Volume of an n-ball

Common card · No. 284539

In geometry, a ball is a region comprising all points within a fixed distance, called the radius, from a given point; that is, it is the region enclosed by a sphere or hypersphere. An n-ball is a ball in an n-dimensional Euclidean space. The volume of a n-ball is the Lebesgue measure of this ball, which generalizes to any dimension the usual volume of a ball in 3-dimensional space. The volume of a n-ball of radius R is R n V n , {\displaystyle R^{n}V_{n},} where V n {\displaystyle V_{n}} is the volume of the unit n-ball, the n-ball of radius 1. The real number V n {\displaystyle V_{n}} can be expressed via a two-dimension recurrence...

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