Groupe d’études et de recherche en analyse des décisions

G-2007-56

Simple Polygons of Maximum Perimeter Contained in a Unit Disk

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A polygon is said to be simple if the only points of the plane belonging to two of its edges are its vertices. We answer the question of finding, for a given integer n, the simple n-sided polygon contained in a disk of radius 1 that has the longest perimeter. When n is even, the optimal solution is arbitrarily close to a line segment of length 2n. When n is odd, the optimal solution is arbitrarily close to an isosceles triangle.

, 13 pages

Ce cahier a été révisé en mai 2008