2D Sequences

Separating a Ternary Mixture of Water, 2-Propanol, and Acetone at Atmospheric Pressure

Separating Binary Azeotropes Using Pressure Swing Distillation

Separating Points by a Line or Parabola

Separation of Abietic Acid from Other Acids Using a Fractional Extraction System

Separation of Acetic Acid from Water Using Ethyl Acetate Entrainer

Separation of Air Components by Countercurrent and Co-Current Gas Permeation

Separation of a Partially Miscible Mixture Shown by Graphical Method

Separation of a Reactive Quaternary Mixture in a Distillation Column

Separation of a Reactive Ternary Mixture: Olefin Metathesis

Separation of a Reactive Ternary Mixture with a Distillation Column

Separation of Carbon Dioxide and Methane Using Well-Mixed Gas Permeation

Separation of Methanol from Water by Batch Rectification

Separation of Topological Singularities

Separatory Funnel Extraction

Sequence Alignment of Words

Sequence and Summation Notation

Sequence Sums that are Squares

Sequential Substitution Networks

Sequential Substitution Systems

Series: A Few Examples

Series Approximation for the Nonlinear Pendulum

Series Approximation for the Schwarz D Surface

Series Expansion of 1/(1-x)

Series Expansions of Powers of Trigonometric Functions

Series of Spheres at the Vertices of Polyhedra

Series Reactions in a Batch Reactor

Series Reactions in a CSTR with Time-Varying Input

Series RLC Circuits

Series RLC Circuit Solver

Series Solution of a Cauchy-Euler Equation

Series: Steps on a Number Line

Series with Interval of Convergence Dependent on Structure

Serlio's Ovals

Serra's Torqued Ellipse IV

Serrated Cylinder

Set of Nash Equilibria in 2x2 Mixed Extended Games

Set of Nash Equilibria in 2x2x2 Mixed Extended Games

Set of Nash Equilibria in 2x3 Mixed Extended Games

Set of Points Equidistant from Two Points in Taxicab Geometry

Set Operations on Intervals

Set Operations on Regions

Set Partition Refinement Lattice

Set Partitions Match Restricted Growth Functions

Sets of Faces of the Rhombic Dodecahedron and the Triacontahedron

Sets of Linear Combinations and Their Images under Linear Transformations

Seven-Coloring of a Torus

Seven Cylinders

Seven-Letter Anagrams with High-Frequency Letters

Seven-Letter Anagrams with High-Frequency Letters, Part 2

Seven Points with Integral Distances

Seven-Segment Display

Seven Touching Cylinders Puzzle

Sextic Toroidal Graphs

Shading a Surface Using Mesh

Shadow Pole

Shadows of a 3D Shape

Shakespearean Networks

Shakespearean Play Summaries

Shannon Diversity Index in Population Ecology

Shannon's Noisy-Channel Coding Theorem

Shape Descender

Shape-Invariant Solutions of the Quantum Fokker-Planck Equation for an Optical Oscillator

Shapes from Rhombuses

Shapes Produced by Rotating an Astroid

Shaping a Road and Finding the Corresponding Wheel

Shaping a Tubular B-Spline Surface

Shaping of Polar Zonohedron

Share Prices in the Constant Growth Dividend Discount Model

Sharpening Images

Shear-Angle Models for Oblique Metal Cutting

Shell Parameter Space

Shell Shapes Based on Cellular Automata

Shell Space: Flare, Verm, and Spire

Shell Space: The 'Snugness' Condition

Shell Structure of Noble Gas Atoms

Shepard Tones

Shephard's Algorithm for Two Convex Polyhedra with a Common Net

Sherlock Holmes's Dancing Men Cipher

Shifted Elementary Cellular Automata

Shifting Cube Fractal

Shifts in the Demand Curve

Ship Sailing over the Horizon

Shooting a Ball from a Block Sliding Down a Ramp

Shooting a Bullet from a Car

Shooting Method

Short Computation Patterns I

Short Computation Patterns II

Short Computation Patterns III

Shortening the 29th Olympic Torch Tour

Shortest Distance between a Point and a Line in 2D

Shortest Distance between Two Line Segments

Shortest Distance between Two Skew Lines

Shortest Path between Two Points in the Unit Disk Reflecting off the Circumference

Shortest Path between Two Points on a Sphere

Shortest Path for Forward and Reverse Motion of a Car

Shortest Path for the Dubins Car

Shortest Paths and the Minimum Spanning Tree on a Graph with Cartesian Edge Weights

Shortest Path Using Dijkstra's Algorithm

Shortest Time Problem

Shortest Tour through Large Cities in Selected Countries

Short-Run Cost Curves

Short-Run Production and Cost Curves

Short Simple Continued Fractions

Short-Term Temperature Trends within Long-Term Warming

Short-Time Expansion of Amplitudes for Time-Dependent Potentials

Short-Time Expansion of Quantum Amplitudes

Should You Walk or Run through the Rain?

Showing Faraday's Law with an Oscilloscope

Sicherman Dice

Side Capacity Model of Stagnancy in a Continuous Stirred-Tank Reactor

Side Lengths Opposite Unequal Angles

Sidereal Day and Month

Side-Splitting Triangle Ratios

Sierpinski 3D Arrowhead Curve

Sierpinski Carpet

Sierpinski Sieve

Sieve of Eratosthenes

Sight-Reading Rhythms

Sigmoid Microbial Survival Curves

Signal Detection Theory

Signal-to-Noise Ratio in Absorption Imaging

Signed 2D Triangle Area from the Cross Product of Edge Vectors

Signed and Unsigned Area under a Curve

Signed Area of a Polygon

Signed Determinant Terms

Sign of a Function

Signs in Space

Similar Right Triangles

Similar Triangles Determined by Miquel Circles and the Circumcircle

Simple 2-Column Polyominoes on the Hexagonal Lattice

Simple Arrhenius Model for Activation Energy and Catalysis

Simple Bar Chart

Simple Batch Distillation of an Ethanol-Water Mixture

Simple Batch Distillation of a Partially Miscible Binary Mixture

Simple Best-Fit Line

Simple Caesar Cipher

Simple Chaotic Motion of Quantum Particles According to the Causal Interpretation of Quantum Theory

Simple City Builder

Simple Contrast Adjustment

Simple Crystal Structures and Miller Indices

Simple Distillation Residue Curves for a Mixture of Chloroform and Acetone at 760 mmHg

Simple Distillation Residue Curves for a Mixture of Ethanol and Isopropanol at 750 mmHg

Simple Distillation Residue Curves for a Mixture of Pentane and Dichloromethane at 750 mmHg

