Timeline for understanding the average height of a unit hyper-semisphere
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2015 at 1:20 | comment | added | Manos | @MartinM.W.: Thanks for this explanation. | |
| Mar 11, 2015 at 1:19 | comment | added | Martin M. W. | On a high-dimensional sphere most of the mass is concentrated around the equator, where the height is lowest. That's a heuristic explanation for why the average height goes to zero. | |
| Mar 11, 2015 at 1:18 | comment | added | Manos | So the conclusion is that the average height of the unit hemisphere goes to zero. Interesting. | |
| Mar 11, 2015 at 1:16 | vote | accept | Manos | ||
| Mar 11, 2015 at 1:15 | comment | added | Igor Rivin | The ratio in front can be (essentially) found on the Wiki page on the $n$-sphere (en.wikipedia.org/wiki/N-sphere), The integral is standard, though you can use Mathematica | |
| Mar 11, 2015 at 0:49 | history | answered | Igor Rivin | CC BY-SA 3.0 |