Periodic Orbits of Billiards on an Equilateral Triangle
Dynamical Systems
2009-09-29 v7 Combinatorics
Abstract
We give a complete solution of the following problem: Find, classify and count the (classes of) periodic orbits on an equilateral triangle. We prove that Fagnano's period 3 orbit is the only periodic orbit with odd period. A periodic orbit is either prime or some d-fold iterate thereof. We count prime and iterate periodic orbits of period via a bijection with a certain partition of , then count only prime orbits using the prime factorization of .
Cite
@article{arxiv.math/0509292,
title = {Periodic Orbits of Billiards on an Equilateral Triangle},
author = {Andrew M. Baxter and Ron Umble},
journal= {arXiv preprint arXiv:math/0509292},
year = {2009}
}
Comments
Version 7: Minor edits made, some figures redrawn, Table 1 moved from appendix to body of text.