Blaschke–Lebesgue theorem

In plane geometry the Blaschke–Lebesgue theorem, named after Wilhelm Blaschke and Henri Lebesgue, states that the Reuleaux triangle has the least area of all curves of given constant width. By the isoperimetric inequality, the curve of constant width with the largest area is a circle.

In 1952 Ohmann proved the analogue of the Blaschke–Lebesgue theorem for Minkowski planes which uses a concept analogous to that of the Reuleaux triangle and constructed using the triangle equilateral relative to the given gauge body.