Any mathematician will tell you that the game of billiards does not take much mathematical knowledge. Where the math comes into play is with the path and angles that the ball takes when shot towards one another. Understanding these angles, and how they bounce off of one another, can help someone go from a decent pool player to a "shark". After learning about all the different angles that can be used during a pool game, I was able to see shots that I would have never considered before. I could see how bouncing the cue ball off the edge of the table would shoot the intended target into a pocket. I could see what edge of the eight ball to hit with the cue ball to make the winning shot into the corner pocket.
The concept of angle reflection that is used in billiards, can also be applied to many other situations. There is miniature golf, light reflection, and satellites. While miniature golf is another game aspect, light and satellites are used in real world, everyday situations. Here is an
Miniature golf, a favorite for many families and children, uses angle reflection to get around obstacles on any miniature golf course. On a small scale, the ball reacts the exact same way it does on a billiards table. The angle of incidence will be the exact same angle measurement as the angle of reflection. On a larger scale, it is harder to see the angle of reflection because of the differently angled walls that surround the course, as well as a much larger playing field than an eight foot by four foot table. The laws of math and physics to apply similarly though, as long as there is a spatial understanding of the course.
Another interesting application of angle reflection is light reflection. Light reacts the exact same way as any other object will when hitting a flat surface. This happens when sunlight reflects off something mirror like, such as a watch face. Another interesting aspect that uses light reflection is optics. When we see objects it involves reflecting a ray of light. The light shines on the object we see and then reflects off that same object, and that is what our eyes are seeing. The reflected light allows us to see our world around us. It operates the same way as any reflected angle we have been studying with the game of billiards.
A slightly different angle reflection happens in satellite dishes. The shape of the satellite dish is a three dimensional parabola. A satellite has a focal point which comes out from the center of the dish. When light or other signals like radio waves enter into this dish, the shape of the dish directs the reflections directly to the center of the dish to the receiver. This situation is more comparable to the ellipse pool table that mathematicians have been experimenting with. Here is an interesting video of a mathematician that made his own
All of these different ways angle reflections are present in our daily lives can be related back to the billiards table. This allows for us to see on a smaller, more tangible scale of how these laws work. Satellites and light rays are hard to visualize and see the mathematics in action, but on a billiards table there is room for experimentation which leads to a deeper understanding of the angle concept and helps us learn more about larger areas where the same principle can be applied.