Elliptical Pool Table - Numberphile
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- Опубліковано 27 лип 2024
- A game to play on the elliptical table: • A Game for the Ellipti...
More links & stuff in full description below ↓↓↓
And more extra footage: • Elliptical Pool Table ...
Alex Bellos' Loop Table website: www.loop-the-game.com
Alex discusses the topic in his book Alex Through the Looking-Glass (UK) and The Grapes of Math (US)... bit.ly/BellosBooks
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Thank you for letting the ball fall in the hole before changing camera angles.❤
It felt so satisfying to watch
Yea right. It would be so annoying if they had change it before the ball fell lol
why
TA Parity and you’ve just got an immature mind grow up
@Jay Glenna yeah I guess you could say I'm everywhere, don't look under your bed btw :^)
This just blew my mind
SuperCarlinBrothers sorry
SuperCarlinBrothers Ooo, hi!!!
+Numberphile thanks for the video. can you please make a video of the fact that the ball starts to spin faster and faster as it penetrates the hole? (conversion of energy, gravity, etc ....)
+yogs19 No. That should be physicphile...
OMG what are the super Carlin bros doing here
2:37 when he started talking it got me really worried we weren’t gonna see the ball go the whole way down phewwww
Exactly hahaha
Special recognition goes to the editor for not ending the clip at 2:25 too early.
You should delete your comment because @Buqy already said that 2 years prior
@@Corn0nTheCobb My sincerest apologies for not reading all 2,000 comments on this video to make sure mine is totally unique.
@@jonoghue it's fine, not the end of the world. Let's just be a little more careful next time please 😉
@@Corn0nTheCobb actually you shouldn’t say those sentences because they’ve been used before
@@abdulrahmanalmojil3574 I think you're guilty of hypocrisy there mate.
you can also hit it in from anywhere by aiming through the focal point
That sounds like hitting from the focus with extra steps
Or aim directly away from the focal point.
Indeed... or at the pocket, or directly away.
@@thomasgrubert7819 Directly away from the pocket for a two bank shot
N ytonial gonna have to put the centerline of the ball exactly through the spot, that's gonna be harder to be precise about
How fascinating! It looked kinda gimmicky in the thumbnail but turned out to be pretty interesting! :-)
xisumavoid cheers
Nice to see you here:D
Wow x. I'm seeing who you watch, film theory, and now this
xisumavoid hmm, xisuma seems to be a mathematician...
xisumavoid RIP headphone users
Peter Ebdon would still take 6 minutes to decide on a shot.
6 minutes, hes alot faster now days then I see
Ebdon set his legacy to snooker in stone with that match against Ronnie. I wonder if he regrets it today...
And half hour to hit it.
I love how this is still funny even though I don't know the reference.
@@grammarofficerkrupke4398
He doesn't know it himself.
If he's ever thought about it... he's still thinking about it.
"You have to be very skillful"
Nails it right away
His shirt is glitching out
It's made by EA
ragasdapper lol
@@ragasdapper he'll need to pay extra money for the slight hope it doesnt glitch out again. chances are he'll have to pay extra if this doesnt work
its a vest...
it's called moire effect
His shirt needs to calm down
Lord Humungus
oh
***** Bend over.
+A to Rhombus This string of 2 replies amuses me way more than it should lol
I thought I was the only one xD
Depends on what camera it is, not all have AA filters
1:15 "if it's here (off-focus) it's never going to go in" Not true! There are 4 directions you could hit it and it would go in: directly toward or directly away from either focus.
I just came to the comments to see something like this. I was kind of hoping that he would explain how to play billiards when off the foci.
He seems to have committed himself to saying that on a circular (1 focus, where the hole is that focus) billiards table would be impossible to do *any* successful rebound shot.
Lastly, he just said that more and less power miss, so that means if we adjust the starting point we can adjust the power accordingly to make the shot!
Thank you
@@PhilosophyVajda On a circular table with the hole in the center there is one way to make a successful rebound shot - directly away from the center towards the edge. Theoretically this should hit and rebound at a perfect 90 degree angle from the tangent of the circle an rebound staight to the hole.
