Re: [Phys-l] a mathematical curiosity

[brian whatcott <betwys1@sbcglobal.net>]

On 1/9/2012 11:25 AM, Bob Sciamanda wrote:
> J Denker wrote:
>
> “
> Similarly all the surface-area is near the equator. You can see this already
> in D=3, on the earth, where the area of the tropical regions is
> large compared to the area of the arctic regions ... “
>
> I am befuddled.  One could just as arbitrarily choose an equator running
> through a rotational pole.  Without the earth’s spin and/or its orientation
> relative to the sun the choice of an equator is completely arbitrary.
I rationalize this assertion to mean for any band of latitudes, those 
nearer the equator have more surface area.

While on the topic of hyperspheres, I note that the volume max occurs 
near 5 1/4 dimensions, but never reaches zero for arbitrarily large 
dimensions n.

Brian W