Billiards in ellipses revisited
Metric Geometry
2020-01-28 v2 Differential Geometry
Dynamical Systems
Abstract
We prove some recent experimental observations of D. Reznik concerning periodic billiard orbits in ellipses. For example, the sum of cosines of the angles of a periodic billiard polygon remains constant in the one-parameter family of such polygons (that exist due to the Poncelet porism). In our proofs, we use geometric and complex analytic methods.
Keywords
Cite
@article{arxiv.2001.02934,
title = {Billiards in ellipses revisited},
author = {Arseniy Akopyan and Richard Schwartz and Serge Tabachnikov},
journal= {arXiv preprint arXiv:2001.02934},
year = {2020}
}
Comments
12 pages, 9 figures