Isoperimetric Inequality

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


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

See also

Isoperimetric Quotient

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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.

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Isoperimetric Inequality

Cite this as:

Weisstein, Eric W. "Isoperimetric Inequality." From MathWorld--A Wolfram Web Resource.

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