ABSTRACT
A nice result in plane geometry states that in the class of all convex sets of constant width d, the Reuleaux triangle has least area. The first proofs of this theorem are contained in the papers by Lebesgue (1914) and by Blaschke (1915). Subsequently alternative proofs were given by several authors: Fujiwara (1927, 1931), Mayer (1934–35), Eggleston (1952), Besicovitch (1963) and Chakerian (1966).
