Elliptical Pool Table – Numberphile

Elliptical Pool Table – Numberphile


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… …where ever 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. So that’s the theory, and that 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, we’re in the real world… …so now 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, but softly… … it goes to the other side of the pocket. So obviously 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. If I do get it in, it’s really difficult. So you have to be very skilful. Oh, beautiful! It’s so satisfying the way it goes round and round and round. It’s reminding me I 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. I’m not a very skilled pool player. But maybe something like… Oh! [Brady]: Take the camera. I’ll get my first ever shot. It was quite.. Perfect! At first I was a bit disappointed it was so difficult… … and then I realized it’s actually much better that it’s difficult, because it’s more more fun. Starting from cuing off, you put the cue ball somewhere in the line between the black and here. You’ve got to be thinking about this dot and how things would happen if they were coming from this dot. I have to hit the black on this edge…

100 thoughts on “Elliptical Pool Table – Numberphile

  1. This looks more like a circle than an ellipse. If it is an ellipse than why is it not more elliptical? Wouldn't either a perfect circle or longer ellipse be better?

  2. That pocket is so small compared to what I would recognize as a pool table pocket. I've heard that snooker tables are different, is that a regulation snooker pocket?

  3. They always cut scene when they pot the ball since they probably need to unbolt the table from the floor and turn it upside down to retrieve the ball 😂😂

  4. "If it's here it's never going to go in" sorry, that's incorrect.

    It will go in (on a rebound from the edge of the table) from everywhere on the table, as long as you hit it across the focus point; the exception being the line on the far side of the hole to the focus where you have to hit it directly away from the hole along the line extending from between the focus points.

  5. Guess the physicist didn’t take into consideration the lines on his shirt for filming day

  6. as long as it goes through one of the focus points, it's gonna get in. even if it isn't place it the focus itself.

  7. You just admitted that math is worthless in predicting what happens in real life and you don't realize you even admitted it. You science people preach that math and physics explains the whole world but a simple thing like this proves that math and physics are only measuring devices and only predict events with controlled variables like only in a vacume.

  8. A mathematician named Hall
    Made a hexahedronical ball.
    The square of its weight
    Times his pecker plus eight
    Was two thirds of five ninths of fnck all.

  9. 1:26 Wait … you say that if you shoot from another point it will never go in that has to be untrue, what if you shoot it through the first focal point, then it will surely go in.
    I would also think that even a finite set of other directions not doing through the first focal point will also allow it to go in.

  10. It's wrong to say that only from the other foci will a bank shot get in the hole. If you place the ball on the axis that goes trough both foci, between the hole and the nearest cushion, then aim towards the nearest cushion along that axis line, the ball will bounce exactly back along that line and go in the hole. There are an infinity number of other points that would do the same, as long as a rearward projection of the shot goes trough the other foci. Basically, make sure your pool cue is over the other foci and the shot should go in, assuming medium speed and no spin.

  11. They used to have one if these at one of the Southampton university college theatres where I saw bands in the 1980s.
    I've never seen one since.
    Knida related…
    I used to play Bar Billiards frequently at a few pubs in Hampshire back then, my favourite cue orientated game. I haven't seen one for over two decades.
    I'm In-between Winchester and Southampton now, and wondered does anyone know of any bar billiards tables in Hampshire, or even any round pool tables?😵👍🎸😀

  12. الله اكبر .. الله اكبر
    الله اكبر .. لا اله الا الله.. الله اكبر الله اكبر
    و لله الحمد .

  13. Do you need to hit the ball with the same force or different force when changing which direction you hit it for it to go in the hole?

  14. Hello! here's a small YouTuber who makes Educational videos about Mathematics including theorems and basic concepts of Abstract Algebra, Calculus, Real analysis and more. Please check it out 🙂

Leave a Reply

Your email address will not be published. Required fields are marked *