Papers › Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons
Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons
Christian Bingane
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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 ≥7. In this paper, we construct, for each n=2m and m≥3, a small n-gon whose area is the maximal value of a one-variable function. We show that, for all even n≥6, the area obtained improves by O(1/n⁵) that of the best prior small n-gon constructed by Mossinghoff. In particular, for n=6, the small 6-gon constructed has maximal area.
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