11,000+
Interactive Demonstrations Powered by Notebook Technology »
TOPICS
LATEST
ABOUT
AUTHORING AREA
PARTICIPATE
Your browser does not support JavaScript or it may be disabled!
Points and Lines on Folded Paper
Drag the locator to fold the piece of piece of A4 paper, which is yellow on one side and light blue on the other. You can add points
,
,
or
using the 2D sliders on the left. Vary these controls to verify Huzita's axioms.
Contributed by:
Izidor Hafner
Using code by:
Borut Levart
THINGS TO TRY
Drag Locators
SNAPSHOTS
DETAILS
Huzita's axioms [1, pp. 285–286]:
A1. Given two points, one can fold a crease line through them.
A2. Given two points, one can fold a crease along their perpendicular bisector, folding one point on top of the other.
A3. Given two lines, one can fold their bisector crease, folding one line on top of the other.
A4. Given a point and a line, one can fold a crease through one point perpendicular to the line, folding the line onto itself.
A5. Given two points and a line, one can fold a crease through one point that maps the other point onto the line.
A6. Given two points and two lines, one can fold a crease that simultaneously maps one point to one line and the other point to the other line.
Reference
[1] E. D. Demaine and J. O'Rourke,
Geometric Folding Algorithms: Linkages, Origami, Polyhedra
, New York: Cambridge University Press, 2007.
RELATED LINKS
Folding
(
Wolfram
MathWorld
)
Paper Folding
(
Wolfram Demonstrations Project
)
Folding a Strip to Converge to an Equilateral Triangle
(
Wolfram Demonstrations Project
)
Paper-Folding an Ellipse
(
Wolfram Demonstrations Project
)
Dividing Segments by Origami
(
Wolfram Demonstrations Project
)
Folding a Strip of Paper to Make an n-Gon
(
Wolfram Demonstrations Project
)
PERMANENT CITATION
Izidor Hafner
"
Points and Lines on Folded Paper
"
http://demonstrations.wolfram.com/PointsAndLinesOnFoldedPaper/
Wolfram Demonstrations Project
Published: March 15, 2019
Share:
Embed Interactive Demonstration
New!
Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site.
More details »
Download Demonstration as CDF »
Download Author Code »
(preview »)
Files require
Wolfram
CDF Player
or
Mathematica
.
Related Demonstrations
More by Author
Folding a Strip of Paper to Make an n-Gon
Izidor Hafner
Folding a Rectangle into an Envelope
Izidor Hafner
Epicycloids from an Envelope of Lines
Jamie Wickham-Jones
Through Any Three Points
Mark D. Normand
One-Vertex Origami Folding
Anugrah Chemparathy
No-Three-in-Line Problem
Ed Pegg Jr
Montucla's Rectangle-to-Rectangle Dissection
Izidor Hafner
Tarski's Adaptation of Wojtowicz's Argument on Optimal Dissection of a Unit Square
Izidor Hafner
Paper Folding
Borut Levart
Rotate and Fold Back
Michael Trott
Related Topics
Plane Geometry
Recreational Mathematics
Browse all topics