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ball_volume [2013/09/08 17:52] nikolaj |
ball_volume [2014/03/21 11:11] (current) |
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| ===== Ball volume ===== | ===== Ball volume ===== | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ p\in \mathbb N $ | | + | | @#55CCEE: context | @#55CCEE: $ p\in \mathbb N $ | |
| - | | @#FFBB00: $V_p:\mathbb R_+\to \mathbb R_+$ | | + | | @#FFBB00: definiendum | @#FFBB00: $V_p:\mathbb R_+\to \mathbb R_+$ | |
| - | | @#FFBB00: $V_p(r):=\beta^p(B_0(r))$ | | + | | @#FFBB00: definiendum | @#FFBB00: $V_p(r):=\beta^p(B_0(r))$ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 10: | Line 10: | ||
| For all $a\in \mathbb R^p$, the volume of the ball $B_a(r)$ is the same and given by | For all $a\in \mathbb R^p$, the volume of the ball $B_a(r)$ is the same and given by | ||
| - | ^ $V_p(r)=\frac{\pi^{p/2}}{\Gamma(p/2+1)} r^p$ ^ | + | ^ $V_p(r)= \pi^{p/2}\ \Gamma(p/2+1)^{-1}\ r^p $ ^ |
| === Reference === | === Reference === | ||
| Wikipedia: [[http://en.wikipedia.org/wiki/Volume_of_an_n-ball|Volume of an n-ball]] | Wikipedia: [[http://en.wikipedia.org/wiki/Volume_of_an_n-ball|Volume of an n-ball]] | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Lebesgue-Borel measure]], [[Open ball]] | [[Lebesgue-Borel measure]], [[Open ball]] | ||
