They are a fun way to demonstrate LCM and GCD too https://en.wikipedia.org/wiki/Arithmetic_billiards https://en.wikipedia.org/wiki/Arithmetic_billiards With c

They are a fun way to demonstrate LCM and GCD too https://en.wikipedia.org/wiki/Arithmetic_billiards https://en.wikipedia.org/wiki/Arithmetic_billiards With curved reflecting boundaries and parallel rays you get the beauty of catacaustics. A familiar site in a cup of coffee https://en.wikipedia.org/wiki/Caustic_(mathematics) https://en.wikipedia.org/wiki/Caustic_(mathematics)