Periodic paths on regular polygons

Speaker. Diana Davis
Date. 14.03.22 at 3:30 pm

Abstract. Periodic trajectories in polygons are rare and beautiful, and have several surprising properties, such as being related to continued fractions. Beginning during the lockdown period in spring 2020, my collaborator and I wrote a Sage program to draw every periodic trajectory on every regular polygon. I’ll explain their underlying group structure, show lots of pictures from this vast menagerie, and discuss their interesting properties.