Periodic Orbits on Obtuse Edge Tessellating Polygons
Abstract
A periodic orbit on a frictionless billiard table is a piecewise linear path of a billiard ball that begins and ends at the same point with the same angle of incidence. The period of a primitive periodic orbit is the number of times the ball strikes a side of the table as it traverses its trajectory exactly once. In this paper we find and classify the periodic orbits on a billiard table in the shape of a 120-isosceles triangle, a 60-rhombus, a 60-90-120-kite, and a 30-right triangle. In each case, we use the edge tessellation (also known as tiling) of the plane generated by the figure to unfold a periodic orbit into a straight line segment and to derive a formula for its period in terms of the initial angle and initial position.
Cite
@article{arxiv.1911.01397,
title = {Periodic Orbits on Obtuse Edge Tessellating Polygons},
author = {Benjamin R. Baer and Faheem Gilani and Zhigang Han and Ronald Umble},
journal= {arXiv preprint arXiv:1911.01397},
year = {2021}
}
Comments
New Version (Submitted to PME)