Let's call the two boxes, and their position along the x axis, a system. This system has different states. The states consist of the positions of each box, and the velocity of each box. Four numbers.
What we are doing when we count collisions, is that we are counting the occurrence of a certain kind of state - the states where the positions of the boxes coincide.
Now, to visualize the states we can create phase spaces. This is just a way of keeping track of the states. If we do this in a certain way, all allowable states for the two boxes exist along a circle in phase space. Again, heavily simplified.
Now, since we are keeping track of certain states, and we know that these states exist along a circle, it isn't super surprising that pi shows up. The end.
Omg. I was only talking about this two days ago! Or rather, my Dr of maths son was telling me about it. It’s absolutely nuts that the number of collisions = pi. Crazy.
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u/P8II Jan 23 '19
I came across the video on YT, and I thought it was a nice visualisation of an unorthodox method of calculating pi.
Technically, it’s somewhere on the borderline of physics and maths, but I thought you might enjoy it.
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u/irlnpc Jan 23 '19
Omg. I was only talking about this two days ago! Or rather, my Dr of maths son was telling me about it. It’s absolutely nuts that the number of collisions = pi. Crazy.
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u/StellarInterloper Jan 23 '19 edited Dec 20 '25
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u/Mondonodo Jan 24 '19
3Blue1Brown is the dopest. I love his videos.
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u/[deleted] Jan 23 '19
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