Isoperimetric inequality

Common card · No. 390484

In mathematics, the isoperimetric inequality is a geometric inequality involving the square of the circumference of a closed curve in the plane and the area of a plane region it encloses, as well as its various generalizations. Isoperimetric literally means "having the same perimeter". Specifically, the isoperimetric inequality states, for the length L of a closed plane curve and the area A of the region that it encloses, that 4 π A ≤ L 2 , {\displaystyle 4\pi A\leq L^{2},} and that equality holds if and only if the curve is a circle. The isoperimetric problem is to determine a plane figure of the largest possible area whose boundary has a specified length. The closely related Dido's problem asks for a region of the maximal area bounded by a straight line and a curvilinear arc whose endpoints belong to that line. It is named after Dido, the legendary...

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