So why do the volumes of all even dimensional unit spheres sum to e^π?

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This is a follow up to my video on Euler's number (https://youtu.be/AAir4vcxRPU). Here you'll see why all unit spheres in even dimensions have volumes that sum to e^π

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Proof of Volume Formula: https://www.youtube.com/watch?v=eEJtMFdkzzU

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