|Two short presentations are scheduled|
Abstract: Speaker: Dr. Wacharin Wichiramala, UIUC Department of Mathematics.
Title: Admissible arcs are drapeable. Circumscribed arcs are drapeable?
Abstract: Wetzel conjectured that admissible arcs and circumscribed arcs are drapeable. For admissible arcs, he settled the case of simple arcs and suggested a few ways to prove the general case. For circumscribed arcs, he gave the main idea how to attack. In this talk, we complete the first problem and give an attempt to prove the second problem. The arguments contain some messy, mind-twisting, bone-crushing analytical approximations that might not be suitable for audiences with high blood pressure. (Please bring 4 handouts from last seminar with you.)
Speaker: Prof. John E. Wetzel, UIUC Department of Mathematics.
Title: Projections of a regular tetrahedron
Abstract: We establish the following recent elegant result of Michael Eastwood and Roger Penrose:
Four points a, b, c, d in the complex plane are the orthogonal projections of the vertices of a regular tetrahedron if and only if
(a + b + c + d)^2 = 4(a^2 + b^2 + c^2 + d^2)
The principal tool is a similar result for a cube known as the Gauss's Fundamental Theorem of Axonometry, stated by Gauss without proof and proved in 1844 by J. L. Weisbach.