c*******e 发帖数: 8624 | | b**g 发帖数: 335 | 2 Measure in R^d "usually" means length, area or volume (depends on d)
【在 c*******e 的大作中提到】![](/moin_static193/solenoid/img/up.png) : thanks
| c*******e 发帖数: 8624 | 3 okay, so how to compute the volume of a ball in R^d
【在 b**g 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Measure in R^d "usually" means length, area or volume (depends on d)
| f******k 发帖数: 297 | 4 in Euclidean measure it can be done in a simple recursion. for
a ball with radius 1,
if d=2k, V=(2*pi)^k/(2*k)!!
if d=2k+1, V=2*(2*pi)^k/(2*k+1)!!
it is interesting to note that the volume of the smallest cube
containing the ball is infinitely larger than that of the ball
when d goes infinity.
【在 c*******e 的大作中提到】![](/moin_static193/solenoid/img/up.png) : okay, so how to compute the volume of a ball in R^d
| w**a 发帖数: 1024 | 5
interesting ...
【在 b**g 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Measure in R^d "usually" means length, area or volume (depends on d)
| H****h 发帖数: 1037 | 6 笼统地写成一个式子:V=pi^{d/2}/(d/2)!,x!=Gamma(x+1)。
【在 f******k 的大作中提到】![](/moin_static193/solenoid/img/up.png) : in Euclidean measure it can be done in a simple recursion. for : a ball with radius 1, : if d=2k, V=(2*pi)^k/(2*k)!! : if d=2k+1, V=2*(2*pi)^k/(2*k+1)!! : it is interesting to note that the volume of the smallest cube : containing the ball is infinitely larger than that of the ball : when d goes infinity.
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