Arithmetic billiards

Arithmetic Billiard

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. For the convenience of the general public we plan to make a website where it is possible to insert the side lengths of the billiard tables (as variables) and the starting point, and then one automatically has the nice image of the billiard path. This is surely doable and easy in dimension 2, and we will also see what we can do in dimension 3. We will also consider adding more information, for example the set of boundary points. Arithmetic Billiard

Supervisors: Antonella Perucca, Sebastiano Tronto

Difficulty level: EML 2,3

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