Ideal Billiards Table

Suppose you have an ideal rectangular billiards table on which a ball collides with any wall (called the cushion) so that the angles of incidence and reflection are equal. Let there be pockets at the corners only. Describe how to shoot a given ball into a specific corner pocket with either zero, one, two, or three banks of the ball.

Answer

On this ideal billiards table for which the incident and reflection angles at the cushion are equal, one simply considers adjacent mirror image copies of the table in a grid work. Imagine placing the ball in appropriate adjacent tables at mirror image positions; then draw the straight line to the pocket to find the collision points on the cushions.

Normal billiards and pool tables are marked around the perimeter to accomplish precision bank shots. Using these markers takes practice. These real tables with their markings are not very similar to the ideal table discussed above. Moreover, the rolling ball before the collision with the cushion may have additional spin “English” about an axis not parallel to the table and perpendicular to the travel direction. The professional player uses all these quantities in the particular shot, but we amateurs simply enjoy the results as we practice more of the many possible improvements to our games.