Simple Dynamics of Epidemics, the Reproduction Number

Simple Graphs and Their Binomial Edge Ideals

Simple Harmonic Motion

Simple Harmonic Motion for a Spring

Simple Harmonic Motion of an Electric Dipole

Simple Harmonic Motion of a Spring

Simple Inequalities in the Unit Cube

Simple Initial Conditions in Code 20

Simple Line and Point Spiral Flower

Simple Manipulation of Pachelbel's Canon in D

Simple Model for Magnetic Hysteresis

Simple Nomogram for 95% Confidence Intervals in Small-Sample Binomial Statistics

Simple Phone Dialer

Simple Probabilistic Cellular Automata

Simple Programs in Turtle Geometry

Simple Rational Functions

Simple Reaction with Segregation in a Batch Reactor

Simple Schlieren Apparatus

Simple Simulation of Tides

Simple Solow Model

Simple Space Visualization Test

Simple Space Visualization Test 2

Simple Sphereman

Simple Spline Curves

Simple Spring Mass Damping

Simple Stair Calculator

Simplest Chaotic Circuit

Simple Stirling Engine

Simple Three-Letter Cube

Simple Trial-and-Error Algorithm to Determine Distillation Boundaries

Simple Unconstrained Optimization Method

Simple versus Compound Interest

Simplicial Homology of the Alpha Complex

Simplified Hartree-Fock Computations on Second-Row Atoms

Simplified Model of Quantum Scattering

Simplified Models of Terrestrial Arthropod Gaits

Simplified Social Amoebae

Simplified Statistical Model for Equilibrium Constant

Simplifying Some Algebraic Expressions Using Mathematica

Simpson's Paradox

Simson's Line

Simson's Theorem

Simulated Coin Tossing Experiments and the Law of Large Numbers

Simulated Epidemics in Random Networks of Varying Density and Size

Simulated Jagged Force-Displacement Curves

Simulated Moiré Patterns Using a Voronoi Mesh

Simulated Quantum Computer Algorithm for Database Searching

Simulating a Catastrophe Insurer

Simulating a Minimal ORAC Kinetic System

Simulating a Multiple Server Queue

Simulating a Normal Process from Sums of Uniform Distributions

Simulating Ascorbic Acid Degradation

Simulating Asset Prices with a GARCH(1,1) Model

Simulating a Three-Armed Pendulum

Simulating a Water Wave Using a Cycloid

Simulating Flickering Fire with Noisy Cellular Automaton

Simulating Gas Exchange in a Model of Pulmonary Fibrosis

Simulating Harmonographs

Simulating Microbial Count Records with an Expanded Fermi Solution Model

Simulating Real Gases in 2D

Simulating Temperature versus Time Relationships in the Thermal Preservation of Foods

Simulating the 2008 U.S. Presidential Election

Simulating the Bernoulli-Laplace Model of Diffusion

Simulating the Birthday Problem

Simulating the Birth-Death Process

Simulating the Branching Process

Simulating the Coupon Collector Problem

Simulating the IRR

Simulating the M/M/1 Queue

Simulating the Neutral Current of an AC System

Simulating the Poisson Process

Simulating the Power Factor of an AC System

Simulating the Simple Random Walk

Simulating Vehicle Suspension with a Simplified Quarter-Car Model

Simulation Domain for a Microelectrode: Is It Large Enough?

Simulation of 1D Diffusion Using the Monte Carlo Method

Simulation of 3D Diffusion Using the Monte Carlo Method

Simulation of a Simple Gas Pressure Model

Simulation of a Steady-State Binary Distillation Column

Simulation of a Steady-State Ternary Distillation Column

Simulation of a Turing Machine

Simulation of Feedback Control System with Controller and Second-Order Plant

Simulation of Pythagorean Cup

Simulation of Speaker and Reverb Output by Convolution Process

Simultaneity Bias

Simultaneous Approximation of Two Real Numbers by Rationals

Simultaneous Confidence Interval for the Weibull Parameters

Simultaneous Heat and Moisture Transfer in a Porous Cylinder

Sinai Billiard

Sinc Interpolation for Signal Reconstruction

Sin/Cos Function Game

Sine and Cosine Graph Generator

Sine and Cosine Helix

Sine and Cosine in 3D

Sine, Cosine, and Tangent Using Ratios of Sides of a Right-Angled Triangle

Sine, Cosine, Tangent and the Unit Circle

Sine-Gaussian Signals

Sine Oval and Nested Trig Functions

Sines of the Dihedral Angles of a Tetrahedron

Sine Wave Example of the Epsilon-Delta Definition of Limit

Sine Wave Generation Using an Unstable IIR Filter

Sine Waves for Musical Scales

Single- and Multibank Engines Using Four-Stroke Cycle

Single Character Image Steganography

Single Color Images

Single-Component Fugacity

Single-Component P-V and T-V Diagrams

Single Factor Analysis of Variance

Single-Layer Model for Planetary Atmospheres

Single-Phase Rectifier Fed from an Inductive AC Source

Single Photon Response for Rods in a Toad's Eye

Single-Qubit Quantum Error Correction

Single-Qubit Quantum Gates on a Bloch Sphere

Single-Share Password-Protected Visual Cryptography via Cellular Automata

Single Signals in Nuclear Magnetic Resonance

Single-Slit Diffraction

Single-Slit Diffraction Pattern

Single-Slit Diffraction Using Feynman's Method

Single-Slit Optical Diffraction Pattern and Profile Based on Cornu Spiral

Single Solute Batch Two-Phase Extraction

Single-Step Reaction Kinetics Using Collision Theory

Singularities of an Ellipsoidal Wave Front

Singular Value Decomposition

Singular Values in 2D

sin(t)=cos(pi/2-t)

Sinusoidal Bellows

Sinusoidal Building with Polygons

Sinusoidal Spirals

SIRD Model for Analyzing Coronavirus (COVID-19) Pandemic

SIR Epidemic Dynamics

Six-Astroid Designs

Six Basic Arithmetic Functions

Six-Box Game of Chance

Six Circles Theorem

Six Decagons and Six Great Circles of a Sphere

Six Hexagons

Six Incircles in an Equilateral Triangle

Six Interwoven Loops

Six-Piece Dissection of a Tetrahedron into Its Mirror Image

Six-Piece Dissection of Hill's Tetrahedron of Type 3 into a Triangular Prism

Six Polyhedra with 240 Equilateral Triangular Faces

Six-Sphere Coordinates

Six Square Pyramids

Six Triangle Orbits

Sixty Truncated Icosahedra

Skewed Cone

Skew Lines

Skin Effects in Straight Wires

Skolemization

Slanted Line Integral

Sledding on a Bumpy Slope: Chaos and Strange Attractor

Sleepless Knights Puzzle

Slices of Three-Manifolds

Slicing a Cylinder

Slicing an Indented Sphere

Slicing a One-Sided Polyhedron

Slicing a Solid of Revolution

Slicing a Sphere along Two Parallel Planes

Slicing a Torus

Slide and Swap on Cubic Graphs

Slider and Crank Mechanism

Slider Puzzle

Slide Rule

Sliding along a Curved Track

Sliding Along a Tautochrone Path

Sliding Block Displacing a Wedge

Sliding Block Puzzles

Sliding Cubes

Sliding Filament Model of Muscle Contraction

Sliding Octahedra

Sliding on a Parabolic Track

Sliding or Rolling of a Sphere, Cylinder, and Tube down a Semicircular Well

Sliding Puzzle with Periodic Boundary Conditions

Sliding the Roots of Cubics

Sliding the Roots of Quadratics

Sliding Tiles

Sliding to the Fermat Point

Sliding Window Maximums in O(N)

