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posted by martyb on Thursday March 14 2019, @07:13PM   Printer-friendly
from the ouch dept.

Submitted via IRC for chromas

For Pi Day, Calculate Pi Yourself Using Two Colliding Balls

This is at least my ninth year of writing about Pi Day—here is my post from 2010. Of course it's called Pi Day because the date, 3/14, is similar to the first three digits of pi (3.1415 …). At this point I've built up a whole library of fun things in honor of Pi Day.

Here is a new one. You can calculate the digits of pi using elastic collisions between two objects of different masses and a wall.

[...] There are two balls, A and B. Ball A has a larger mass and is initially moving. It collides with ball B such that ball B speeds up and ball A slows down just a little bit (this is a perfectly elastic collision). After this, ball B starts moving toward the wall and eventually bounces off it back toward ball A for another collision. This continues until ball A is moving away from the wall instead of toward it, and there are no longer any collisions.

Now for the pi part. If you know that the mass of ball A is 100 times greater than that of ball B, there will be 31 collisions. If the ratio of masses is 10,000 to 1, there will be 314 collisions. Yes, that is the first 3 digits of pi. If you had a mass ratio of 1 million to 1, you would get 3,141 collisions. (Remember the first few digits of pi are 3.1415 …) In general, if you want "d" digits of pi, then you need mass A divided by mass B to be 100 raised to the d-1 power.

This is not a very efficient method for calculating the digits of pi, but it seems to work. Here is a great video from 3Brown1Blue that explains this situation. [YouTube link] Also, here is an older video from Numberphile that also goes over this problem.

[What I want to know is which one is better: apple, raspberry, or apricot? --ed.]


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  • (Score: 2) by opinionated_science on Thursday March 14 2019, @07:25PM (1 child)

    by opinionated_science (4031) on Thursday March 14 2019, @07:25PM (#814392)

    for some reason when I read this, I had a horse tapping out the digits of pi....

    I'd be interesting the mathematics of this physical manifestation...

    • (Score: 3, Funny) by DannyB on Thursday March 14 2019, @08:08PM

      by DannyB (5839) Subscriber Badge on Thursday March 14 2019, @08:08PM (#814420) Journal

      I was thinking two colliding balls where one has slightly more mass . . . sounds painful.

      --
      People today are educated enough to repeat what they are taught but not to question what they are taught.
  • (Score: 2) by looorg on Thursday March 14 2019, @07:43PM (3 children)

    by looorg (578) on Thursday March 14 2019, @07:43PM (#814402)

    [What I want to know is which one is better: apple, raspberry, or apricot? --ed.]

    Blueberry is number one, then apple, then raspberry.

    • (Score: 0) by Anonymous Coward on Thursday March 14 2019, @07:48PM

      by Anonymous Coward on Thursday March 14 2019, @07:48PM (#814405)

      Never had Olallieberry I see.

    • (Score: 2) by SpockLogic on Friday March 15 2019, @12:21AM (1 child)

      by SpockLogic (2762) on Friday March 15 2019, @12:21AM (#814554)

      And none can compare to the Key Lime I consumed to celebrate the day.

      --
      Overreacting is one thing, sticking your head up your ass hoping the problem goes away is another - edIII
      • (Score: 2) by AthanasiusKircher on Friday March 15 2019, @02:07AM

        by AthanasiusKircher (5291) on Friday March 15 2019, @02:07AM (#814596) Journal

        Agreed. Mine was also frozen, covered in chocolate, and on a stick. A bit gimmicky but still good -- made with real key limes, which are obviously (ahem) the key.

  • (Score: 3, Interesting) by sjames on Thursday March 14 2019, @08:13PM (2 children)

    by sjames (2882) on Thursday March 14 2019, @08:13PM (#814422) Journal

    Alexa, this is a class a compulsory directive, compute to the last digit the value of Pi.

  • (Score: 2) by krishnoid on Thursday March 14 2019, @08:40PM (2 children)

    by krishnoid (1156) on Thursday March 14 2019, @08:40PM (#814444)

    You can remember 113355 -> 355/113 -> pi to better than 1 in 1E6. I've seen it in equations sometimes.

    • (Score: 2) by DannyB on Thursday March 14 2019, @09:06PM (1 child)

      by DannyB (5839) Subscriber Badge on Thursday March 14 2019, @09:06PM (#814469) Journal

      But I thought PI was Irrational. Unhinged. Deranged.

      --
      People today are educated enough to repeat what they are taught but not to question what they are taught.
      • (Score: 0) by Anonymous Coward on Thursday March 14 2019, @09:32PM

        by Anonymous Coward on Thursday March 14 2019, @09:32PM (#814492)

        But I thought PI was Irrational. Unhinged. Deranged.
        Reply

        Can't read one sentence?

  • (Score: 1, Touché) by Anonymous Coward on Thursday March 14 2019, @09:39PM

    by Anonymous Coward on Thursday March 14 2019, @09:39PM (#814498)

    "USAnians can't even"-day

  • (Score: 2) by darkfeline on Saturday March 16 2019, @04:29AM

    by darkfeline (1030) on Saturday March 16 2019, @04:29AM (#815285) Homepage

    Where am I supposed to get two balls where one of the balls is billions of times more massive than the other? How am I supposed to move such a ball? With a nuke? Do the balls have to be perfectly spherical frictionless cows in a perfect vacuum?

    --
    Join the SDF Public Access UNIX System today!
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