# Plane Figure with Maximum Area for given Perimeter is Circle

## Theorem

Let $F$ be a plane figure.

Let $P$ be the length of the perimeter of $F$.

Let the area of $F$ be the largest of all the plane figures whose perimeters are of length $P$.

Then $F$ is a circle.

## Historical Note

The problem of determining the plane figure which has the maximum area for a given perimeter was first solved by Jacob Bernoulli.

He also went ahead with a generalisation of the problem.