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Other fun fact about spheres: as the dimension grows to infinity, the function of the area of the section along a diameter converges to a Gaussian (!) If you a
by ot 14y ago
Other fun fact about spheres: as the dimension grows to infinity, the function of the area of the section along a diameter converges to a Gaussian (!)
If you are interested in these things, this survey is amazing: http://www.math.ucdavis.edu/~deloera/MISC/BIBLIOTECA/trunk/Ball/ball.pdf http://www.math.ucdavis.edu/~deloera/MISC/BIBLIOTECA/trunk/B...
- mturmon 14y agoThanks for this nice link. It's a robust phenomenon that kicks in pretty well even in modestly large dimensions. One name for this is concentration of measure http://en.wikipedia.org/wiki/Concentration_of_measure http://en.wikipedia.org/wiki/Concentration_of_measure See figure 6 in the paper linked in the above comment for a nice illustration of how this works.
- Panoramix 14y agoFascinating stuff, thanks for the link