Slope and Equations of Lines through Points

Slope between Two Points on a Curve

Slope Field and Solutions of a Nonlinear Differential Equation

Slope Fields

Sloshing Modes in a Cuboidal Tank

Slurry Reactor with Declining Catalyst Activity

Small-Digit Addition

Smallest Circle Problem

Small Everyday Objects

Small Hadamard Matrices

Small Intervals where the Partial Sums of a Series Fail to Alternate

Small Lattice Ellipses

Small Set Partitions

Small Signal (AC) Bipolar Parameters from SPICE Parameters

Small Signed Integer Addition 3D

Small Turing Machines with Halting State: Enumeration and Running on a Blank Tape

Small World Networks

SmartSmith

Smiley Changer

Smirnoff's Graphic Solution of a Second-Order Differential Equation

Smith's Second-Order Method in Process Dynamics

Smooth Density Histograms for Cellular Automata

Smoothly Interpolating a Set of Data

Snails Counting Game

Snake-Arm Robot

Snell's Law of Refraction (Wave Fronts)

Snowboarding over Derivatives

Snowflake Designs

Snowflake Growth

Snowflake-Like 3D Growth

Snowflake-Like Patterns

Snub Tetrahedron

Soap Film between Two Equal and Parallel Rings

Sobel Edge Detection Filter

Soccer Penalty Kicks

Social Golfer Problem

Social Networking

SOHCAHTOA Triangle

Soil Temperature

Solar and Lunar Eclipses

Solar and Sidereal Days 2D

Solar Energy Incident on Earth's Surface

Solar Energy Yield for Three Mounting Systems

Solar Irradiance Using Hottel's Clear-Sky Model

Solar Neighborhood

Solar Panel of NASA's Phoenix Mars Lander

Solar Position Chart in Cartesian Coordinates

Solar Position Chart in Polar Coordinates

Solar System Mandalas

Solar Time Calculator

Solar Updraft Tower

Solid and Dihedral Angles of a Tetrahedron

Solid Angles on a Sphere

Solid Cylinder Rolling in a Turnable Hollow Cylinder

Solid Made of Rectangular Boxes Given by Three Views

Solid of Revolution

Solid Pendulum with a Spring-Mass System

Solids

Solids of Known Cross Section

Solids of Revolution

Solid-Solid-Liquid Equilibrium

Solids Whose Cross Sections Have the Same Shape

Solid Wood Texture

Solitary Wave Solution to the Nonlinear Schrödinger Equation

Solitons from the Korteweg-de Vries Equation

Soliton Trajectories According to Bohmian Quantum Mechanics

Soliton Trajectories for the Kadomtsev-Petviashvili Equation

Soliton Trajectories of the Modified Korteweg-de Vries Equation (mKdV)

Sol LeWitt (Virtual) Wall Drawing #146

Solow Growth Model

Solubilization Model for Ionic Compounds

Solute Extraction Cascade with Solvent Recycle

Solution and Stability of a 1-Periodic Differential Equation

Solution of a Boundary Value Problem Using the Differential Transformation Method

Solution of a Nonlinear Schrödinger Equation

Solution of a PDE Using the Differential Transformation Method

Solution of One-Dimensional Stefan Problem with Orthogonal Collocation

Solution of Quadratic Equations

Solution of Some Second-Order Differential Equations with Constant Coefficients

Solution of the 2D Heat Equation Using the Method of Lines

Solution of the First Underwood Equation Formulated as a Generalized Eigenvalue Problem

Solution of the Heat Equation for a Couple in Bed with a Cat

Solution of the Laplace Equation for Temperature Distribution in a Square

Solution of the Laplace Equation Using Coordinates Fitted to the Boundary Conditions

Solution of Two Equations in Two Unknowns

Solutions of 1D Fourier Heat Equation

Solutions of Fermat's Equation

Solutions of Schrödinger Equation for a Particle in a Finite Spherical Well

Solutions of the Elliptic Membrane Problem

Solutions of the Finite Difference Discretized Laplace Equation

Solutions to a Functional Equation via Stern-Brocot Tree Fractions

Solution to Differential Equations Using Discrete Green's Function and Duhamel's Methods

Solvent Swap Distillation

Solve Quadratic Equations with Integer Coefficients

Solve the Cryptoquote

Solve the Cryptoquote Automatically

Solve the Loculus of Archimedes

Solving a Cubic via the Trisection of an Angle

Solving a Double Scissor Truss

Solving a Linear Diophantine Equation by Tabulation

Solving a Linear Diophantine Equation in Two Variables by the Euclidean Algorithm

Solving a Linear Equation in One Variable and Two Parameters

Solving a Linear System with Uncertain Coefficients

Solving a System of Two Linear Equations with Substitution

Solving a Type of Equation with a Square Root

Solving Decanting Problems by Graph Theory

Solving Hard Traveling Salesman Problems

Solving Linear Inequalities

Solving Logic Puzzles with Binary Trees

Solving Mass Balances on a Distillation Column

Solving Matrix Systems with Real, Interval, or Uncertain Elements

Solving Mazes by Coloring

Solving Multiplication Equations

Solving Oblique Triangles

Solving Simple Equations

Solving Stefan-Maxwell Equations Using Orthogonal Collocation and Shooting Method

