Timeline for Intuitive proof that the first $(n-2)$ coordinates on a sphere are uniform in a ball
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
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| Jul 26, 2010 at 13:22 | comment | added | Mark Meckes | I'd be happier with the rest of your answer if I knew anything about projective toric varieties; now I guess I have an excuse to go learn something about them. Maybe if I did I'd consider this as nice an answer as I'd hoped for in the first place. In any case, it's nice to see that this is part of a larger story. | |
| Jul 26, 2010 at 13:19 | comment | added | Mark Meckes | I'd be happier with your first observation, that the $n\ge 4$ case follows from the $n=3$ case, if I knew a nice intuitive geometric argument for that reduction, that didn't include anything that looked like a happy numerical coincidence. Even so, it's a very good point and does address the question "Why the 2?" at least halfway. ("Because 3-1=2.") | |
| Jul 24, 2010 at 19:07 | comment | added | Greg Kuperberg | Your self-promotion needs no excuse. As long we've started that, I used Archimedes' theorem and other moment maps in a paper on numerical quadrature. arxiv.org/abs/math/0405366 | |
| Jul 24, 2010 at 6:34 | comment | added | Joel Fine | When Richard Thomas taught me toric geometry he proved Delzant's theorem - on the correspondence between toric symplectic manifolds and Delzant polytopes - using Archimedes's Theorem. I give a brief version of his argument in an answer to this question (please excuse the shameless self-promotion!): mathoverflow.net/questions/4982/look-into-delzant-polytope | |
| Jul 23, 2010 at 20:05 | history | answered | Greg Kuperberg | CC BY-SA 2.5 |