Then-diameter of planar sets of constant width

Abstract

where the maximum is taken over all z k ∈ E, k = 1, 2, . . . , n. We prove that if n = 5, then the Reuleaux n-gons have the largest n-diameter among all sets of given constant width. The proof is based on the solution of an extremal problem for n-diameter. MSC2010: primary 30C65; secondary 05C25.