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.
Isoperimetric Inequality
See also
Isoperimetric QuotientExplore with Wolfram|Alpha
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 InequalityCite this as:
Weisstein, Eric W. "Isoperimetric Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IsoperimetricInequality.html