How can billiard be used to illustrate any laws of mathematics?

[Thallium]

I indulged in a billiard match on Euro Sport and it got me wondering. How can billiard be used to illustrate any laws of mathematics?

 

[matt grime]

well it would only be approximate because of the inherent imperfection of models over theory, but you could demonstrate that the angle of incidence equals the angle of reflection, if the billiard table were elliptic then the motion is deterministic, if there are more than three balls on an ordinary table it is chaotic, circular tables are also i think chaotic (these ideas arise in (quantum) cryptography etc but i can only point you at the relevant papers (yuri suhov i think)), and general mechanics laws up to a point.
it also demonstrates the amazing ability of the human mind and body to learn through repetition - despite the seemingly easy nature of the game, in simple terms of potting of snooker (not european billiards perhaps), machines are incredibly bad at it.