The Maths of Pool (Billiards)
Geometry & Trigonometry
Predict where to aim a pool ball using the law of reflection, then test whether a real table obeys it as cleanly as the simple model predicts.
Where this idea comes from
Start here — this is the source that inspired this exploration.
Introduction
When a ball bounces off a cushion, the angle it leaves at equals the angle it arrived at — the same rule light obeys when it reflects off a mirror. This idea uses that reflection rule to work out exactly where to aim so a ball reaches a target after bouncing off one or more cushions, then compares the prediction against a real table, where cushion wear, ball spin and table imperfections cause small departures from the ideal.
Guiding Questions
- When a pool ball bounces off a cushion, how do the angles before and after compare?
- Use reflections to predict where to aim so the ball hits a target after one cushion. Does it work on a real table?
- How can you extend the reflection trick to two or more cushions?
- Real tables aren't perfect — how much does the bounce differ from the simple rule, and can you measure it?