Is pool actually just mathematics? 

remember, these are mathematicians, not physicists.

"There's more air in the room than I assumed." 😆🤣😆

2 mathematicians enter a bar with a measuring tape...

As a physicist, if my shot doesn't miss the pocket by 10 pocket lengths, it is pretty accurate and should thus count as a perfect hit.

"The math doesn't make a difference if you don't know how to hit the cue ball." Genius.

I think you need a bit more janky Python code for this one.

"The table is 100 inches long, so when you divide into 80 segments, each segment is 1 inch." New unit unlocked: the Parker Inch.

Pool Players: “They’ll never get it because they’re measuring based on the walls and not the diamonds.” Mathematicians: “Jokes on you, we’re pretending that we’re playing in a hall of mirrors!”

the scene of a pair of mathematicians breaking out the notes and measuring tape in the middle of a pool game is something straight out of a comedic skit

3:18 i love how Grant expected that exact reaction from Matt to the use of inches that he had is face ready for the comeback

Alternative title - "Mathematicians discover how engineers feel when handed drawing plans from architects

So many spherical, weightless cows in a vacuum.

"there's more air in the room then I assumed" Matt Parker, 2024

"These guys have been failing up for their whole lives, I don't want that to happen at this table'' -- Man who affixes all mics with blue tape

"My brain REFUSES to look at the inches"

@12:00 you completely misunderstood what Jenn was telling you. In the animation the spin you gave the ball is reverse spin, it's working against the natural way the ball wants to spin off the rail. Jenn tells you to give running spin (in this case left spin). Recall that in your first attempt the ball went to the right of the 8 ball (from the POV of the balls movement). This is because you hit too far to the left on the second rail. Using reverse spin makes the cue ball rebound at a greater angle than incident which makes it move even further left before it hits the rail, missing by an even larger margin. Instead, you should have used running/left spin so that it rebounds at a lesser angle, rebounding to the second rail further to the right, and putting you more on track to the 8 ball.

obviously math can account for every possible thing... friction, humidity, air drag, etc etc... it's just a matter of building all these factors into the simulation I would LOVE a part two where you over-engineer a simulation program running on a laptop and try to beat them using THAT !!!!!!!!!!

Matt: "is there friction?" Me: "You leave physics out of my maths, mister!"

As soon as Grant started measuring in inches I immediately switched allegiances to the pros, a travesty of practical calculation.

What a great way to show the difference between theory and application. Jenn was super patient and cool about everything, she's a great communicator. Rollie was there too!

Annimation at 12:08 is incorrect. The cue should be applying left (running) spin on the ball so that the bounce off of the first cushion has a smaller angle of reflection, which then means the impact on the second cushion is closer to the left side of the screen and then the ball, again, has a smaller angle of reflection than incidence and goes towards the pocket. (backed up by viewing the ball at 22:20 and Jenns explantion of "opening the angle" i.e opening the angle between the incident and reflected line)

"Is there friction?", "I assume not" LMAO🤣

OK WHEN DID GRANT GET MUSCLES 3blue1built

Reminds me of the time in high school where I proclaimed, "I CAN SEE GEOMETRY," and proceeded to totally whiff my pool shot. My friend was dying with laughter 😂

"100.4 inches" Wow, you upset both metric AND imperial users in one phrase. That's next level!

23:38 - Matt invents raytracing.

If you were doing this on a snooker table you’d have to factor in the Higgins Boss particle

First thought: Can professional pool players do math better by playing pool than math professionals? 😂

Should've chosen air hockey, not pool.

Hi Matt, the animation at 12:08 is wrong. Jen uses running spin, which in this case is left spin - the left spin widens the angle after hitting the first rail, making the ball hit the second rail higher. This compensates for the induced spin, and the cue ball will reach the ideal target point.

as a math student who's obsessed with pool, this crossover makes me so happy :')

“Donald in Mathmagic Land” is when I first learned about math and billiards.

When I was a kid, I used to watch this Disney VHS all the time called “Donald in Mathemagic land” (or something very similar), and there was a whole segment about using math for making shots in pool.

