# ðŸ”— Volume of an n-ball tends to a limiting value of 0 as n goes to infinity

ðŸ”— Mathematics

In geometry, a ball is a region in a space 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 $R^{n}V_{n},$ where $V_{n}$ is the volume of the unit n-ball, the n-ball of radius 1.

The real number $V_{n}$ can be expressed by a expression involving the gamma function. It can be computed with several recurrence relations. It can be expressed in terms of $A_{n},$ the area of the unit n-sphere.

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- "Volume of an n-ball tends to a limiting value of 0 as n goes to infinity" | 2022-05-12 | 90 Upvotes 50 Comments