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Last updated: Mon Jan 5 2009

Created, developed, and nurtured by Eric Weisstein
at Wolfram Research
Calculus and Analysis > Inequalities >
Interactive Entries > Interactive Demonstrations >

Isoperimetric Inequality

Let a plane figure have area A and perimeter p. Then

Q=(4piA)/(p^2)<=1,

where Q is known as the isoperimetric quotient. The equation becomes an equality only for a circle.

SEE ALSO: Isoperimetric Quotient

REFERENCES:

Osserman, R. "Isoperimetric Inequalities." Appendix 3, §3 in A Survey of Minimal Surfaces. New York: Dover, pp. 147-148, 1986.

Solomon, H. Geometric Probability. Philadelphia, PA: SIAM, p. 35, 1978.




CITE THIS AS:

Weisstein, Eric W. "Isoperimetric Inequality." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IsoperimetricInequality.html

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