All Questions

Imagine a smooth curve $c$ sweeping out a unit-radius disk that is orthogonal to the curve at every point. Call the result a tube. I want to restrict the radius of curvature of $c$ to be at most 1. I ...

Assume you have one shot with the cue ball in pocket billiards (a.k.a. pool), with the game idealized in that no spin is placed on the cue ball in the initial shot, all collisions between billiard ...

Imagine pinball on the infinite plane, with every lattice point $\mathbb{Z}^2$ a point pin. The ball has radius $r < \frac{1}{2}$. It starts just touching the origin pin, and shoots off at angle $\...

I'm looking for software that will give billiard trajectories in arbitrary plane polygons. After much work I was able to produce this figure. (source) It was a good exercise, but at this point I ...

There were at least two earlier MO questions about ideal pocket billiards. (Ideal: frictionless, perfectly elastic collisions.) Perfectly centered break of a perfectly aligned pool ball rack. Does ...

As has been discussed earlier on MO,1,2 recently an impressive advance was proved concerning internally illuminating a mirrored polygon. Here is the result: Let $P$ be a rational polygon. Then for ...