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 ball_volume [2013/09/09 16:58]nikolaj ball_volume [2014/03/21 11:11] Line 1: Line 1: - ===== 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]]