As a pool player, it’s interesting your brought up how the force of the hit changes the angle the ball banks at. I’ve noticed as you demonstrated that with a harder hit, the angle of incidence decreases and the softer the hit it increases. Do you think this is because of the compression of the sides of the table? I’ve always wondered l, and that seems the most logical explanation. Assuming there’s zero English on the ball, with a harder hit the sides get compressed more and perhaps shoot it back at a smaller angle whereas if it hits it softer, the side will compress less and therefore sway the ball off to the side more. Just a theory.
I've always played Bank shots as if they would have a slightly lower angle of reflection then the angle of incidence. My theory was that the rubber cushion gripped the ball ever so slightly.
Perhaps by digging it rebounds some of the sideways velocity making a shallower angle
possibly it’s due to hitting the cushions takes off more force towards the cushions than along the cushion if you get what i mean
"If it's here, wherever I rebound, it's never gonna go in" (1:17) : Wrong.
When you hit it along the line through the hole-less focus point, in either direction, it will go in.
It wouldn't rebound then so it is actually correct.
Zogg from Betelgeuse Zogg, glad to see you here! Are you gathering information about the earthlings' favorite way of sending and receiving information: the Internet, a primitive version of the Great Galactic Grid?
Zogg from Betelgeuse I was thinking the same thing
xx
***** that is what he is saying.
Does that mean that you could technically play from anywhere, just as long as you intersect one of the 2 foci?
Jordan Richards that was my thought as well
that would make sense, yeah
Took a min or half to understand what you said. Yeah, what you said is right
Yup
Congratulations! You've discovered that you can hit a ball at a point!
I remember there was also another youtuber who made an automatic billiards stick. I sense the perfect collab
it was amazing !
“It’s really difficult so you have to be really skilful”
Gets it in first try
Weird flex but ok
2:27 strangely hypnotic and extremely addicting to watch in slow motion.
yup
+rickxhoshinji I got pissed cause it didnt go in
DEMONSTRATE CHAOS THEORY ON THIS TABLE!
sssdddkkksss through the pool ball up and see where it lands.
Michael Adsetts How?
If you are looking for sensitivity to initial conditions, start by looking at the break of say, a rack of eight ball.
or a rack in loop, but it isn't as sensitive
the angle of reflection is also changed by spin, anyone who plays pool or snooker knows this.
The reflection also spins the ball (again, changing its angle of reflection).
Si what is spin
The idea is this ball is not hit with spin. It's not a pool,, snooker or billiard experiment. it's regarding physics.
@@plutoniumisotope205 Hitting the cue ball off centre, for example towards the left or the top.
@@zanussidish8144 thanks for explaining how spin is not included in physics
Every once in a while this gets in recommended, and every time I always click on it
I can't get over how tight the hole is :)
fla playa The tighter the better.
.. Usually ;) not in billiards though.
fla playa Can't say that about your mom
that's what he said..
Danieny Brandelli really? I'd like to find out myself
the "Goldilocks Hit" omg you're killing me
The term for a planet that is the right distance from it's star to support life is also called the "Goldilocks zone".
i know, but think dirty my friend
Try Goldi
Blasphemy
Did anyone else feel anxiety at 2:33 because you thought they might cut away before we watched the ball go in?
Omg yes! I thought I was alone there
Just a few days ago, I posted on my favorite message board a question about the diamond system on non-traditional shape tables; in my question, those were round tables and hexagonal tables. How would the diamond system work on the elliptical table, specifically for carom and 3-cushion billiards without a pocket on the table?
And thanks for expending the time, energy, and no doubt a fair chunk of change for the construction, to make this video. I find it fascinating.
What's your favorite message board?
(I have no idea what the diamond system is btw)
Oh lord that waistcoat gives some funky Moire patterns...
Yes, but that makes it even more awesome from a mathematical standpoint! It just means the (spacial) sampling frequency wasn't high enough!
;)
tobywilson My maths teacher wears a similar kind of vest when he's feeling fancy as well. Interesting coincidence? hmm
tobywilson watch it in 4K, no moiré there! just kidding, there is no 4K.
tobywilson aL1e
When a grid's misaligned
With another behind
That's a moiré
If the pool table were filled with water, then a stone dropped in at one focus would (after a little while) produce a splash at the other focus...
