Folding and Unfolding in Computational Geometry

EECS Joint Colloquium Distinguished Lecture Series

Erik Demaine
University of Waterloo
Faculty Candidate

Wednesday, April 18, 2001
Hewlett Packard Auditorium, 306 Soda Hall
4:00-5:00 p.m.


I will present several recent results about geometric folding and unfolding problems. For example, place several rigid rods down on the table, and hinge them together at their ends to form a chain. Is it always possible to fold the hinges in such a way that the linkage is straightened into a line? The rods cannot change in length or cross each other, and must remain on the table. While at first glance it may seem intuitive that any chain can be "unraveled" into a straight line, this "carpenter's rule problem" has proved difficult and remained unsolved for over 25 years.

This problem was solved in a recent burst of interest in folding and unfolding, a branch of discrete and computational geometry. In the past few years, several intriguing and surprising results have been proved about various contexts of folding and unfolding: reconfiguring linkages, paper folding (origami), unfolding polyhedra into nonoverlapping "nets," and gluing polygons into polyhedra. Many of these problems have applications in areas including manufacturing, robotics, and protein folding.