Isoperimetric inequality

id: isoperimetric-inequality-180-12745481
title: Isoperimetric inequality
text: In mathematics, the isoperimetric inequality is a geometric inequality involving the perimeter of a set and its volume. In n -dimensional space R n the inequality lower bounds the surface area or perimeter per ⁡ of a set S ⊂ R n by its volume vol ⁡, - per ⁡ ≥ n vol ⁡ / n vol ⁡ 1 / n, where B 1 ⊂ R n is a unit sphere. The equality holds only when S is a sphere in R n. On a plane, i.e. when n = 2, the isoperimetric inequality relates the square of the circumference of a closed curve and the area
brand slug: wiki
category slug: encyclopedia
description: Geometric inequality which sets a lower bound on the surface area of a set given its volume
original url: https://en.wikipedia.org/wiki/Isoperimetric_inequality
date created: 2003-09-24T15:43:08Z
date modified: 2024-09-05T13:22:53Z
main entity: {"identifier":"Q617417","url":"https://www.wikidata.org/entity/Q617417"}
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fields total: 13
integrity: 15

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