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

@inproceedings{Bingane2021TightBO, title={Tight bounds on the maximal area of small polygons: Improved Mossinghoff polygons}, author={Christian Bingane}, year={2021} }

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.

## One Citation

Tight bounds on the maximal perimeter of convex equilateral small polygons

- Mathematics
- 2021

A small polygon is a polygon of unit diameter. The maximal perimeter of a convex equilateral small polygon with $n=2^s$ vertices is not known when $s \ge 4$. In this paper, we construct a family of…

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