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】
: 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】
: 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】
: 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】
: 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】
: 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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