Cauchy’s theorem and rigidity of circle polyhedra in the 2-sphere.
Speaker: John Bowers (James Madison University)
November 30th at 4:00 pm in Robinson Hall 105
Refreshments at 3:40 pm in Robinson Hall foyer
Abstract: This talk is two stories given in 3 acts. In Act I, I will present some of the rich history of the study of polyhedra, from Euclid on to the present day. In particular, I will sketch the proof of Cauchy's celebrated rigidity theorem for convex polyhedra in Euclidean space--most certainly a "proof from the book". In Act II, I will discuss the development of geometry beyond Euclid and the ancient geometers. Our focus will be on introducing two alternatives to Euclidean geometry--hyperbolic geometry, and the inversive geometry of circle packings on the sphere. We will explore the basic concepts, and discuss the connections between them. Finally, in Act III, we will sketch how the beautiful proof of Cauchy's can be generalized to prove a result of interest to the modern study of circle packings on the sphere. No prior knowledge beyond basic concepts from Euclidean geometry are assumed.
What We Did Last Summer (Parents and Family Weekend Event)
Speakers: W&L Math students Aaron Schmitt, Justin Pusztay, Austin Jennings, Luke Farley and Hung Chu
September 30th at 4:40 pm in Robinson Hall 105
Refreshments at 4:20 pm in Robinson Hall foyer
Abstract: The students will talk about their summer research.