Group for Research in Decision Analysis


Extremal Problems for Convex Polygons - An Update

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Consider a convex polygon Vn with n sides, perimeter Pn, diameter Dn, area An, sum of distances between vertices Sn and width Wn. Minimizing or maximizing any of these quantities while fixing another defines ten pairs of extremal polygon problems (one of which usually has a trivial solution or no solution at all). In a previous paper, we surveyed research on these problems up to 2005. It appears that geometric reasoning is increasingly complemented by global optimization methods. As several new results have been obtained very recently, we present an update to that survey.

, 22 pages