Infinite Billiard Paths:Let {$x,y$} be the dimensions of a rectangle. If {$\frac xy$} is irrational then the path from any corner is infinite. Proof: The diagram introduced in the proof of Billiards and the LCM  shows that if a corner is reached, then {$jx=ky$} for some positive whole numbers {$j$} and {$k$}, that is, {$\frac xy$} is rational. |