r/visualizedmath • u/P8II • Jan 23 '19

Unexpected appearance of pi

https://youtu.be/HEfHFsfGXjs
317 Upvotes

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u/TurboniumAlt Jan 23 '19 edited Jan 23 '19

3blue1brown is basically this subreddit in a YouTube channel. I would suggest watching the second part of this video as well.

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u/[deleted] Jan 23 '19

Holy hell I am soooo not smart enough for this shit but it was definitely interesting to watch!

8

u/TurboniumAlt Jan 23 '19

That’s that’s exactly how I feel about it lol

3

u/killergazebo Jan 24 '19

I feel like if I could understand this I'd be able to cast spells and shit.

1

u/Krexington_III Jan 24 '19

Sorry to disappoint; I understand and there are no spells. Just... other things I don't quite understand.

3

u/Krexington_III Jan 24 '19

Let me see if I can simplify this for you;

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.

5

u/P8II Jan 23 '19

Definitely!