# Limiting Area of Polygon with given Perimeter

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## Theorem

Let $\PP$ be the set of plane geometric figures with perimeter $L$.

The element of $P$ with the largest area is the circle of radius $\dfrac L {2 \pi}$ which has area $\dfrac {L^2} {4 \pi}$.

## Proof

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## Historical Note

This result was demonstrated by Pappus of Alexandria.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $6$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $6$