Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons

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A small polygon is a polygon of unit diameter. The maximal area of a small polygon with \(n=2m\) vertices is not known when \(m \ge 7\). In this paper, we construct, for each \(n=2m\) and \(m\ge 3\), a small \(n\)-gon whose area is the maximal value of a one-variable function. We show that, for all even \(n\ge 6\), the area obtained improves by \(O(1/n^5)\) that of the best prior small \(n\)-gon constructed by Mossinghoff. In particular, for \(n=6\), the small \(6\)-gon constructed has maximal area.

, 12 pages

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