New Properties of Triangular Orbits in Elliptic Billiards
Dynamical Systems
2021-12-14 v3 Computational Geometry
Robotics
Abstract
New invariants in the one-dimensional family of 3-periodic orbits in the elliptic billiard were introduced by the authors in "Can the Elliptic Billiard Still Surprise Us?" (2020), Math. Intelligencer, 42(1): 6--17, some of which were generalized to . Invariants mentioned there included ratios of radii and/or areas, sum of angle cosines, and a special stationary circle. Here we present some of the proofs omitted there as well as a few new related facts.
Keywords
Cite
@article{arxiv.2001.08054,
title = {New Properties of Triangular Orbits in Elliptic Billiards},
author = {Ronaldo Garcia and Dan Reznik and Jair Koiller},
journal= {arXiv preprint arXiv:2001.08054},
year = {2021}
}
Comments
17 pages, 8 figures, 1 table, 6 videos