Bank shot
Aim off the cushions to sink the ball. No luck, just angles.
The maths Reflection: angle in equals angle out
Aim 216 degrees. The ball must touch at least 1 cushion before the pocket.
Pool table 200 by 100 units. Cue ball at 53, 25. Pocket at 100, 100. Current aim 216 degrees. The straight line to the pocket lies at 58 degrees.
216°
- Cue ball
How to play
Drag anywhere on the table to point the cue, then take the shot. The ball travels in a straight line and bounces off the cushions, leaving each one at exactly the angle it arrived. It has to touch at least one cushion before it drops, or it is not a bank shot.
The ball loses pace as it goes, so it only has a few cushions in it. A shot that runs out, or that clips a red blocking ball, is a miss. The path of your last shot stays drawn on the table so you can see exactly where it went and correct the angle.
The trick. Reflect the pocket across the cushion you want to use and aim straight at that mirror image. The bounce unfolds into a straight line. Show the reflection draws that picture for the shot in front of you: the mirrored table, the ghost pocket, the straight line through the bounce, and the two equal angles at the cushion marked θ. It gives the answer away, so try the angle first.
Keyboard. Tab to the blue aim handle. Left and right arrows turn the cue one degree, hold shift for five, Page Up and Page Down for fifteen. Home aims right along 0°, End aims left along 180°. Enter or Space takes the shot.
Why this is mathematics
A ball bouncing off a cushion leaves at the same angle it arrived. That single fact turns an impossible-looking shot into a straight line — reflect the pocket across the cushion and aim at the ghost. It is the same reflection you use for mirrors in optics and for shortest-path problems in geometry.