5:43 genuinely had no idea that air conditioning makes a difference in how pool is played

As much as I love Rollie, he really didn't need to be here for this video haha, he just stands in the back silently the whole video

Using Let's Play: Bar Billiards as my other data point, see you in 10 years.

can't believe this is how I learn Rollie has a channel about pool

Paused to comment, JENNIFER BARRETTA on your channel?!?!?! Played pool against a friend (an aeronautical engineer) half a lifetime ago, I was already okay at pool but the maths data dump he put on me regarding angles changed my pool game. This video excites me and I've not watched it yet, pool, Jennifer Barretta and another maths data dump... triple combo of the finest kind in the early hours no less. Life is good.

12:04 is incorrect. Running side is the opposite. It opens the angle, and therefore will arrive at the same point on the third rail, but coming from a different line of the second rail. Jennifer explained it correct at 13:17

Matt! You got the explanation at 12:05 wrong! They don't add 'check side' (as you've animated - side spin to narrow the angle of reflection) to counteract the imparted spin. They add 'running side' (the opposite), so the angle off the first cushion is widened, causing an earlier second-cushion bounce (i.e., further to the left as we look at your diagram) such that, during this second bounce, the angle of reflection widening due to the running side actually brings the cue ball back on to a line that leads to the target!

As an excellent mathematician and pretty good pool player, my money is on the pool players. Every time. As a mathematician, I love the collaboration between Matt and Grant. As a pool player, I love having the pool players here to teach them a lesson.

I wouldn’t have been shocked if the punchline was that Grant is a pro-level pool player. Because Grant.

Grant’s animations are just always out of this world.

"There's more air in the room than I'd assumed" that actually broke me

I love that it's implied that rollie doesn't have a specific editing style, random eagle and explosion effects just kinda show up in whatever video he's in

I remember watching Rollie's pool videos years ago, then finding his climate town channel and other colab with Matt. Very sweet to see him playing pool again

23:30 Oh. I just realized that if you have to bounce off two walls, it's basically a retro-reflector (in 2d) and so that singular point should work for anywhere along that side of the table...

I liked the visual comparison between the add-to-80 method and the radial fan at the end. I wonder if the amount of english that a pro pool player would intuitively know to use would reduce the error between the add-to-80 lines and the purely mathematical ones.

Should have invited Steve Mould; he has experience with balls picking up spin as they bounce.

"You're such an imperialist" said the one using the IMPERIAL system 😂

Just read the corresponding chapter in "Love Triangles" and am excited that it's actually documented on video! Great stuff!

the collab I never expect but very glad to watch.

There’s an old Disney cartoon, _Donald Duck in Mathmagic Land,_ that has a segment explaining how to use the diamonds on a pool table.

The animation at 12:03 is totally wrong... actually in your animation you show a reverse spin which is counter clock-wise, but actually they are talking about a running spin which is clock-wise, and it is called running spin since it helps the ball run easily from the cushion, on the other hand reverse spin does not allow the ball to run but slow down since it works against the direction. You assumed that they give the spin to compensate the spin the ball will take on the first cushion, but it would not end at the same point of the second cushion it hit before, actually it will hit longer (right side of the animation) because of the spin. Also the ball would be a lot slower because of the reverse spin. Actually they are aiming to hit the second cushion shorter (left side of the animation) in order to compensate the affect of the spin, so even with the spin the ball bounces wide, they actually try to reduce (closer to vertical) incoming angle so it bounces wider and goes to the target area with the spin. Additionally, it is not mentioned on the video but the usage of the diamonds on the rails rather than the points on the bed (as you did by assuming that this is a mirror acts like in optics) are actually to compensate the affects of the friction. It is very hard to explain this in writing but let me try. When the ball goes towards the cushion it gains a rolling momentum, but when it hits the cushion and bounces it keeps this momentum and this momentum creates a friction between the ball and the cloth working against the ball and acts like a brake, this leads to ball to curve towards that cushion a little and makes it go wider. So the diamonds show these wider angles, but speed makes this affect change a lot. Also the cushion is not a solid surface as you assume on your calculations, it is a flexible material (some kind of rubber) and it actually shrinks and wraps the ball when it hits. This makes the ball start to spin even you hit it without any spin.

I really enjoyed this, thank you to all of you!

Can't get enough of Rollie on this channel. Keep the partnership up, two of the best people on youtube!

