Some questions concerning the orbits of a billiard ball in a polygon are studied. It is shown that almost all such orbits come arbitrarily close to a vertex of the polygon, implying that the entropy of the corresponding geodesic flow is zero. For polygons with rational angles, we show by using interval exchange transformations that almost all orbits are spatially dense. Two applications are given.
"Billiards in Polygons." Ann. Probab. 6 (4) 532 - 540, August, 1978. https://doi.org/10.1214/aop/1176995475