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

Abstract

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.

arXiv admin note: text overlap with arXiv:2009.07893

References in corpus (3)

• Tight bounds on the maximal perimeter and the maximal width of convex small polygons
• Tight bounds on the maximal perimeter of convex equilateral small polygons
• The equilateral small octagon of maximal width

Cited by in corpus (2)

• The equilateral small octagon of maximal width
• Tight bounds on the maximal perimeter of convex equilateral small polygons