Timeline for Limit of distance between two random points in a unit-radius $n$-sphere
Current License: CC BY-SA 3.0
8 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 15, 2014 at 21:15 | comment | added | Kevin P. Costello | If instead we look at the ratio of expected distance to diameter, then for spheres the limit is asymptotically $\frac{1}{\sqrt{2}}$, while for cubes it is (from Nate Eldredge's answer to the linked question) $\frac{1}{\sqrt{6}}$. Is it known whether Spheres maximize this ratio, whether in finite dimensions or asymptotically? | |
| Apr 15, 2014 at 1:35 | vote | accept | Joseph O'Rourke | ||
| Apr 15, 2014 at 1:08 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Clarified that within the sphere means in the ball.
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| Apr 15, 2014 at 0:44 | comment | added | Henry Cohn | I'm not sure there's such a contrast between cubes and spheres. In high dimensions a unit cube is vastly larger than a unit sphere, as measured by diameter or volume, so it's not as fair a comparison as the word "unit" suggests. | |
| Apr 15, 2014 at 0:15 | answer | added | Christian Remling | timeline score: 15 | |
| Apr 14, 2014 at 23:22 | history | edited | Joseph O'Rourke | CC BY-SA 3.0 |
Caveat: For odd n. $n$ in title for consistency with earlier question.
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| Apr 14, 2014 at 23:03 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |