# Blaschke-Lebesgue Theorem

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## Theorem

Let $C$ be a closed contour in the complex plane.

Let the minimum width $w$ of $C$ be such that $w \ge 1$.

Then $C$ can contain a circle whose radius $\dfrac 1 3$.

## Proof

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## Also known as

The **Blaschke-Lebesgue Theorem** is also seen as **Blaschke's Theorem**.

## Source of Name

This entry was named for Wilhelm Johann Eugen Blaschke and Henri Léon Lebesgue.

## Sources

- 1983: François Le Lionnais and Jean Brette:
*Les Nombres Remarquables*... (previous) ... (next): $0,33333 33333 33 \ldots$ - 1991: David Wells:
*Curious and Interesting Geometry*... (previous) ... (next): Blashke's Theorem