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A zero-dimensional sphere is a point and it's 0-dimensional volume is 1. That makes some sense, since it's *one* point.
I’m actually not sure.. I think the sum should actually start at 1, making the answer e^pi -1
That looks like the evil twin brother of Euler's formula.
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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..
