Wednesday, 14 March 2012

Pi and The Simulated Bouncing Balls

We love it when viewers get involved with what we're doing - and here's a brilliant example from Numberphile.

First, here's a recent video about Pi from Professor Ed Copeland involving a strange way that Pi "appears" when objects collide.

Of course what Ed described was really a "thought experiment" because it would be difficult to create a frictionless environment and elastic collisions.

But that's viewer where Lukas Wolf comes to the rescue.

He was captivated by our video and re-created the experiment using a piece of software called Algodoo.

Lukas has also made his code available at this link (for those who have the Algodoo software, which can be downloaded for free).

And Lukas sent us this image, which I believe charts the velocity of the small ball.

In his email to us, Lukas said:
"I was quite amazed by your 'pi and bouncing balls' video, certainly a cool fact about pi that I didn't know. Because it was so amazing, I replicated the scenario in a simulator and plotted the velocities of the balls over time while counting the collisions between the balls. The results were great: On the 32nd collision big M started to move backwards."
Many thanks Lukas.

And don't miss our full collection of Pi videos.


  1. Is there any chance at all of seeing the full video with Prof. Ed? Yeah, his notes have been uploaded, but honestly I'd much rather hear him talk about the maths behind it, because it's just not easy to understand something like this from looking at a single sheet of paper with notes. I think it's a shame that it's been cut out, for one it's a really interesting fact about pi, that I want to see proven, but also because the prof. made the effort of deriving it for us because he probably thought viewers would be interested to see it.
    I don't understand why it was cut out in the first place. Do you think viewers are afraid of seeing slightly complicated maths? Then why have a channel called numberphile in the first place? The videos on this channel are obviously really well made and keep a lot of people interested, but it's a shame we only get half of the story. Be careful not to underestimate your audience.

  2. I THINK I found out why this happens... I found it when I was playing with my calculator after science class. I told it to find the square root of 9.8m/1sec/1sec, the rate of acceleration due to gravity. It showed me ~3.033, which made me think of pi. So, I told it to multiply pi by pi. Guess what. I got ~9.869. Even though it wasn't exactly 9.8, it had 9.8 IN it. Coincidence? Is the rate of acceleration on earth actually pi squared? Do people even make square pies? Is it that square pies fall at a rate of ~9.86960406437476m/s/s? Why did I just ask those two questions? Lol, ok, that's enough. Just a side note: I'm 13. :D

    1. No; g and π are not related. Remember, the exact value of g = 9.80665 m/s^2. π^2 ~ 9.86, which would round to 9.9. 9.9 and 9.8 are not the same value; what you observed is a coincidence. Not bad for a 13-year-old, though =)

    2. Also gravity does not come into this example at all, we're moving in the horizontal plane without friction. You could just as easily set this example in deep space. Nice observation about g and pi though :P

  3. Is it just as elegant if you use a different number base?

    1. Yes it will be. But then you would have to have the ratios of the two balls according to the powers of the number base you are working in.

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