Abstract: Periodic trajectories in polygons are rare and beautiful, and have several surprising properties, such as being related to continued fractions. During the lockdown period in spring 2020, my collaborator and I wrote a Sage program to draw every periodic trajectory on every regular polygon that has an odd number of edges. I'll explain their underlying group structure, show lots of pictures from this vast menagerie, and discuss their interesting properties.
This was a talk given by Dr. Diana Davis of Phillips Exeter Academy
