Let a plane figure have area
and perimeter . Then

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

## See also

Isoperimetric Quotient
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## 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.## Referenced
on Wolfram|Alpha

Isoperimetric Inequality
## Cite this as:

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

## Subject classifications