I recently understood the meaning of focus points and how to abuse them for generating some fun games like Loop. (Reading pool backwards)
In Loop one uses a pool table in the shape of an ellipse and puts the hole in of its focus points. Thus one can always hole a ball by making it go through its other focus point.
I believe in 2-dimensional there are just ellipse to have this property, also that an object can't have more than 2 focus points. However I cannot prove it.
Therefore I would like to read up on that topic. I am particularly interested, which kind of properties an n-dimensional shape, table or whatever has to fulfill for it to have 2,3 or more focus points.
As always thanks in advance for any constructive comment or answer.
You believe wrongly ! You can have as many foci as you want, even in $2$D, and the shape thus obtained is called an n-ellipse or a “multifocal ellipse”. My advice to you is to do what I did: Go to the Desmos page, draw two points at $(\pm1,0)$, and a third one of variable coordinates which is mobile $($you will have to use sliders$)$. Then type in the equation of the $3$-ellipse, and modify the position of the last point to inspect its behavior.