Kempe's Universality Theorem: An Example

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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 .


On the curve, , so that .


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



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

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