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 $\dfrac 1 3$.

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