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ball_volume [2013/09/09 16:58] nikolaj |
ball_volume [2014/03/21 11:11] |
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| - | ===== Ball volume ===== | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $ p\in \mathbb N $ | | ||
| - | | @#FFBB00: $V_p:\mathbb R_+\to \mathbb R_+$ | | ||
| - | | @#FFBB00: $V_p(r):=\beta^p(B_0(r))$ | | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | === Theorems === | ||
| - | For all $a\in \mathbb R^p$, the volume of the ball $B_a(r)$ is the same and given by | ||
| - | |||
| - | ^ $V_p(r)= \pi^{p/2}\ \Gamma(p/2+1)^{-1}\ r^p $ ^ | ||
| - | === Reference === | ||
| - | Wikipedia: [[http://en.wikipedia.org/wiki/Volume_of_an_n-ball|Volume of an n-ball]] | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Lebesgue-Borel measure]], [[Open ball]] | ||
| - | === Context === | ||
| - | [[Archimedes' constant π]] | ||
