The game of billiards on a concave shaped table was the inspiration of a George Birkhoff, whom in 1927 proposed the ideology. Instead of the standard billiard game where ball spin and shorter orbits (due to deceleration of the ball) were involved, Birkhoff limited his to balls with trajectories of arbitrary length which hit and rebounded off the cushion according to the laws of reflection.
The idea of looking at a stadium shape and the resultant path of billiard motion thereon was that of the mathematician Bunimovich of Georgia Tech University. He also proved that this motion was chaotic.