Billiard Paths and the LCM:Let m,nāā be the dimensions of a rectangle. Then the length of the path from any corner is equal to [m,n], the least common multiple of m and n. If the ratio of the dimensions of a rectangle is irrational then the path from any corner is infinite. Proof: As the path begins from a corner,  We can look at a straight-line version of the path by reflecting the rectangle,  every time it hits a side.  |