Some Remarks on Periodic Billiard Orbits in Rational Polygons


A billiard ball, i.e. a point mass, moves inside a polygon Q with unit speed along a straight line until it reaches the boundary ∂Q of the polygon, then instantaneously changes direction according to the mirror law: “the angle of incidence is equal to the angle of reflection,” and continues along the new line (Fig. 1(a)). Despite the simplicity of this description there is much that is unknown about the existence and the description of periodic orbits in arbitrary polygons. On the other hand, quite a bit is known about a special class of polygons, namely, rational polygons. A polygon is called rational if the angle between each pair of sides is a rational multiple of π. The main theorem we will prove is

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@inproceedings{Boshernitzan1994SomeRO, title={Some Remarks on Periodic Billiard Orbits in Rational Polygons}, author={Michael Boshernitzan}, year={1994} }