New Properties of Triangular Orbits in Elliptic Billiards
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 $N>3$. 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.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.08054
- arXiv:
- arXiv:2001.08054
- Bibcode:
- 2020arXiv200108054G
- Keywords:
-
- Mathematics - Dynamical Systems;
- Computer Science - Computational Geometry;
- Computer Science - Robotics;
- 51M04;
- 37D50;
- 51N20;
- 51N35;
- 68T20
- E-Print:
- 17 pages, 8 figures, 1 table, 6 videos