===== Ball volume =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ p\in \mathbb N $ |

| @#FFBB00: definiendum | @#FFBB00: $V_p:\mathbb R_+\to \mathbb R_+$ |
| @#FFBB00: definiendum | @#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 ====
=== Context ===
[[Lebesgue-Borel measure]], [[Open ball]]