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arXiv · 1911.01397

Periodic Orbits on Obtuse Edge Tessellating Polygons

Benjamin R. Baer·Faheem Gilani·Zhigang Han·Ronald Umble
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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.

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Benjamin R. Baer, Faheem Gilani, Zhigang Han, Ronald Umble. 2019-11-04. Periodic Orbits on Obtuse Edge Tessellating Polygons. https://arxiv.org/abs/1911.01397

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