**Goal:** Arithmetic billiards are a geometric construction which allow an
interesting visualisation for the greatest common divisor and the least
common multiple of two positive integers.
For an introduction to the subject, see this article.
At least the following two generalizations can be addressed:

- Allowing the starting point not to be a corner.
- Considering three (or even more) integers i.e. the trajectory of a ball bouncing inside a parallelepiped rather than a rectangle.

Collecting experimental data will allow to make conjectures concerning the shape of the path, which then one can try to prove. It is possible that the key ideas used for the base case can be extended to prove the conjectures.

**Supervisors:** Antonella Perucca, Sebastiano Tronto

**Difficulty level:** Bachelor thesis / EML 2,3

**Tools:** Any computer language suffices to describe the integer
coordinates (however, a geometric visualisation could be very helpful).