Isoperimetrical Problem

Classic Problem

What shape is the largest area that can be surrounded by a plane curve of a given length?

Solution

The solution is: a circle.

Proof

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Also see

• Dido's Problem, which is a variant of this.

Sources

• 1963: Charles Fox: An Introduction to the Calculus of Variations (2nd ed.) ... (previous) ... (next): Chapter $\text I$. The First Variation: $1.1$. Introduction