Groupe d’études et de recherche en analyse des décisions

G-2005-49

The Small Octagon with Longest Perimeter

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The convex octagon with unit diameter and maximum perimeter is determined. This answers an open question dating from 1922. The proof uses geometric reasoning and an interval arithmetic based global optimization algorithm to solve a series of non-linear and non-convex programs involving trigonometric functions.

, 24 pages