How would Alex feel about flooding his creation? ;-)
AlanKey86 unlikely - but we can ask!
AlanKey86 I wouldn't want to see an expensive table flooded like that, but now I really am interested to see that done in an elliptical pool of water.
AlanKey86 Great idea. Then it really would merit the term pool...
AlanKey86 were can I get this table
AlanKey86 "
You can also place the ball anywhere in the pool and aim at the focus point with a bit more force.
Or you can directly aim at the hole.
2:12 You gotta be very skillful
The ball : i will destroy this man whole career
Ellipse table : Not Today Bro
one of my fathers best friends was one of the engineers for the engines on the f-111, and he could break down how aerodynamics work going through a jet engine work so somebody like a child could understand it, and he could do it on a cocktail napkin. Genius of a man, but could break things down to as simple as a few lines with a bic pen.
You are going to have to build a parabolic pool table now
Judd Niemann not a bad idea
+Judd Niemann In a university I worked there was an elliptical, a parabolic and an hyperbolic table. Didn't work so well, but were convincing enough. It is not easy to build such tables with accuracy. His table is not quite elliptical, because the ball has not the size of point, the ellipse is the set of points whose distance from the border equals to the radius of the ball (if you are really thinking on built it actually have this in mind).
He said that you can only hit the ball into the hole if it begins at the other focus point, but I think there's another set of options: imagine placing the ball on the line that passes through the foci, but on the part of the green between the hole and the wall. Then hit the ball toward the wall. Wouldn't that work?
Alex: Anywhere you hit the ball, it will go in
Also Alex: It usually doesn't go in
I know. That kinda pissed me off
Inaccurate - he says if it is not positioned on the focal point it will never go in. This is not correct. All that is needed is for you to aim the ball at either focal point, as this puts the path of the ball on a path for both focal points (assuming the proper pressure to rebound at the correct cushion depth, which is why too light or hard causes it to miss the hole).
Watch the second video!
Numberphile Yes, it still dances around the core concept - a ball passing through one focal point will pass through both focal points due to the geometry of the table (ignoring cushion depth and the pocket itself).
Don't get me wrong, it's a really nice video (or I wouldn't have commented), but for a numberphile video I expected a better explanation/higher standard. Perhaps if you added a text overlay to the video the numerous comments like mine would cease. ;)
Either way, keep up the good work, I love (most of) your videos, and this one only fell short on the technicality of your phrasing.
Alternative game design (starting positions): place the 8 ball on the second focal point, and the two player balls on the mid-point of the far line of the isosceles triangles formed with both focal points and the cushion on either side. Then place the cue ball at the mid point between the pocket and the nadir at the "head" of the table. This starting position shouldn't favor either player (geometrically), but should present a challenge by maximizing the obstructions in sinking either of the player balls.
John Doe Wow, you either got it all wrong or you are out trolling in the deep end without a preserver. You are wrong about my motivation, you are wrong about my statement being whiny/bitchy, and you are wrong to believe that the second video addresses the accuracy of the statement I quoted from this video.
Perhaps you are simply unaware of the general quality of the posts in numberphile. They are exceptionally well done 99% of the time, so when they get something so obviously wrong as what I've pointed out, there is every reason to call them to task for it, and I'm fairly certain that the fine folks in numberphile appreciate every bit of that. My original statement is valid, even with a full "correction" (which they have not done) in the second video - leaving the first video out there with an uncorrected line of "if it is not positioned on the focal point it will never go in" - will only create more people reacting with the obvious (and correct) "not true" line of thought. The correction is needed on the first video, not some vague adjustment in another video.
Or perhaps you simply lack the emotional maturity to understand the modality of my second post, and projected your own gleeful "find" of something you (incorrectly) perceived as being wrong. Your post is both ironic and hypocritical, given that my post was on topic, correct, and not invalidated by any secondary video; while your post was off-topic, trollish, and childish - amounting to the bitchy little whiner that you projected onto me.
