Groupe d’études et de recherche en analyse des décisions

G-2010-37

Maximal Perimeter, Diameter and Area of Equilateral Unit-Width Convex Polygons

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The paper answers the three distinct questions of maximizing the perimeter, diameter and area of equilateral unit-width convex polygons. The solution to each of these these problems is trivially unbounded when the number of sides is even. We show that when the number is odd, the optimal solution to these three problems is identical, and arbitrarily close to a trapezoid.

, 13 pages