Billiards on regular polygons | Vidéo | Carmin.tv

00:00:00 / 00:00:00

Billiards on regular polygons

Appears in collection : Differential Geometry, Billiards, and Geometric Optics / Géométrie différentielle, billards et optique géométrique

Periodic trajectories in polygons are rare and beautiful, and have several surprising properties. During the lockdown period in 2020, we wrote a Sage program to draw every periodic trajectory on every regular polygon with an odd number of edges. I’ll explain the underlying structure, and show lots of pictures from this vast menagerie. This is joint work with Samuel Lelièvre.

Information about the video

Date of recording 04/10/2021
Date of publication 15/11/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19820003
Cite this video Davis, Diana (04/10/2021). Billiards on regular polygons. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19820003
URL https://dx.doi.org/10.24350/CIRM.V.19820003

Domain(s)

Dynamical Systems

Bibliography

DAVIS, Diana et LELIEVRE, Samuel. Periodic paths on the pentagon, double pentagon and golden L. arXiv preprint arXiv:1810.11310, 2018. - https://arxiv.org/abs/1810.11310
MCMULLEN, Curtis T. Modular symbols for Teichmüller curves. Journal für die reine und angewandte Mathematik, 2021. - https://doi.org/10.1515/crelle-2021-0019

MSC codes

Last related questions on MathOverflow

You have to connect your Carmin.tv account with mathoverflow to add question

Ask a question on MathOverflow

Copyright Carmin.tv 2025

Give feedback