Understanding the mathematics in billiards will help you improve your game. Billiards is a complicated game and offers endless mathematical explanations. However, for most people the basic understanding of geometry is all that is needed to really help your game. Practice not mathematical formulas seem to be most effective.
Geometry is among other things, the study of the relationship of points, lines, angles and surfaces. It is a study of spatial relationships. A pool table and the billiards balls provide a great example of how geometry works. Geometry will help you know where to hit the ball and the reflection that it will cause. The mathematical law that applies to billiards is hat the angle of incidence is always equal to the angle of reflection. That means that the angle the cue ball hits the target will be the same angle it bounces off and continues in the other direction. Whether your target is another ball or the bank off the side of the table, this basic understanding of geometry will help you make the shot an leave your cue ball ready for your next move.
Another geometrical description was provided by Donald Duck in the old film Donald in Mathmagic Land circa 1959, using the diamonds often inscribed around the edge of a billiards table. This helped many people understand the trajectories of a billiards ball. The reflection of the ball and the analysis involves the mathematical principle of dynamical systems.
Because there are other factors taken into consideration when playing pool than just the angles, mathematics in billiards can be very complicated. Mathematicians have found ways to explain and prove other constants in billiards, particularly the physics created by the spin and momentum. The friction caused by the spin of a ball and the force of the hit will cause changes in the refraction of the cue ball. While these explanations are left to the post-graduate mathematicians and physicists, the important thing to understand is the spin of a ball can cause it to not travel in a straight line.
Take a look at some Mathmatics in Billiards Here.