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ball_volume [2013/09/08 17:52] nikolaj |
ball_volume [2013/09/08 18:05] nikolaj |
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| 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 = \frac{\pi}{2}^{p/2}\ \Pi(p/2) 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]] | ||
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| === Requirements === | === Requirements === | ||
| [[Lebesgue-Borel measure]], [[Open ball]] | [[Lebesgue-Borel measure]], [[Open ball]] | ||
| + | === Context === | ||
| + | [[Archimedes' constant π]], [[Archimedes' constant τ]] | ||
