I stumbled across the following mathematical curiosity:
One can calculate the volume of a unit sphere in D-dimensions (a
"hypersphere"). For D=2 one gets pi (area of a unit circle), for D=3
one gets 4*pi/3, and so on.
It looks like the volume is slowly increasing with D. But that trend
does NOT continue. The general formula for the volume is
pi^(D/2)/gamma(D/2+1). One reaches a maximum volume at D=5.
Thereafter the volume *decreases to zero* as D continues to increase.
I find that surprising!
I am wondering what physical applications this result might affect.
For example, volume of a hypersphere enters into one way of
calculating the partition function of an ideal gas.
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Carl E Mungan, Assoc Prof of Physics 410-293-6680 (O) -3729 (F)
Naval Academy Stop 9c, 572C Holloway Rd, Annapolis MD 21402-1363 mailto:mungan@usna.eduhttp://usna.edu/Users/physics/mungan/