The isoperimetric quotient of a closed curve is defined as the ratio of the curve area to the area of a circle (A = π r_A^2) with same perimeter (p = 2π r_p) as the curve, Q | congruent | r_A/r_p^2 | = | (A/π)/(p/(2π))^2 | = | (4π A)/p^2, where A is the area of the plane figure and p is its perimeter. The isoperimetric inequality gives Q<=1, with equality only in the case of the circle.

isoperimetric inequality | Kelvin's conjecture