Kempe's Universality Theorem: An Example

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Roughly, Kempe's universality theorem states that any finite part of a plane algebraic curve can be traced out by a vertex of some linkage. This Demonstration illustrates a particular example: there exists a linkage such that, if the point is forced to move on the straight line , the point moves on the hyperbola .

[more]

On the curve, , so that .

[less]

Contributed by: Izidor Hafner (August 2008)
Based on description given by: Erik D. Demaine and Joseph O'Rourke
Open content licensed under CC BY-NC-SA


Snapshots


Details

E. D. Demaine and J. O'Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra, New York: Cambridge University Press, 2007 pp. 31–36.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send