I was playing around, and stumbled upon something quite beautiful..
If you sum over the volumes of all 2k-dimensional unit spheres, that sum converges to e^π.
I have no idea why this should be true..pic.twitter.com/QvsQJkAuc2
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Here's a reasonably nice proof that the volume of the unit 2n-ball is pi/n times the volume of the unit (2n-2)-ball: https://en.wikipedia.org/wiki/Volume_of_an_n-ball#The_two-dimension_recursion_formula …
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