Do us all a favor, and go find a less educated, professional, and mature channel to troll - or simply grow up and stay out of things you are unable to comprehend altogether.
i just read "meer lezen (42 regels)", which translates to "read more (42 lines)" i guess you have a serious ego problem man. I'm not gonna waste my time on your ramblings, which are just you trying to convince yourself you are clever
Why are you guys arguing and fighting? Wouldn't it be better to teach, learn and understand together?
as someone who programs in their spare time nothing makes me more happy than turning interesting mathematical truths into something that we can physically appreciate
3:07 OMFG, I CAN'T TAKE THIS ANYMORE, I CAN'T I HAD ENOUGH
love this type of stuff. thanks for the tip.
This video is epicly produced! Love the effort of building a pool table in an elliptical shape.
Every year this is recommended, Every year I rewatch it regardless
You also have to factor where on the ball you hit it because it'll spin differently. To much on the bottom will make it spin back towards you, to much on top will make it roll forward even after hitting something, to much left or right will curve it
Was thinking precisely the same. I don't think error has to do with speed so much, but rather hitting the ball in the middle.
Wtf is up with his vest
Aliasing.
is that not what i said
***** I didn't get the 'line up' part. To me it's an aliasing error, not about lining up, more about having to approximate between 2 values because of the lower resolution. I believe it does indeed line up, otherwise the camera wouldn't pick it up.
Malcolm Sparks professional pool players wear a dress code vest for big matches
Moire pattern. You can look it up for more detail, but I can put a messy explanation here. If you take two mesh screens (like window screens), hold one in front of the other, stand back, and move your head back and forth, you'll see patterns that are bigger and more complicated than the mesh. Similar effect here: something about the grid of his vest (maybe the reflective qualities of the weave?) is aligning strangely with the camera sensor grid and resulting in larger interference patterns.
1:18 hmm, while it's true that if it's in the focus it should rebound to the pocket regardless of where you shoot, when it's not in the focus you can still rebound to the pocket, it's just that you are limited to shoot it in the direction of the focus and then it will rebound correctly
I’ve seen this video like 10 time but whenever it comes into my recommended I always watch it
Mad. Fascinating, but loopy. Well done.
Give me a beer. I can make it not go in the hole.
is that Andy Serkis
i thought it was Martin Sheen
+Calsta84 is it not?
Love this soft sweet boy!
No it’s the lycanthrope from Underworld
i thought same :D
3:03 That might be the most satisfying thing I've ever seen.
Love how they did not crop the slow motion ball from rounding around the hole faster and faster for satisfaction reasons while he continiued talking
And that's a bad miss. ..
visualdragon *snaps a quick salute, since this guy gets it*
Next up, elliptical dog poker...
+visualdragon That bar is badly understaffed
British English for you
That's a cracking pot!
so the shot may be harder because the hole is so small but oooo I can feel for myself how satisfying it must be to get it in and see it circle around the rim before finally settling in knowing full well that youve made it and are just savoring the anticipation
you can place the ball anywhere and aim for the focus point, or exactly away from the focus point. so you can hit the hole via rebound from everywhere
Love this! Thanks for building and sharing. IF each different shot (ie. different angle) is hit with exactly the same energy, is the duration of the shot (ie. transit time to the pocket) the exact same?
If the distances are the same, yes.
But you should be able to get it in from anywhere on the table if you send it through the focus point right?
Randomositydude watch the second video --- ua-cam.com/video/3WHBlPvK3Ek/v-deo.html
Thanks (I do normally also watch the second videos don't know why I didn't today)
+Randomositydude I reckon the spin you put on the ball will also play a role
Or directly away from the focus point...
What I find the most interesting part is the size of the table.
This could catch on for that reason.
Refined the rules and put in on Dragon's Den would be my suggestion.
The reason that it takes a certain force to get it into the pocket is due to the soft sides, they compress more with more force, changing the curve of the circle slightly, causing the angle to change.
thanks for showing me this, now I want to play on it
New game: Kepler's pool. You play in microgravity, add a massive "sun" at the center and try to get the balls to orbit their way into the pocket.
+Edan Coll
Kepler makes a great janitor. He doesn't mind the monotony, he sweeps out the same area every night.
shut up, take my money, I want this pool table :-)
The slow motion of it going into the hole is a great visualization of precession.
