# 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. Sorin Șuba says:

Is this Michael Sheen? :))

2. sujit choudhari says:

1:44 you also tried to spin both shots

3. couldn’t decide a name says:

you could really play from anywhere if you just know how to play pool with english and angles

4. nidya says:

😍❤️

5. tüv geprüft says:

6. Grant Jonathan Sanford says:

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?

7. Heinrich Crouse says:

Much smaller hole than those of a regular pool table

8. Gökhan Sözeri says:

Terrible choice of vest. Sorry🙂

9. djfritz2001 says:

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?

10. Brian Doom says:

Go bears

11. Robinson Hogan says:

This is the neurotypical disease at play.

12. Jaberwoky says:

WHERE'S THE CUE BALL GOING ?!

13. Kanav Bhardwaj says:

This is a property of ellipse

14. Leg112 says:

where can i buy one of these???

15. David Lloyd says:

Shut up and take my money!!!!

16. Dr8gos Solo says:

I thought this channel was a pool one.

17. Julian Sternberg says:

“It’s really difficult so you have to be really skilful”
Gets it in first try

Weird flex but ok

18. Micah Y. says:

Smeagol found his ring!

19. Roe Jogan says:

His vest looks weird!

20. Jane Doe says:

This is a game changer.

21. crni195 says:

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 😂😂

22. N2 B-1986 says:

I think this guy is on to something. This can be a unique 9 ball table.

that's golf

24. Tr3ze says:

falação do carai

25. Shalen Singh says:

Hostage from Unthinkable, dat you???

26. Dir Hell says:

Idk
Looks like golf tp me

27. Captain Obvious says:

When you combine golf and billiards together…

28. Repodudeify says:

HI CAMERAMAN, nice to meet you finally 😀

29. Max Ambient says:

I played on a hexagonal table once. It was too easy – nearly every missed shot would end up in a pocket.

30. steve d says:

I saw this decades ago on a children's programme, probably Johnny Ball Reveals All but can't be sure…

31. Matthew Bleasdale says:

"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.

32. Jared Jones says:

What a virgin

33. Sweet Trap Magi says:

All that BS you're talking ,

34. Kristoffer Agustin says:

Efren?

35. Mang Crow says:

Not if you shoot it at the hole.

What if you add spin to the ball, like snooker trick shots? Making curved paths!

37. Orbital Wig says:

Golf

38. Gutsu says:

So a table golf?

Hi ! I’m the Official Youtube Cucumber🥒 Follow me to increase the cucumber team 💪💪

40. U SioN says:

is it possible to bounce twice instead of once?

41. Brendan McCabe says:

Where could I get one of these made

42. Herr Stromi says:

43. Major Production says:

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

44. zno3 says:

Make the hole 2x bigger

45. Wolfgang Von Zubaz says:

This is the kind of pool table you see when you've had too many lagers

46. Faisal Alali says:

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.

47. Jack Zeidan says:

dude perfect want to know your location

48. Lindsay Tang says:

You're using a snooker cue…

49. D'ran Dana says:

I mean isn't an eclipse just two parabolas?

50. Ten Again says:

What type of mathematician doesn't take into account side and drag.

51. Buqy says:

Thank you for letting the ball fall in the hole before changing camera angles.❤

52. soowambar ian says:

Amazing. 👍

53. Banana Banana says:

hi to the people visiting in 2019 and the future

54. Partha Banerjee says:

👍🏻👍🏻👍🏻👍🏻👍🏻👍🏻

55. MICRO Ruchit says:

I comeback to this video time and time again.

56. lance wilson says:

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.

57. Yayo Rafael Nsvarro Peña Navarro says:

Fome

58. Olwen Morgan says:

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

59. Andras Libal says:

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.

60. arK MaRk says:

I feel bad for his t shirt

61. Bowen Fulwood-Griffiths says:

It's opposites

62. Bowen Fulwood-Griffiths says:

What are the odds

63. Robert Gregg says:

I had an octagon pool table once. It was so much fun.

64. Swi ckens says:

Should make one with holes actually on the pockets/edge of the table, like the outside

65. Aaron Allgrunn says:

So why does the ball try to roll out then in then out then in.?

66. Faizal Ramliy says:

Banyak ckp bodo kau

67. Riccardo Gentili says:

That's obvious, it is an ellipse with the hole in one of the two fires…

68. theodark says:

Anybody else remembered the pool table in Silent Running ?

69. Jody Mitoma • Canadian Entrepreneur says:

This is really cool.

70. craig t says:

Baby bears was just right.

71. Emanuel Wanzeler says:

Sinuca de baiano

72. S Userman says:

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.

73. Sebastián Torres says:

2.4 k fail Math.

74. Mello says:

Finally a table where I can show my talent

75. Nolan Glomski says:

wherever you shoot from there will always be two shots to make the ball in

76. frank 47 says:

When the ball rolled in slow mo I got hella anxiety

77. misterjohn john says:

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?😵👍🎸😀

78. octane says:

the dudes clothe is giving my vid card epilepsy

79. Gabriel Slater says:

Until you add right and left English. Say in American accent

80. Yaj John says:

Tang ina mo wala kang kwentang gago ka

81. Jonathan Arokapiti says:

😱😱😱❤❤❤

82. ** GOATY ** says:

Who else gets mad every time that dang ball spins around that hole😑

83. Bryan Vazquez says:

Y'all cant even lie that intro was smooth af

84. Alex Paulsen says:

Tabletop mini golf… add some loops, windmills, etc.

85. Judy Chen says:

2:18

2:27 REEEEEEEEE GO INNNN

87. BrancYJ3 says:

it's a matter of angle at the center and circumference, you used geometry

88. Icyice Games says:

Use spin and it won’t work

89. Zoinks Media says:

His jacket is glitching

90. ALVIN YONG says:

Bruhhh

91. عبد القيوم says:

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

92. Bei Bei Miao says:

Interesting ….

93. Hamoud Alzayed says:

And then?

Idiot you.. and ur idea

95. Joseph Van says:

Paying pocket billiards on a traditional table is difficult enough. Forget this gimmick.

96. White Boy Reacts says:

If you hit it with a steady force it will eventually hit the pocket no matter where you shoot it.

97. Surfing On Squarewaves says:

2:26 "I don't want to go!"

98. joseph jackson says:

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?

99. ryan kelly says:

What would happen if you put side on the cue ball?