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
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