Timeline for What are some fundamental "sources" for the appearance of pi in mathematics?
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| Aug 9, 2011 at 22:04 | comment | added | Sridhar Ramesh | In the same way: horizontal projection from a sphere to a circumscribing cylinder preserves surface measure in any number of dimensions >= 2, so long as "circumscribing cylinder" means "Those points which would land on the sphere if all but their first two coordinates were changed to zero" and "horizontal projection" means "Scaling up the first two coordinates as needed while preserving the rest". This, along with that the interior content of a sphere in n-dimensional space is 1/n * its radius * its surface content, keeps $pi$ coming up in sphere surface and interior content in any dimension. | |
| Mar 14, 2010 at 17:57 | history | answered | Douglas Zare | CC BY-SA 2.5 |