Papers › Small polygons with large area
Small polygons with large area
Christian Bingane, Michael J. Mossinghoff
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A polygon is \textit{small} if it has unit diameter. The maximal area of a small polygon with a fixed number of sides n is not known when n is even and n≥14. We determine an improved lower bound for the maximal area of a small n-gon for this case. The improvement affects the 1/n³ term of an asymptotic expansion; prior advances affected less significant terms. This bound cannot be improved by more than O(1/n³). For n=6, $8$, $10$, and $12$, the polygon we construct has maximal area.
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