Elliptical Pool Table
Ever since pool billiards has existed, mathematicians and physicists have had these thought experiments about mathematical pool of mathematical billiards. Because it’s great for working
out how a particle or in this case a pool ball will rebound against the sides and where it will go. So I thought enough of these thought experiments, let’s build one.
The shape is an ellipse and ellipses are an interesting type of shape because they can come in an infinite number of varieties. The geometrical property of ellipses, which is why I have made this table, is the fact that if you place a ball on a focus point wherever you hit it in whichever direction. I get hit over and over and over and over here, it will always rebound into that pocket. That is because from any point on the side, it makes the same angle to each focus point and as you know when you rebound something against a surface the angle of incidence equals the angle of reflection.
Wwhenever it is positioned on this focus point wherever I hit it will go in. If it’s here wherever I rebound it it’s never going to go in. it’s only when it’s exactly on this dot and so that’s the theory and that wouldn’t makes this really good fun.
I will demonstrate it but obviously I’m a mathematician and I love things to be perfect but this is where in the real world. So now out kind of annoying physics gets in the way things like friction things like, the difficulty of manufacture.
You also have to hit it with just the right force. For example if I hit it really hard it rebounds to this side of the pocket if I hit it bit softly it goes to the other side of the pocket. So obviously if there is the Goldilocks hit the one that’s neither too hard, nor too soft that should get it in and let’s see if I can do that.
I have to go get it it’s really difficult so you got to be very skillful. Oh beautiful that’s so satisfying like it rolls round round and round is reminding me but I’ve got it in okay so I chose to hit it over here. We can nominate any other part of the board again. It’s going to be difficult because I don’t have much time to practice on this.