Reuleaux triangle [SEP] named after
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Reuleaux triangles have also been called spherical triangles, but that term more properly refers to triangles on the curved surface of a sphere.
They are named after Franz Reuleaux, a 19th-century German engineer who pioneered the study of machines for translating one type of motion into another, and who used Reuleaux triangles in his designs. However, these shapes were known before his time, for instance by the designers of Gothic church windows,
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.