Solving Systems of Transcendental Equations

Solving the 1D Helmholtz Differential Equation Using Finite Differences

Solving the 2D Helmholtz Partial Differential Equation Using Finite Differences

Solving the 2D Poisson PDE by Eight Different Methods

Solving the Cable Equation

Solving the Convection-Diffusion Equation in 1D Using Finite Differences

Solving the Diffusion-Advection-Reaction Equation in 1D Using Finite Differences

Solving the Hole in the Square Problem with a Neural Network

Solving the Secular Equation for Zigzag and Bearded Graphene Nanoribbons

Solving the Subprime Loan Problem

Some Archimedean Solids in the Icosahedral Lattice

Some Common Biochemical Molecules

Some Examples of Molecule Orbitals

Some Examples of Ordinary Differential Equations with Missing x or y

Some Formulas Involving Quantifiers and Propositional Connections

Some Gaussian Integrals

Some Homogeneous Ordinary Differential Equations

Some Integer Functions Involving Division

Some Irreptiles of Order Greater than 20

Some Named Algebraic Surfaces

Some Numbers behind Rubik's Cube

Some Partial Differential Equations with Chaotic Solutions

Some Peptide Properties

Some Polar Plots

Some Polyhedra with Identical Triangular Faces

Some Polynomial Curves on the Torus

Some Ratios for Regular Inscribed Polygons

Some Representative Crystal Structures

Some Rotations in 3D

Some Simple Logic Problems

Some Special Types of Matrices

Some Symmetry Operations in Crystallography

Some Time-Delay Differential Equations

Some Triple Integrals for Mass

Some Uniform Polyhedra

Some Unistable Polyhedra

Sonar

Sonar and Radio Navigation Techniques

Sorted Evolutions of Cellular Automata

Sorting Algorithms

Sorting Networks

Sorting the Values of Two Number Theoretic Functions

Sound Examples

Sound Produced by Open and Closed Pipes

Sounds from Amplitude and Frequency

Sounds of Waveforms

Sources, Saddle Points, and Sinks in Vector Fields

South Indian Ocean Currents, Flight MH370

South Pacific Currents and Dispersion of Coconuts

Spacecraft Flying in Formation

Space Curve Tubes

Space-Filling Fractal Curves

Space-Filling Polyhedra

Space-Filling Polyhedra Based on a Truncated Octahedron

Space-Filling Tetrahedra

Space Filling with a Prismatoid

Space Filling with a Rhombic Dodecahedron of the Second Kind

Space Filling with Rhombic Dodecahedra and Cubic Close Packing

Space Filling with Stella Octangulas and Octahedra

Space Filling with Trapezoid-Rhombic Dodecahedra and Hexagonal Close Packing

Space Filling with Two Bilinski Dodecahedra and Four Obtuse Golden Rhombohedra

Space Filling with Two Kinds of Polyhedra

Space Filling with Two Kinds of Triacontahedra

Space-Quantization of Angular Momentum

Spacetime Curvature Due to the Earth-Moon System

Spacetime Curvature for a Falling Object near the Earth's Surface

Spacetime Diagram

Spacetime versus Spacespace

Space Visualization Test on Prism Edges

Space Visualization Test on Pyramid Edges

Spacing Distribution of Random Numbers

Spanning Tree of Points on Sphere

Sparse Rulers

Sparse Triangle Tiling

Spatio-Temporal Epidemic Spread

Special Case of Vandermonde's Identity

Special Colored Sudoku

Special Prime Circles

Special Regular Rings with Involution

Special Rose Surfaces

Spectral Broadening Induced by Self-Phase Modulation

Spectral Distribution of Total Energy Emitted by a Black Body versus Temperature

Spectral Measures

Spectral Properties of 1D Fibonacci Quasicrystals

Spectral Properties of Directed Cayley Graphs

Spectral Sensitivity of Rods in Human Retina

Spectral Series of the Hydrogen Atom

Spectral-Temporal Distribution of Biphotons from a Spontaneous Parametric Down Conversion (SPDC) Process

Spectra of Substitution Systems

Spectra of the D-Lines of Alkali Vapors

Spectrum of Fused Silica Microspheres

Specular and Diffuse Reflection

Specularity in Computer Graphics

Speculative Superluminal Regime for Relativistic Addition of Velocities

Speed, Motion, Pursuit, and Depth (Visual Depth Perception 15)

Speed of a Point on the Surface of the Earth

Speed of Sound

Speed of Sound in Water-Air Mixtures

Speed, Pursuit, M/P Ratio, and Depth (Visual Depth Perception 16)

Speed Regulation for Visualization of Elementary Cellular Automata

Speedup and Slowdown Phenomena in Turing Machines

Sphere and Torus Made of Segments

Sphere Editor

Sphere-of-Influence Graphs

Sphere Packing

Sphere Rolling on Rails

Spheres at the Vertices of Polyhedra

Spheres Construction Set

Spheres in a Sierpinski Tetrahedron

Spheres on a Cylinder

Spheres on a Truncated Icosahedron

Sphere Volume and Area

Sphere with Tunnel Brachistochrone

Spherical Aberration in a Plane-Convex Lens

Spherical Asymptote

Spherical Cap and Ring

Spherical Coordinates

Spherical Coordinate System with Unit Vectors

Spherical Cosine Rule for Angles

Spherical Cycloid

Spherical Cycloids Generated by One Cone Rolling on Another

Spherical Harmonic on Constant Latitude or Longitude

Spherical Harmonics

Spherical Law of Cosines

Spherical Law of Sines

Spherical Lens Aberration

Spherical Mirror Anamorphosis of Regular Polygons

Spherical Models of Polyhedra

Spherical Pendulum

Spherical Plain Bearing

Spherical Product of Two Superformulas

Spherical Pythagorean Theorem

Spherical Right Triangles

Spherical Seismic Waves

Spherical Shell in a Magnetic Field

Spherical Signature of Two Planets

Spherical Triangle Solutions

Spherical Trigonometry on a Gnomonic Projection

Spherical Trochoid

Spherical Yin-Yang

Sphericon

Spheroidal Foci

Spheroidal Protrusion in a Uniform Electric Field

SPICE Program for Electronic Circuits

Spieker Center Triangle Construction

Spies and Double Agents

Spikey and Dodecahedron

Spikey Diamond

Spikey Gear

Spikey to Wolfram|Alpha Logo

Spin Echo Pulse Sequence in Magnetic Resonance Imaging

Spin Game

Spinning Action

Spinning Bicycle Wheel on Chair

Spinning Circles Optical Illusion

Spinning Disk Pendulum Swinging on Top of a Rotating Table

Spinning Double Yin-Yang

Spinning Ice Skater

Spinning Mass with Variable Radius

Spinning Out Sine and Cosine

Spinthariscope

Spin-Weighted Spherical Harmonics

Spiral Explorer

Spiral Formations from Iterated Exponentiation

Spiral of Circles Optical Illusion

Spiral of Primes

Spiral or Not?

Spirals!

