by Lael Shelton Costa on January 10, 2024

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What's that structure?

Do you enjoy a game of pool or billiards? I certainly do; I find it very satisfying to pocket a ball with a complicated shot following several bounces. I’m not a very skilled player, though, so I miss a lot of shots. Luckily, I can blame these failures on friction and inelasticity in the collisions, or on the unexpected interference of a different ball. You can imagine my relief when I learned of the existence of mathematical billiards!

In this post, I will describe several varieties of mathematical billiards and discuss how I use computer experiments to make progress in studying these games. The images you see partially come from Geogebra and from a piece of software I created and host on my website. More on that later; let’s dive into the first game.

Inner Billiards

Imagine you’re playing billiards, but instead of a standard rectangular table, you’re using a custom-made one with no pockets and in a shape of your choice.…