## 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra

**6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra (Fall 2012, MIT OCW)**. Instructor: Professor Erik Demaine. This course focuses on the algorithms for analyzing and designing geometric foldings.
Topics include reconfiguration of foldable structures, linkages made from one-dimensional rods connected by hinges, folding two-dimensional paper (origami), and unfolding and folding three-dimensional polyhedra.
Applications to architecture, robotics, manufacturing, and biology are also covered in this course.
(from **ocw.mit.edu**)

Lecture 10 - Kempe's Universality Theorem |

This lecture begins by defining folding motion by a series of folded state, linkages, graphs, and configuration space. A proof of Kempe's universality theorem is presented along with Kempe's gadgets, and also the Weierstrass approximation theorem.

Class 10 - Kempe's Universality Theorem |

This class presents open problems involving holes, sliding linkages, and generalizations of Kempe. A proof for the semi-algebraic sets for Kempe is presented and various origami axioms are given. The class ends with a continuation of hypar folding.

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