Spirals and Helices

Spirals in Squares

Spirals of Kite-Shaped Blocks

Spirals of Squares

Spirals of Trapezoids

Spirals of Triangles, Hexagons, Circles and Spheres

Spirals to the Unit Circle from Trigonometric Series

Spire Star with Rhombic Pyramids

Spirograph

Spirographic Orbit of a Star in Extended Mass Distribution

Spirolateral

Spline Sketchpad

Splitting a Cube

Splitting the Sides of a Triangle by Its Pedal Triangle

Spoked Wheel

Spontaneous Emission in a Free-Electron Laser

Spontaneous Oscillations in Yeast Chemostat Cultures

Sporadic Groups

Sports Arbitrage: Two-Agency, Two-Outcome Efficient Pricing Test

Sports Scores

Sports Seasons Based on Score Distributions

Spot the Difference

Spotting a Liquidity Trap

Spreading Particles in a Disk

Spread-Location Regression Diagnostic Check

Spread of a Gaussian Wave Packet with Time

Spread of Zika in Brazil Using the Ross-MacDonald Model

Spreadsheet-Like Solution of Large-Scale Systems of Equations: Comprehensive Corporate Model Example

Spring-Cart-Pendulum System

Spring in Field of Two Magnets

Spring-Launched Ball

Spring-Mass-Damper (SMD) System with Proportional Derivative (PD) Controller

Spring-Mass-Damping System with Two Degrees of Freedom

Spring-Mass System on a Rotating Table

Spring Pendulum

Spring Return Button

Springs in Parallel and in Series

Sprott's Jerk Equations

Spurious Forces on a Brownian Particle in a Diffusion Gradient

Sputnik 1 Orbiting the Earth

Sputnik 1 Simulation

Squared Chain Puzzle

Square Helmholtz Coils

Square-Hole Drill in Three Dimensions

Square Koch Fractal Curves

Square Koch Fractal Surface

Square Matrix Permutations

Square of Opposition in Aristotelian Logic

Square of the Sum of Two Numbers

Square Passing through Four Points

Square Pyramid and Its Right Triangles

Square Pyramid Made from Cubes or Rhombic Dodecahedra

Square Representation of Farey Sequences

Square Root Model for Rates of Microbial Growth or Inactivation

Square Roots with Newton's Method

Square Shuffle Puzzle

Square Size Illusions

Squares of Sine and Cosine

Squares on a Line Segment

Squares on the Sides of a Quadrilateral

Square Spiral for a Given Number of Divisors

Square Spiral Tiling

Square with Lines and Points

Squaring a Binomial

Squaring a Number

Squaring Numbers

Squeeze Theorem

Squiggle Art

Squigonometric Sine Function

Stability and Critical Angle of a Box

Stability of a Linear Two-Dimensional Autonomous System

Stability of Polygons Inscribed in an Ellipse

Stability of the Lorenz System

Stability Radius for the Shortest Path Problem

Stabilization of the Wave Equation by Direct Fourier Filtering

Stabilizers and Fixes of the Action of D4 on the Two-Colorings of a 2 by 2 Chessboard

Stabilizing a Mast

Stable and Unstable Faces of Antiprisms

Stable Density Function

Stable Distribution Computed with the Zolotarev Integral

Stable Distribution Function

Stable Equilibria

Stable Lévy Process

Stable Marriages

Stack Diagram for 1D Box-Counting Steps

Stacked Bar Chart for Neighborhood Residential Composition

Stackelberg Equilibrium Set in 2x2 Mixed Extended Games

Stacking Cannonballs

Stacking Cylinders to Form a Solid of Revolution

Stacking Dominoes to the Limit

Stacking Squares on a Circle

Stacks of Reflecting Plates

Stage Illumination Problem

Stained-Glass Filter from a Voronoi Mesh

Stained Glass Window Generator

Stairs from Cube

Stairstep Interpretation of Catalan Numbers

Stalactites

Stamping Out Shaped Disks

Standard American and European Options

Standard and Generalized Versions of the Monty Hall Problem

Standard Colorimetric Observer Color-Matching Functions

Standard Form of the Equation of a Circle

Standard Normal Distribution Areas

Standing on a Beam Supported by a Cable

Standing Waves and Chords

Stanley's Congo Expedition

Stapler Puzzle

Star Dipyramid

Stardust-NExT Spaceflight

Star Neighborhoods in Double Barycentric Subdivision

Star of David Theorem

Star Polygons

Star Prisms

Star Pyramids

Starr Plots

Starr Rose Mesh

Star Trek

Startup and Steady State in a Chemostat

Start-Up of a Plate Gas Absorption Unit

Start-up of Poiseuille Flow in a Newtonian Fluid

State Emphasis for 2,3 Turing Machine 596440

State of Light Polarization

State Population Growth

State Sequences in the Wolfram 2,3 Turing Machine

States from All Possible Elementary Cellular Automata

State-Switching Damped Harmonic Oscillator Model

State Transition Diagrams for Modular Multiplication

State Transition Diagrams for Modular Powers

State Transition Graphs for Integer Torus Maps

Static Deformations of Timoshenko Beams

Static Equilibrium and Triangle of Forces

Static Equilibrium for an Extended Object

Static Equilibrium for a Plate with Support at Three Points

Static Friction

Static Longitudinal Stability of Fixed Wing Aircraft

Stationary Precession of a Spinning Top

Stationary Precession of a Spinning Top (Revised)

Stationary States in a Nonisothermal Continuous Stirred-Tank Reactor

Stationary States of Maximal Entropy Random Walk and Generic Random Walk on Cayley Trees

Statistical Behavior of a Set of Uniformly Rotating Independent Particles with Random Frequencies

Statistical Justification of a Representative Democracy

Statistical Mechanics of Money

Statistical Nature of Maxwell-Boltzmann Distribution

Statistical Power

Statistical Thermodynamics of Ideal Gases

Statistics Associated with Normal Samples

Statistics for Throwing a Die Three Times

Steady Flow over a Rotating Disk: von Kármán Swirling Flow

Steady Potential Flow through Box with Staggered Inlet and Outlet

Steady-State 1D Conduction through a Composite Wall

Steady-State Binary Fickian Diffusion

Steady-State Distillation of a Methanol-Water Mixture

Steady-State Distillation of a Quaternary Mixture

Steady-State Heat Conduction in a Cylinder

Steady-State Heat Conduction in an Annulus

Steady-State Heat Transfer through a Composite Plane Wall

Steady-State Heat Transfer through an Insulated Wall

Steady State of an Extractive Distillation Column

Steady-State Operation of the Cardiovascular System

Steady States for a Dynamical System in 2D

Steady-States of a Nonlinear Chemical System Using the Arc Length Continuation Method

