Math Colloquium: Periodic Paths on the Pentagon

Wednesday, April 25, 2018

3:00 PM-4:00 PM

Diana Davis, Swarthmore College

 

Abstract: Periodic billiard paths on regularpolygons are beautiful to look at, and have an elegant mathematical structure related to continued fractions. I'll show you what happens on the familiar square, and then delve into my recent work with Samuel Lelièvre on the regular pentagon. There are infinite "families"of periodic paths on the pentagon, whose members all have a similar appearance but get more and more complicated. I'll show some beautiful examples of these families, and explain how we use the group structure on the set of periodic directions to obtain them. You can see six such families here: youtube.com/watch?v=98olU9ANGns

Contact Information

Georgi Medvedev
gsm29@drexel.edu