Billiards

I started playing pool in 2018 when I was studying at the University of Washington, because my dorm was really close to Area01, which has 3 Brunswick pool tables. Pool soon became my go-to game and I would play for 3,4 hours (almost) everyday. 

Now I enjoy playing pool more than ever, because it motivates me to learn about physics and I'm able to meet a lot of people who are enthusiastic about pool and science. Big shoutout to DrDave  (and his YouTube channel), who is a professor Emeritus in Mechanical Engineering and researches on billiard physics.

I'm particularly interested in the fast speed interactions on a pool table. For example, what happens when you shoot the cue ball in line with two frozen balls?Does the middle ball stop in place? Does it go forward, or backward? When I'm free, I like to film these kinds of things using a high-speed camera.

OK, so why does math has anything to do with billiard? Apart from being a tool for billiard physics, mathematics has a research area called dynamical billiards, or simply billiards. In its simplest form, billiard is about finding periodic trajectories on a pool table. Imagine an ideal pool table with no friction and perfect rebound (angle in = angle out, ball = a point, ball travels in straight line and no sidespin. No jumpshot of course!). If you put down the cue ball anywhere on the table and play a shot, what will the trajectory look like in the long run? There are some trajectories that are easy to visualize: if you play the shot up and down the table, perpendicular to the rails, then the trajectory is a line segment and will remain that way forever; or if you start at the midpoint of one side and play the shot towards another midpoint, the trajectory will be a rhombus and remain that way forever. These are examples of periodic trajectories, trajectories that come back to themselves and repeat.