Steady-State Temperature Distribution in Conducting Square

Steady-State Temperature Profile of Two-Layer Pipe

Steady-State Two-Dimensional Convection-Diffusion Equation

Steam Distillation of a Mixture of Hydrocarbons

Steam Locomotive Drive

Steam Reforming of Propane

Steering Multiple Radio Control (RC) Cars with One Joystick

Stefan-Boltzmann Law

Steffen's Flexible Polyhedron

Steiner Chain Inversion

Steiner Chain of Circles

Steiner Formula for Cassini Oval

Steiner Networks for Four Points

Steiner Surfaces

Steinhart-Hart Approximations for Thermistor

Steinhaus' Billiard Ball Loop

Stella Octangula

Stellar Luminosity

Stellar Nucleosynthesis

Stellar Parallax

Stellating an Icosahedron with Triangular Slabs

Stengel's Theorem

Step and Impulse Response of a Second-Order System

Step-by-Step Julia Sets

Stepping through k=3, r=1 Cellular Automata Rule Space

Step Response of a Manometer

Step Response Using Padé Approximants

Step Response with a P Controller

Stepwise Trisection of a Square

Stereochemistry of E2 Elimination Reactions

Stereogram of 4D Pentachoron Rotations

Stereographic Projection

Stereographic Projection of a 3-Sphere

Stereographic Projection of a 4D Clifford Torus

Stereographic Projection of a Cube

Stereographic Projection of a Hypercube

Stereographic Projection of Platonic Solids

Stereographic Projection of Some Double Groups

Stereoscopic View of Polyhedra

Stereo View without Glasses

Stern-Brocot Tree

Stern-Gerlach Experiment

Stern-Gerlach Simulations on a Quantum Computer

Stewart's Theorem

Stippling Effect for Photographic Images

Stirling Numbers of the First Kind

Stirling Numbers of the Second Kind

Stirling Numbers of the Second Kind and Nonattacking Rooks

Stirling's Approximation versus n!

Stirling's Triangles

Stochastic Diploid Model for Gene Frequency in a Population

Stochastic Gradient Descent

Stochastic Model of Microbial Injury and Mortality

Stochastic Model of Seed and Spore Germination

Stochastic Resonance

Stochastic Rock-Paper-Scissors Population Dynamics

Stochastic Simulation of Test Results with Guessing

Stochastic Time-Averaged Moiré Fringes

Stock Forecasting

Stock Market Crossover

Stock Market Returns by Party

Stock Option Strategies

Stock Price Envelopes

Stock Price Probability with Stable Distributions

Stock Price Simulation Using Stable Random Variables

Stock Prices of Technology Companies

Stoichiometry: With Excess or Limiting Reagents

Stokes Boundary Layer

Stokes Flow in Container with Concave Bottom

Stokes Parameters for Superposition of Two Slightly Noncollinear Polarized Beams

Stokes Parameters for the Superposition of Two Slightly Noncollinear Light Beams with Orthogonal Polarizations

Stolarsky Approximations to Popular Means

Stolz Angle

Straight Across Puzzle

Straight Cylinder Engine

Straightening Tool for Photographic Images

Straightening Up an Image

Strange Attractor of Gumowski-Mira

Strang's Strange Figures

Stratification as a Device for Variance Reduction

Streamlines for Laminar Flow Past a Rotating Solid Cylinder

Streptohedron and Trapezohedron

Stress Distribution in a Circular Plate with Concentrated Radial Loadings

Stress Propagation in a Truss Bridge

Stress-Strain Analysis by the Finite Element Method

String Matching Automaton

Strings That Are Derivable in a Certain Number of Steps by a Multiway System

Stripping a Hydrocarbon from Oil Using Live Steam

Stripping and Rectifying Cascades for Isopropyl Acetate Chemistry

Stripping Column Operation

Strips of Equal Width on a Sphere Have Equal Surface Areas

Stroboscopic Photograph of a Bouncing Ball

Strong RSA Cryptosystem

Stroop Effect: Reading Colored Words

Structural Analysis of a Pyramid

Structural Instability of a Supercritical Pitchfork Bifurcation

Structure and Bonding of Second-Row Hydrides

Structured Model for Intracellular PHB Production

Structure of Binary Numbers

Structure of Dilute Suspensions

Structure of Double Triacontahedron

Structure of the Flute

Structure of Water in Acid and Basic Media

Student's t-Distribution

Student's t-Distribution and Its Normal Approximation

Study of a Batch Reactive Rectifier

Study of a Four-Stage Batch Distillation Column

Study of Successive First-Order Reversible Reactions

Study of the Dynamic Behavior of the Lorenz System

Study of the Dynamic Behavior of the Rossler System

Sturm's Theorem for Polynomials

Styles of Faulting

Styling Line Caps and Line Joins

Stylized Pie and Bar Charts for Fast Food Nutrition

Subdivision Algorithm for Bézier Curves

Subgroup Lattices of Finite Cyclic Groups

Subgroup Lattices of Groups of Small Order

Subrange Data View

Subrogation

Substitute and Complementary Goods

Substituted Pyrimidines and Purines

Substitution System Defined by Splitting Each Cell into Four

Substitution System Defined by Splitting Each Cell into Nine

Substitution Systems for Elements of Two Kinds

Substitution Systems in 3D

Substitution Systems in Two Dimensions

Substitution System Trees

Substitution Tilings

Subtraction Bingo with Negatives

Subtraction Bingo with No Negatives

Subtriangles Formed by Concurrent Lines Parallel to the Sides of a Triangle

Successes and Failures in a Run of Bernoulli Trials

Successive Averages of the Vertices of a Polygon

Successive Derivatives of a Polynomial

Successive Differences and Accumulations of the Jacobi Symbol

Successive Differences of Sequences

Successive Dissociations of Polyprotic Acid H_4A as Regulated by pH

Successive Finite Difference Triangle

Successive Three-Point Method for Weibullian Chemical Degradation

Successive Truncations of a Polygon

Successive Truncations of a Polygon, Stacked in 3D

Sudoku Game

Sudoku Logic

Sugarscape: Agent-Based Modeling

Summation by Parts

Summer Insect Pandemics in the United States

Summing an Arithmetic Progression

Sum of a Geometric Series

Sum of an Arithmetic Progression

Sum of a Telescoping Series

Sum of a Telescoping Series (II)

Sum of Empty Skies for a Set of Planets

Sum of Exterior Angles of a Polygon

Sum of Medians Divided by the Perimeter

Sum of Numbers on Invisible Faces

Sum of Odd Numbers

Sum of Powers of Divisors

Sum of Reciprocals of Triangular Numbers

Sum of Sines

Sum of the Alternating Harmonic Series (I)

Sum of the Alternating Harmonic Series (II)

Sum of the First 10 Terms of a Generalized Fibonacci Sequence

Sum of the Squares of the Sides of a Projected Regular Tetrahedron

Sum of Three Triangular Numbers

Sum of Two Vectors

Sum of Volumes of Several Platonic and Archimedean Solids

Sums of Consecutive Integers

Sums of Generalized Cantor Sets

Sums of Sine Waves with Several Step Sizes (Sawtooth or Square Approximations)

