The Mathematics of Billiards: Summer Course

1.1. Billiard trajectories and “unfolding”. The mathematics of billiards might be considered an abstraction of the game of billiards, but the sense in which this is true is (sadly) guaranteed not to improve your pool game. First, we remove the pockets and consider a single ball’s motion to be modeled by a point moving in straight lines. Then, we replace the rectangular boundary of the table by a Euclidean polygon. And of course, we neglect friction and spin. What we preserve is the boundary rule: angle of incidence equals angle of reflection for trajectories on this idealized “table.”