Strange billiard tables

Abstract

A billiard table is any compact convex body T in the plane bounded by a continuously differentiable curve ∂ T \partial T . An idealized billiard ball is a point which moves at unit speed in a straight line except when it hits the boundary ∂ T \partial T where it rebounds making the angle of incidence equal to the angle of reflection. A rather surprising phenomenon can happen on such a table.