Sums of Squares of Segments Created by a Pedal Triangle

Sums of Squares of the Side Lengths and Various Radii of a Triangle

Sundaresan-Krishnaswamy Technique for Estimation of Process Parameters

Sunflower Seed Arrangements

Sunny Random Rays

Sunshine Logo

Superannuation Calculator

Superdense Coding

Superellipse Shapes

Superellipsoid Shapes

Superimposed Gaussians

Super Moiré Patterns

Superposed Contour and Parametric Plots in the Complex Plane

Superposition of Quantum Harmonic Oscillator Eigenstates: Expectation Values and Uncertainties

Superposition of Sound Waves

Superposition of Standing Waves

Superposition of Standing Waves on a String

Superposition of Transverse Simple Harmonic Waves

Superposition of Two Sine Waves with Sum and Beats

Superposition of Wave Pulses

Superposition of Waves

Superquadrics

Supersymmetric Partner Bessel Functions

Supersymmetry for the Square-Well Potential

Supplemental Jurisdiction

Supplementary Solid Angles for Trihedron

Supply and Demand

Supply and Demand Excise Tax

Supply and Demand Quantity Restriction

Supply Curve from Piecewise Linear Cost Function

Supporting Lattice Structure

Support Your World Cup Team

Supremum of an Increasing Bounded Sequence

Surface Area Increase by Size Reduction

Surface Area of a Solid of Revolution

Surface Displacements Due to Underground Faults

Surface Integrals over Segments of Parametrized Surfaces

Surface Kinetics with Pore Diffusion Resistance

Surface Morphing

Surface of Revolution from Wavelets

Surface Parametrizations and Their Jacobians

Surface Property Editor

Surfaces and Gradients

Surfaces Defined on Torus Knots

Surfaces of Constant Tisserand Parameter

Surfaces of Revolution with Constant Gaussian Curvature

Surfaces of Wave Normals in Crystals

Surface Tension: Walking on Water

Surface with Branch Cuts

Surge Propagation in a Transmission Line

Surplus Production in Logistic Growth

Surplus Production Models and Equilibrium Harvest

Surveyor-Hunveyor Tripod

Survival Curves of Bacilli Spores with an Activation Shoulder

Survival of the Quasispecies

Survival Rate for Patients with Pulmonary Arterial Hypertension (PAH)

Swapping Qubit States

Swapping Rule and Initial Condition

Swash Plate Drive

Sweeping Integral Examples

Sweet Heart

Swerve Drive Robot

Swimming in Curved Space

Swim, Swim and Walk, or Walk?

Swing-and-Twist-Hinged Dissection of an Octagon to Two Octagons

Swing-and-Twist Hinged Dissection of One Regular Heptagon into Eight

Swing-and-Twist Hinged Dissection of One Regular Heptagon into Seven

Swingboat Ride

Swinging Atwood's Machine

Swinging Double Slider-Crank

Swinging Pendulum

Swing the Logarithmic Curve around (1, 0)

Swirl and the Curl

Swirl Arcs

Swirl Points

Swirls

Swirly

Swiss Compass

Switching between Overloaded Sliders

Sydler's Dissection of a Hill Tetrahedron into an Isosceles Triangular Prism

Sydler's Dissection of a Pyramid into a Prism

Sylver Coinage

Sylvester Matrix

Sylvester's Four-Point Problem

Sylvester's Postage Stamp Problem

Symbolic Systems

Symbolon Hemisphere

Symbol Rotation Patterns

Symmetrical Spline Curves

Symmetric Chaos in the Complex Plane

Symmetric Compositions of Rhombic Dodecahedra of the Second Kind

Symmetric Decompositions of a Rhombic Triacontahedron

Symmetric Independent Families of Four Isosceles Triangles

Symmetric Substitution Systems

Symmetries and Antisymmetries of Truchet Rosettes

Symmetries of a Prism

Symmetries of a Space-Filling Polyhedron with 54 Faces

Symmetries of a Square and an Equilateral Triangle

Symmetries of the Dodecahedron

Symmetries of the Octahedron

Symmetrizing Positive Random Variables

Symmetry Breaking in the Perovskite SrTiO3

Symmetry, Energy Levels and Optical Selection Rules for Naphthalene Molecule

Symmetry in Graphs of Functions and Relations

Symmetry of a Mystery Curve

Symmetry Planes and Optical Isomerism

Symmetry Planes and Stereoisomers

Synchronization of Chaotic Attractors

Synchronization of Coupled Phase Oscillators

Synchronizing Pendulum Clocks

Synchrotron Radiation

Synergism and Antagonism

Synergistic Enzyme Hydrolysis of Cellulose in Biomass

Synthesis of Ethanol by Hydration of Ethylene

Synthesis of Hydrogen Bromide by Free-Radical Chain Reaction

Synthesis of Rugate Optical Filter

Synthesis with Even and Odd Functions

Synthetic Division (Ruffini's Rule)

Synthetic ECG

Synthetic Fetal Electrocardiogram

Synthetic Legal Precedent Structures: Feature Distance

Synthetic Legal Precedent Structures: Lévy Flight

System Availability

System Bandwidth for Cascaded Amplifiers

System of Pendulums: A Realization of the Sine-Gordon Model

System of Three Linear Equations with One Parameter

System Reliability

Systems of Two Linear Equations with One Parameter

Szegö Curve

Table Legs Made of a Single Bent Bar

Table of Dirichlet Characters

Table of Nuclides

Table of Primes

Tacoma Narrows Bridge Collapse

Tafel Curve in Electrochemistry

Tag Systems

Tail Areas under Chi-Squared Distributions

Tail Conditional Expectations

Tail Rotor of a Helicopter

Takagi Curve

Taking Apart a Cube

Talbot Carpet

Talbot Carpet for a Ronchi Grating

Tamari Attractor

Tamari Lattice

Tangent Chord Angle

Tangent Circle and Arbelos

Tangent Circles

Tangent Circles and Parallel Diameters

Tangent Circles to Two Circles

Tangent Circles to Two Parallel Lines and Passing through a Point

Tangent Lines to a Conic Section

Tangent Lines to a Parabola

Tangent Lines to Exponential and Logarithmic Functions through the Origin

Tangent Line Using Many Different Limit Configurations

Tangent ODE Chase

Tangent on a Logarithmic Spiral

Tangent Planes on a 3D Graph

Tangent Planes to Quadratic Surfaces

Tangent Plane to a Sphere

Tangent Points on a Semicircle

Tangents to a Circle

Tangents to an Ellipse from a Given Point

Tangents to an Excircle

Tangents to a Rotating Ellipse

Tangents to the Circumcircle at the Vertices

Tangents to the Incircle from a Point on the Circumcircle

Tangent to a Catenary

Tangent to a Curve

Tangent to a Cycloid

Tangent to a Surface

Tangram

Tangram (Variation)