I always wondered, wouldn't you always pot the ball in a normal biliard if you hit it with the right amount of power? (with the contition that you can put as much power as you want.)
No, if you hit it perfectly perpendicular to a wall (provided the hole isn't at that point of the wall) it will just bounce back and forth between the walls indefinitely.
I need a gif of 2:27
make one then
so lewd tho
DUDE I'M ABOUT TO SMASH THAT SCREEN IF THE BALL DOESN'T FALL IN
It looks kinda sexual
JakobyGames i
It's pool. But not like you've ever seen it before. Welcome to Loop.
Prem Ghinde legend
You do not belong to this world
Y'all cant even lie that intro was smooth af
"It's nice that you dressed up for the occasion."
"I what?"
Finally a table where I can show my talent
OMG!
This is awesome! How can I buy one of these?
I'm glad 2 million people are following a maths channel.
Cool demo!
1:15 it can still go in through rebound even if the ball is not on the focus point. The key for doing this is that you have to hit the ball along the line segment joining the focus point(without hole), the perimeter of the table and the position of the ball
Or you can simplify this sentence and say you just need to aim at the focal point
@@GoriIIaTactics that's not what i meant but i guess that will work too
@@tbd5330 that's exactly what you meant. If you aim a ball through a line segment that contains the focus point, you're aiming at the focus point. No need to make it more complicated
@@GoriIIaTactics yeah but i was aiming for the perimeter of the table
"Ellipses are an interesting type of shape because they can come in an infinite number of varieties."
Isn't this true for any type of shape?
No. Think of squares. Resizing =/= changing variety.
Agent1220
It is, however, true for triangles, rectangles, parallelograms, rhombuses, trapezoids, pentagons, hexagons...
Square
@@imveryangryitsnotbutter You're forgetting that mathematicians will find any type of shape interesting
@@tykimkim Sure, but if you're going to geek out over one kind of shape, you should at least mention one kind of property that makes it unique from all the other shapes.
I remember playing on a hexagon shaped table once, and you could swivel the table so you took a shot from where you always stood, as it was stuck in the corner, was in reding actually
You’re almost at 3.14 mil and your pfp will be even better
Interesting! One correction: at 1:17 you say "if it's here, wherever I rebound it it will never go in", that's not actually true. It's always on one of the 'sure to go in' paths, so if you hit it while the cue is over the focus point the ball will continue on the path and go in.
I was just about to say the same! ;)
Where are all the other balls? - Guys, I want to see you play this with the whole set of billard balls.
Matthias J. Déjà seen the second video? ua-cam.com/video/3WHBlPvK3Ek/v-deo.html
If you hit with a tiny amount of running english, just enough to be the gearing amount to counteract the friction on a rail... and if you stun the ball at the moment it hits the rail (so it has no forward roll when it hits the rail), I'm interested to see if this works every single time.
I comeback to this video time and time again.
ughhh the moire on his shirt from the tight pattern
Someone needs to gif the ball going in when they zoomed in, but really fast
This is the best thing I've seen all day
Thus far
Numberphile : i won’t get this first try, its really hard
also Numberphile : nails it first try
What is the eccentricity of the table? Or does it not matter?
0.43
I'm pretty sure it was in the video...
But no, it doesn't matter, it will work the same in pretty much any ellipse.
"It'll always go into the hole provided you hit it exactly perfectly right" is a little less impressive than it might initially seem.
Having said that, man oh man do I want that table.
I'm in love with this video.
You have very interesting videos. Subbed
2:27 REEEEEEEEE GO INNNN
I studied computer graphics, and while, one of my projects was to code a pool table game, I'm more fascinated by the interferention on his vest at the beginning :P
Cool table though and I love the attitude of "why build it? It's science, the question should be why not!" :P
Also, I remember reading a theory that, on a regular pool table, if you place a ball on any place and hit it with enough force, and it hits the pool wall on any non-right angle, it will, eventually fall into the socket. Is that true?
DemoBytom no. things like recurring decimals show this in that the ball, if it rebounds perfectly (no side deformation/chaotic instability), it could fall into a recurring pattern that never encounters a pocket. however with the chaotic effects of friction, spin and the deformation of the sides you could probably set something up that covers every point on the table, let alone the pockets.
