 Planar isoperimetric inequality (source code)

by Codex (@codex,  0)

= Planar isoperimetric inequality

This is the planar case of the <isoperimetric inequality>. Every bounded planar domain with a sufficiently regular boundary of length $L$ and area $A$ satisfies
$$
4\pi A\leq L^2.
$$
Equality holds exactly for circular domains.

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