Tank Equilibria

Target Motion with the Metropolis-Hastings Algorithm

TARP Toxic (Illiquid) Assets Pricing Model

Tarski's Adaptation of Wojtowicz's Argument on Optimal Dissection of a Unit Square

Task Partitioning in Insect Societies: A Model Based on Electric Circuits

Tautochrone Problem

Tax Deferral

Taxicab Geometry

Taxicab Voronoi Diagram by a Cellular Automaton

Tax Incidence

Tax Rates and Tax Revenue

Taylor Approximations in Two Variables

Taylor Expansions with Noninteger Number of Terms

Taylor Polynomials

Taylor Polynomials Approximated by Interpolations

Taylor Series

Taylor's Hinged Dissection of One Parallelogram into Another

Teaching Limit of a Function

Teichmüller Space of a Torus

Telescopic Tower

Television Monitor Based on a Cathode Ray Tube

Temperature and Entropy of a Black Hole

Temperature Changes for Inhalant Gases

Temperature Changes in an Ideal Gas

Temperature-Composition Diagram for Immiscible Liquids

Temperature Control of a Batch Fermentor

Temperature Dependence of Dehydrogenation of Ethyl Benzene to Styrene

Temperature Dependence of Equilibrium Constant for Reaction of Water and Carbon Monoxide to Carbon Dioxide and Hydrogen

Temperature Dependence of Henry's Law Constant

Temperature-Dependent Rotational Energy Spectrum

Temperature Distribution in Convective Fins with Variable Thermal Conductivity

Temperature Distribution in Four-Layer Skin Tissue

Temperature-Entropy Diagram for Water

Temperature-Programmed Desorption

Temperature Propagation in a Thin Steel Rod

Temperature Scales

Temperature Variation of Heat Capacity for an Ideal Diatomic Gas

Tempered Fractionally Differenced White Noise

Tempestuous Teapot

Templator Model of Chemical Self-Replication

Ten Billion Barrel Puzzle

Tendency of a Curve

Ten Models for Tumors

Tensegrity

Tension in a Hanging Chain

Tension of a Rope with a Hanging Mass

Tensions between a Chain of Blocks

Tensor Equation of a Plane

Ten Year Calendar

Terminal Velocity of Falling Particles

Terminal Wealth Optimization with Power and Log Utility

Term Structure of Interest Rates

Term Weighting with TF-IDF

Ternary Batch Rectification

Ternary Card Game

Ternary Phase Diagram with Alternate Phase Envelope

Ternary Phase Diagram with Phase Envelope

Testing an Intuitive Random Generator with the Task of Emptying a Cube

Testing a Polygon for Convexity and Self-Intersection

Testing Reading Comprehension

Testing Second-Order Integrators for Motion of a Charge in a Homogeneous Magnetic Field

Test Your Spatial Visualization Abilities

Tetl-Box Synthetic Bacteria Growth Kinetics

Tetrads

Tetrahedra in a Hexagonal 3D Net

Tetrahedral and Octahedral Similarohedrons

Tetrahedral Animated Ring

Tetrahedral Loops

Tetrahedral Spine

Tetrahedron Built from Rhombic Dodecahedra or Spheres

Tetrahedron Centers

Tetrahedron to Cuboctahedron

Tetrahedron Volume

Tetration

Tetraviews of Elementary Functions

Tetrix Viewpoints

Texas Hold 'Em: Possible Outcomes after the "Flop"

Text Positioning in Three Dimensions with Nested Transformations

Textured Conformal Mappings

Texture Perception Patterns

Thales's Theorem: A Vector-Based Proof

Thales' Theorem

The 12 Coin Weighing Problem

The 12x12 Queens Problem

The 14 3D Bravais Lattices

The 1860 US Presidential Election under Different Voting Methods

The 196 Algorithm, Reorder-and-Add Algorithm, and RATS Sequence in Different Bases

The 2001 CSO Mortality Tables

The 2008 Convention Speeches

The 2-(64,8,1) Design

The 26-Sided Unilluminable Room

The 29 Tetrachords and Other Set Classes

The 2D Ising Model Monte Carlo Simulation Using the Metropolis Algorithm

The 30 Subgroups of the Symmetric Group on Four Symbols

The 3n+1 Problem

The 4 Puzzle

The 57-Cell

The 6×6 Points Connection Problem

The Acceleration of a Two-Block System

The Action of the Modular Group on the Fundamental Domain

The Adjusted Winner Procedure

The Aeolipile

The Aging Spring

The Airy Wave Train

The Alcubierre Warp Drive

The Alexander Polynomial of a Knot

The Alpha and Beta Components of the Hodgkin-Huxley Model

The Ambassadors, Interactive

The Ancestral Genetic Code Cube

The Andromeda Paradox

The Apollonius Circle of a Triangle

The Appeals Court Paradox

The Arbelos

The Arcsine Transformation of a Binomial Random Variable

The Area between Two Circles

The Area of a Square in a Square

The Area of a Triangle as Half a Rectangle

The Area of a Triangle inside the Incircle

The Area of a Triangle, its Circumradius, and the Perimeter of its Orthic Triangle

The Area of a Triangle Using a Determinant

The Area of Part of an Isosceles Triangle

The Area of the Contact Triangle

The Area of the Excentral Triangle

The Area of the Incentral Triangle

The Area of the Pedal Triangle of the Centroid

The Area Over a Receiver Operating Characteristic (ROC) Curve as an Index of Diagnostic Inaccuracy

The Areas of a Parallelogram and a Rectangle with the Same Base and Height Are Equal

The Argument Principle

The Argument Principle in Complex Analysis

The Arithmetic-Geometric Mean Inequality (I)

The Arithmetic-Geometric Mean Inequality (II)

The Arithmetic-Geometric Mean Inequality (III)

The Arithmetic-Logarithmic-Geometric Mean Inequality

The Arnold Problem

The Associative Property of Addition and of Multiplication

The Asynchronous Leapfrog Method as a Stiff ODE Solver

The Average Temperature, Humidity, and Windspeed of Tornadoes (2000-2012)

The Backward-Bending Supply Function in Fisheries

The Baker's Map

The Bakos Compound

The Ballot Problem

The Banach-Tarski Paradox

The Banzhaf Power Index of States for Presidential Candidates

The Base-Phi Number System

The Basic Keynesian Expenditure Model

The Basics of Two-Dimensional Vectors

The Begonia Point