Groupe d’études et de recherche en analyse des décisions

G-2003-59

The Minimum Diameter Octagon with Unit-Length Sides: Vincze's Wife's Octagon is Suboptimal

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This paper answers a query of S. Vincze (Acta Univ. Szeged, Sect. Sci. Math. 12 A (1950) 136-142): find the convex octagon with unit-length sides and minimum diameter. It also shows that the solution is ε-unique. The proof uses geometric arguments and a global optimization algorithm to solve a nonconvex quadratic program.

, 15 pages