Billiards on regular polygons - LMS Popular Lecture for Maths Week Scotland
Dr. Diana Davis (Phillips Exeter Academy)
Tuesday 29th September, 2020 17:00-18:00 Online
Imagine that you hit a ball in a pentagon-shaped billiard table, and after bouncing around for a while, the ball comes back to where it started and then repeats its path. I've been studying these "periodic" paths for a couple of years, and it turns out that they're very beautiful, like mathematical art. I'll show lots of pictures, and explain the math behind them. We've been studying the pentagon for many years. For spring break in March, I went to France to work with my collaborator Samuel Lelièvre, and I ended up staying there for three months due to the pandemic, during which time we extended our work to any regular polygon with an odd number of sides. Bring your favorite numbers, and I'll show you the corresponding paths on the spot!