DemoBytom Hit any cushion at 45 degrees. You can show that the ball will get into a loop without entering a pocket. In fact, I believe you can show that for any angle t for which tan(t) is a rational number, there are places on the cushion where a ball hitting at angle t will never enter a pocket.
yohopostop Ye, the 45 degrees thing is what I thought right after posting that comment.. I must be miss remembering something about that theory, it's been almost 10 years ago that I heard it :/ Or it's just flat out wrong, I dunno anymore :P
DemoBytom If you want to investigate more, you can exploit symmetry. You can show that a ball rebounding and entering a pocket is isomorphic to a diagonal straight line hitting an intersection on a regular square grid (imagine instead of the ball bouncing off a rest, it passes straight through into a mirrored version of the table).
If the angle has a rational tan then starting at one intersection point on the grid, the line will meet another intersection point in a finite distance. Then move this line a little across and it won't hit any intersection points.
If the angle has an irrational tan, I believe it will always intersect with a grid intersection point, but I don't have a proof of this.
DemoBytom I spotted that too. I think it's a Moiré pattern caused by the different angles between the pixels in the camera sensor and the stripes on his shirt. At first I thought it was the pixels on my screen but if you watch it at 240p they're still there so it's encoded in the video.
Source: I came across it on Wikipedia a few months ago: en.wikipedia.org/wiki/Moir%C3%A9_pattern
So would this work with any elipse, where one focus point is a hole, and other is where you hit it from?
sidespin: “laughing hysterically”
1:19 , wrong, if you shoot it through the focus point it will go into the hole
I3estHer0 watch the second video!
When u let the smart kid play sports
💀💀💀
✂️✂️✂️✂️
so cool, a round table... I want this for the 1.April ^^
This just was amazing
What about a perfectly triangular pool table?
I'm sorry but that is just an awful vest to wear on camera. Cool table though.
Max Goldstein ssshhh, Alex loves that vest!
Numberphile I think Alex looks stylish and sharp. But then I am a mathematician.
I think it's a fine vest in person, but on camera it gets distorted and causes artifacts because of the fine pattern.
Max Goldstein Americans (sorry of you're not, I'm assuming here) call a waistcoat a vest..?
But without the vest he loses is billiards power
I do wonder if this will ever take off? It would be pretty cool to see professionals make this into a sport and see it on ESPN.
I'm studying conic sections at University, and this was linked on the problem sheet. I am crying.
I think it's wrong to say the ball will never go in if it lies anywhere but the focal point. I would imagine, that whereever the ball lies, it can go into the pocket, if it is played in such a directions, as to simulate it yoming from the focal point
LutzDerLurch You can get the ball in the hole from anywhere on the board, the focal point is the only place mathematically that hitting the ball in any direction causes the ball to go in.
HoodedAthlete6
yupp. That's what i meant.
Just hit it really hard in any direction, it's most likely going to roll into the hole
Joshua Osuna that is utterly I correct
Did you even watch the video 😂
@@ArtyMars the video showed if you hit it kinda hard, Joshua is suggesting if you hit really hard, it’ll hit another rebound eventually that’ll send it back to the hole again and slow enough.
That's going to help me so much, when I get a round snooker table.
Watching the ball circle the hole made this whole video worth it.
whats the perimeter of that ellipse
ben1996123 The area is pi*a*b where a and b are semi-major and semi-minor axes. That the distance from the centre to farthest edge and shortest edge, a circle is a unique case of an ellipse where the major and minor axes are the same.
The perimeter of a ellipse is a hard problem which inspired a new branch of mathematics check out the wikipedia page: en.wikipedia.org/wiki/Ellipse
Ben Booth yes i know
ben1996123 The perimeter is unimportant. It does, however, have a direct relationship to the focal points, the distance between them and a chosen semi-major axis length. On this table the semi-major and semi-minor axes look near equal (though obviously not since it does have two focal points).
NFITC1 yes i know. but perimeter of an ellipse is an interesting thing to calculate
ben1996123
Oh, so you're suggesting a new video? I'm all for that.