How colliding blocks act like a beam of light…to compute pi.

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The third and final part of the block collision sequence.
Part 1:
Part 2:
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Error correction: I wrote the answer as floor(pi/theta), when really it should be ceiling(pi/theta) – 1 t account for values of theta perfectly dividing pi. For example, the case of equal masses gives an angle of pi/4, and 3 total clacks.

This beautiful result, and the solution shown here, are due to Gregory Galperin:

And here’s a lovely interactive built by GitHub user prajwalsouza after watching this video:

Speaking of looking glass universes…

NY Times blog post about this problem:

The plushie pi shown at the video’s start:

If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then “add subtitles/cc”. I really appreciate those who do this, as it helps make the lessons accessible to more people.

Music by Vincent Rubinetti.
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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe:

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36 COMMENTS

  1. Thank you for all 3 videos, great explainations, nice perspectives, and even cooler animations. I just missed (or maybe overlooked) pointing out that Pi only shows up when using mass ratios scaled by 100 since sqrt of 100 is ten and we use a dezimal system – but that seems not worth noting 😅

  2. every time i watch one of Grant's videos
    1) i'm very glad i studied engineering so i can get the gist of what he's saying and
    2) i'm very glad i don't still work in that highly competitive field.
    very much reminiscent of the old "Watch Mr. Wizard".

  3. Why cant the angle be used in degrees instead of radians. Like useinh 180 instead of pi. Dont know if its a lame question but I'm kind of confused. But a great video. I was smiling the whole time while watching the video thinking that a problem like this can have such an analogy. Incredible!!

  4. Very interesting, I think it would be conceptually easier if you start with how the system evolves in position space, rescale coordinate so that you have speed consistency, make observation it is similar to light bouncing between mirrors, then look at velocity space of the scaled coordinates. Position space also best shows how the initial positions and speed will not affect the final result at all, since it will always be a straight line parallel to x axis

  5. I really like the combination of creativity and science the guy used to define these perspectives…….

  6. A lot of these steps feel awfully contrived, designed specifically to get this pi result. At no point did I feel like the shift in perspective came up naturally or that I could have discovered it myself; at no point did the next step within a current perspective seem obvious (especially the square rooted masses and vector dot products). It felt more like a showcase of what math can be, rather than a guiding hand through a unique solution to a quirky problem.

  7. Hey OP, so I'm not a physicist or really bright at physics, but I have a question. We see that almost everything in our daily lives, and everything in Physics, Maths and Science in general, has Pi in it. And Pi is irrational. We have computed its value to trillions of digits, but we will obviously never compute (or physically witness) the actual value. Only ever approximations upto n digits.
    My question: So what if we use Pi as our standard unit to measure. Our Unit. Make Pi the "One" of Math. Wouldn't that make computation (and in general, every math and every equation) so much simpler? Pi is no longer 3.14159265358979323 of 1. It's just 1.
    It would be like multiplying all equations with 1/Pi, make calculations of "squares" difficult instead, but it would still simplify most equations with Pi in it. Which is a lot.

  8. It actually seems right to see the block as an example of a compound bonded state of e-Pi-i resonant frequency interference positioning, of omnidirectional-dimensional Total Internal Reflection, otherwise known as mass-momentum = latency of Superspin Modulation Superspin, from the superimposed AM-FM communication mechanism of equation E=mC², (short version), in continuous creation connection in time-timing Principle.

    "Very striking" mathematical methodology beautifully illustrated.

  9. Very nice. I think the final answer is difference. I've obtained -floor(-pi/theta)-1
    For example: theta=pi/4 is led to floor(pi/(pi/4))=4 is wrong; but -floor(-pi/(pi/4))-1=3 is correct
    floor(pi/theta) is correct only when pi/theta is not integer.

  10. There's a reason why the light goes in a straight line,
    Light has no mass, that's why it was familiar to the 2 cubes with the same mass .

  11. 😓😓 I'm 17 years older in korea…
    I can't understand!!! 😥😥
    Why korean doesn't like math channel 🤬🤬

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