Blaschke-Lebesgue Theorem

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