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by pervycreeper
2762 days ago
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Not a surprise to see pi in there really, since we're averaging over "surfaces" of circles/spheres. In general (spoiler), it does generalize to arbitrary dimensions. We get a rational factor for odd dimensions, and 1/pi * rational for even. See sections 6-9 here for demonstration: https://arxiv.org/pdf/1109.0595.pdf |
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