"From tensegrities to distance geometry"

Professor Robert Connelly
Cornell University

Thursday, March 20, 2008
4:00 pm, 219 CB
Refreshments at 3:30 pm in 745 POT

Abstract:

Some years ago a young artist, Kenneth Snelson, connected some sticks with string in such a way that they were rigidly held in place, as if by magic. Since then he has made several large sculptures out of large metal tubes and steel cables. Why do these structures hold together? Secrets will be revealed. The key deals with things called stress matrices. As a bonus, stress matrices can also be used to determine when a configuration of points in space are determined uniquely by some subset of their pairwise distances. Some models of tensegrities will be shown, so the audience can test their integrity themselves.

Bio of Robert Connelly

Robert Connelly is a professor at Cornell University who specializes in discrete geometry with interests in rigid structures and circle arrangements. He has held visiting positions at I.H.E.S. in France, Syracuse, New York, University of Bielefeld in Germany, Universite de Montreal, Canada, University of Seattle, Washington, and Cambridge University, UK. He has proved some very stunning results, including the first proof (with Erik Demaine and Gunter Rote) of the Carpenter's Rule Conjecture (all embedded open polygons in the plane can be continuously straightened without overlap keeping the edge lengths fixed), the Kneser-Poulsen Conjecture in the plane (with Karoly Bezdek) (if any finite collection of circular disks in the plane are repositioned such that their centers don't move apart, then the area of the union does not decrease), and the first construction of a nonconvex surface which flexes. A model of this is in the Smithsonian at the National Museum of American History.