Abstract
In the recent paper [1] the authors gave a very nice overview of many solved as well as unsolved extremal problems in plane Euclidean geometry. Among these problems we found the following isoperimetric problem of particular interest. Let n > 3, let xi, ... , xn be the (pairwise different) vertices of a convex polygon with unit perimeter in the Euclidean plane, and let Sn be the sum of the distances between these points, i.e.,
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