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33 votes
4 answers
3k views

Does there exist a shot in ideal pocket billiards?

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 ...
Joseph O'Rourke's user avatar
22 votes
4 answers
2k views

Non-chaotic bouncing-ball curves

I was surprised to learn from two Mathematica Demos by Enrique Zeleny that an elastic ball bouncing in a V or in a sinusoidal channel exhibits chaotic behavior:     (The Poincaré map ...
Joseph O'Rourke's user avatar
14 votes
2 answers
1k views

Polygonal billards programs

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 ...
john mangual's user avatar
  • 22.8k
10 votes
1 answer
494 views

Ping-pong progress through a quincunx

A quincunx or Galton board consists of staggered pegs from which ping-pong balls bounce and eventually display a binomial / normal distribution in catch-bins. I am wondering if the downward progress ...
Joseph O'Rourke's user avatar
9 votes
0 answers
369 views

Periodic orbits of a spinning ball in a square

Periodic orbits of a billiard ball bouncing in a square have been well-studied. I am seeking similar analysis of what is sometimes called a rough ball, one whose high friction causes it to pick up ...
Joseph O'Rourke's user avatar
5 votes
0 answers
166 views

Pocket billiards with balls in general position

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 ...
Joseph O'Rourke's user avatar