The most unexpected answer to a counting puzzle
12,893,414
Published 2019-01-13
Even prettier solution: • How colliding blocks act like a beam ...
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Special thanks to these supporters: 3b1b.co/clacks-thanks
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NY Times blog post about this problem:
wordplay.blogs.nytimes.com/2014/03/10/pi/
The original paper by Gregory Galperin:
www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool…
Evidently, Numberphile also described this problem (I had not known):
• Pi and Bouncing Balls - Numberphile
You'll notice that video has an added factor of 16 throughout, which is not here. That's because they're only counting the collisions between blocks (well, balls in their case), and they're only counting to the point where the big block starts moving the other way.
Thanks to these viewers for their contributions to translations
Bengali: Prayas Sanyal
Hebrew: Omer Tuchfeld
Italian: @Deye27, @hi-anji
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These animations are largely made using manim, a scrappy open source python library: github.com/3b1b/manim
If you want to check it out, I feel compelled to warn you that it's not the most well-documented tool, and it has many other quirks you might expect in a library someone wrote with only their own use in mind.
Music by Vincent Rubinetti.
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vincerubinetti.bandcamp.com/album/the-music-of-3bl…
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open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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All Comments (21)
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Originally discovered in 1995, published in 2003. maybe he DID count the clacks?
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Pi has no business showing up literally everywhere in math.
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2:37 I was watching in the middle of the night and got absolutely flashbanged by the sudden swap from dark coloured example to bright white paper.
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Another interesting observation : When the masses colliding are powers of some other base (say 3), the number of collisions still equal the digits of Pi, but in the same base. Eg : Pi in base 3 is 10.010211012222010211002111110221222220111201212121... If you run the simulation with masses of 1, 3^(2 * 1), 3^(2 * 2), 3^(2 * 3),..., then the number of collisions will be 1 (base 3), 10 (base 3), 100 (base 3), and 1001 (base 3) respectively. Number of collisions for 1,3^(2 * 50) will be first 50 digits of Pi in base 3 : 10010211012222010211002111110221222220111201212121 , or 2255343044159619899886237 in decimals.
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Physicists: "Noo! You can't have ideal collisions make a sound!" 3B1B: "Haha, blocks go brr"
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That animation of the spherical cow actually made me wheeze. That was unexpected
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This is why I love math. You always look at a problem, read it out loud, then discover something about that problem. It's like there is always a hidden puzzle in math equations. For example, in 7th grade, we were learning about circumference. My teacher showed the class a video which said that if you take the diameter and try to wrap it around a circle, there's a tiny bit left, to which I realized that that tiny bit looked EXACTLY like pi, or 3.14. It's so cool finding small details that make so much since!
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the clacking sound is so satisfying i want it on repeat forever in my brain
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Highest quality Youtuber out there. And I mean that in every dimension.
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1:40 Me opening the door at 1:43 am
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I thought your video on relating the Basel Problem to the circle was simply gorgeous, astonishing and unforgettable. These three surpass even that! Thank you so very much!
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i love coming back to this video every once in a while because it's just so mind boggling that it reblows my mind every time
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Teacher: "gimme some digits of pi" Me: "clack clack clackclackclackcla... clackclack clack clack... Wait for it" Teacher: "what on earth is that supp...?" Me: "... clack"
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gets this on recommendations for the 10th time Brain: click on it. Me: but I've already wa- Brain: do it.
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I like how the speed of the last collision is an expression of the remaining digits. So when it's 314(15...) collisions it juuuust reaches the line, but when it's 31415(92...), it gives the moving block a proper final spank to send it on its way.
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Im not here for the math stuff. Im here for the colliding noise..
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Clack.
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Pi is a creep. I'm gonna file a restraining order on him. He has started to show up on my integration problems now. He's gone too far.
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3Blue1Brown never fails to make me question reality!
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thank you for giving me a math project! this was very fun to work on and you explain this very well.
