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"}
image:
fields total:
13
integrity:
15