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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