The minimum diameter octagon with unit-length sides: Vincze's wife's octagon is suboptimal

摘要

This paper answers a query of Vincze (Acta Univ. Szeged, Sect. Sci. Math. 12 A (1950) 136142): find the convex octagon with unit-length sides and minimum diameter. It also shows that the solution is e-unique. The proof uses geometric arguments and a global optimization algorithm to solve a nonconvex quadratic program. (C) 2004 Elsevier Inc. All rights reserved.