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

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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  • 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 😅

    Master Mind May 17, 2020 3:16 pm Reply
  • My blown,,,How amazingg!! SImply mindblown

    ahmad syamim May 17, 2020 3:16 pm Reply
  • 12:01 that reminds me of the spokes of a bicycle wheel.

    Harry M May 17, 2020 3:16 pm Reply
  • 0:30 Sufficient reason to hit like button.

    Rayerdyne May 17, 2020 3:16 pm Reply
  • angles of light are measured with respect to the normal

    Bob Fearnley May 17, 2020 3:16 pm Reply
  • 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".

    charles ranalli May 17, 2020 3:16 pm Reply
  • This literally turned me on

    Wissam El Kadamani May 17, 2020 3:16 pm Reply
  • 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!!

    Kaushik Iyer May 17, 2020 3:16 pm Reply
  • You are crazy !!!

    Pranav sirodaria May 17, 2020 3:16 pm Reply
  • 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

    Miller Four May 17, 2020 3:16 pm Reply
  • "is worth 80 IQ points"
    Me: ok then let's collect IQ

    Yusril Atfan May 17, 2020 3:16 pm Reply
  • Math is so beautiful

    Kreavita May 17, 2020 3:16 pm Reply
  • I really like the combination of creativity and science the guy used to define these perspectives…….

    Soumyashree Patra May 17, 2020 3:16 pm Reply
  • I have never learned so much yet understood so little

    Hi Friends May 17, 2020 3:16 pm Reply
  • 10:46 Looking Glass Universe. 😅

    samarendra chandan bindu Dash May 17, 2020 3:16 pm Reply
  • I don’t know how these videos came up in my recommended but it was really satisfying

    Elijah Olsen May 17, 2020 3:16 pm Reply
  • Awesome!!!

    Mauricio Micoski May 17, 2020 3:16 pm Reply
  • 2020: 999

    Alexandra Delliou May 17, 2020 3:16 pm Reply
  • That was incredibly elegant

    Luke Hartmann May 17, 2020 3:16 pm Reply
  • 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.

    wundrweapon May 17, 2020 3:16 pm Reply
  • 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.

    Varun Gupta May 17, 2020 3:16 pm Reply
  • 11:20
    and that's how you can model refraction
    when the practical/appearent speed – is not constant

    Julian Danzer May 17, 2020 3:16 pm Reply
  • Glad I caught this during the last hour of pi day!

    Charles Van Noland May 17, 2020 3:16 pm Reply
  • So is the maximum amount of times light can get reflected 180? Or 179 degrees?

    Sky but May 17, 2020 3:16 pm Reply
  • Anything that involves distorting the fabric of space is my jam.

    3l H4ck3r C0mf0r7 May 17, 2020 3:16 pm Reply
  • Fantastic! This vid increased my IQ point.

    没人, May 17, 2020 3:16 pm Reply
  • There is brilliance, then there's genius … then there's this.

    Aaron Hollander May 17, 2020 3:16 pm Reply
  • Me watching the first part:
    Wow, why is PI there?
    Me at the end of this video:
    Wow, why is PI there?

    Elissio May 17, 2020 3:16 pm Reply
  • 12:57 just had a mathgasm

    dealer of deeth May 17, 2020 3:16 pm Reply
  • You r marvelous

    Aram Malkhasyan May 17, 2020 3:16 pm Reply
  • 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.

    David Wilkie May 17, 2020 3:16 pm Reply
  • 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.

    Bahram Sarabi May 17, 2020 3:16 pm Reply
  • (in math test)
    (Forgets pi)
    (Grabs two blocks)

    Huh Neat May 17, 2020 3:16 pm Reply
  • I don't understand what's happening here but it's so satysfying to watch

    l adrix5521 l May 17, 2020 3:16 pm Reply
  • 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 .

    Lev Just lev May 17, 2020 3:16 pm Reply
  • 😓😓 I'm 17 years older in korea…
    I can't understand!!! 😥😥
    Why korean doesn't like math channel 🤬🤬

    Albin Song May 17, 2020 3:16 pm Reply

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