Chronology | Current Month | Current Thread | Current Date |
[Year List] [Month List (current year)] | [Date Index] [Thread Index] | [Thread Prev] [Thread Next] | [Date Prev] [Date Next] |
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.