In the game of mathematical billiards a single ball travels on the table at a single constant speed.The ball has no means of deceleration as there is no friction, air resistance nor incline. It simply continues to travel until it impacts with the billiard cushion in a perfectly elastic fashion in accordance with the Law of Reflection, (ie. the angle of incidence equals the angle of reflection) and continues, repeating the process everytime it comes in contact with the cushion. In our project we are interested in the path that the ball ultimately travels. We have to imagine that the ball leaves a trail on the surface of the table. We will look at this resulting trail and determine if it is chaotic and whether any patterns can be seen.