It was simply a fantastic video. Significantly better than ever before. When I’ve been in my studies, the very best and most inspiring sessions have been when we’ve had guidance, and several of us have stood by a board discussing and collaborating to solve questions or explore a topic. Where there has still been an adult to steer the conversation or provide help. Somehow, you capture exactly that feeling in your video - a sense of being in that room. Congratulations. Really impressive.

This is why elliptical pool tables were invented.

This is the Math vs Physics pool battle i didn't know always wanted to see. Thanks.

love this! unexpected as ever and still amazing

I am fairly good at putting the cue ball where I want it to go, but not so good at calculating where that should be. I have a friend who is the opposite. We made a killer team the few times we played.

Inches?!?!

This was so fascinating! Loved this video! Would love to see more pool maths videos :D

The edit on this was INCREDIBLE!!!

"inches" 😭

Ahh, mathematically simple function approximations to save time calculating, neat.

12:09 actually, they give it the opposite spin in this case! Running spin is spin in the direction that the ball is hitting the rail, and check spin is opposite the direction the ball is hitting the rail (which is what the animation shows in this case) Essentially any time a ball hits the rail with spin, it’s going to change the angle that the ball comes off the rail. Running spin will make the angle slightly larger than a perfect reflection, and check spin would make the angle slightly smaller than a perfect reflection In the animation shown, the friction between the ball with check spin and the cushion would actually change that first angle to be slightly smaller, meaning it would land even further down that second rail and miss the ball by even more! What Jen suggests in this case is actually to use running spin, so the angle off the first rail will be larger and therefore hit higher up on the second rail. There’s a little more physics that goes into how spin wears off over time, but generally running spin will last longer than check spin because not as much energy is transferred for each bounce. So in this case there would still be some spin when the cue ball hits the second rail, increasing the angle again and taking the cue ball on line to hit the 8 ball :)

Watching two of my favorite math guys working together and seeing their minds bounce off each other is just a joyous sight to see.

5:18 did he.. fake drinking the coffee?

Need to add a third group, and bring in stuff made here for the engineers

i love watching people who are really good at what they do

This was a super fun and interesting video, thanks!

I'm sorry, the concept of doing maths in inches just makes my brain break. If I have to measure anything in inches I just think "meh... that's close enough"

1:23 Nice typo, mister mathmematician.

That's really interesting! Great video!

love Matt and Grant hanging out videos!

What next, you two go to Las Vegas?

If you haven't already seen it, you should watch "Automatic pool stick vs. strangers" by Stuff Made Here

I really want to see this be a series

such a pleasure to watch these interactions, I love these moments in life.

Aiming through the diamonds compensates for the cushion, is what I have always been told.

Inches????😂😂😂

This is such a good idea for a video

6:30 This is basically the way they made the reflective floors in Tony Hawk's OG shopping centre level

In a way, the problem you had was that you were assuming an inelastic collision, where the ball just immediately bounces off the surface. But because the edge compresses a bit and the ball rolls while pressing it, the "elastic" nature of the edge makes the collision act as if the contact point is further back

the calculations required to predict the ball's motion must surely be a solved problem, via some complex system of equations, lest computer simulated pool games wouldn't be possible.

glad to see rollie still playing pool. Missed the updates on the road to the US open!

This was a really good video for showing the limitations of models. Great work

@6:12 "Your such an Imperialist!" Surely "Your such a metricist!" (And don't call me Shirley!!)

matt has a real parker square of a team ;p

This was a very insightful video!

maths vs physics vs real world, game's on! love it!

Ive lost all respect for Grant. Using inches for maths? Disgusting

In the diagram at 24:00, I notice that the phantom tables are all lined up based on the positions of the *cushions*. What happens if you instead use slightly larger tables that are the size of the region within the *diamonds* , and align them so that the positions of the *diamonds* match? How does that affect the convergence of the lines on that target pocket?

I really love the Matt and Grant duo! Please more collab videos in the future.

This is awesome! Thanks

11:46 - for a moment there I was genuinely expecting you to complement "angle of incidence" with "angle of outcidence"... Since you didn't, I'm now officially disappointed.

Here he comes, the crush of all youtube math, Grant himself

I'm here for Rollie Williams. I highly, highly recommend his "average pool player" series where he tried to recreate famous pool shots by himself. It's excellent.

great collab, cool maths, nice vibes, 10/10