Ever since pool or billiards has existed, Mathematicians and physicists have had these thought experiments about mathematical pool and 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, lets build one!" The shape is an ellipse.
And ellipses are an interesting type of shape because they can come in a infinite number of varieties.
The geometrical property of ellipses, which is why I made this table, Is the fact that if you place a ball on a focus point, Whereever you hit it, in which ever direction I hit it, over there, over there, over there, over there, 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.
Whenever it is positioned on this focus point, wherever I hit it, 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.
