• Corpus ID: 235443244

# Maximal perimeter and maximal width of a convex small polygon

@inproceedings{Bingane2021MaximalPA,
title={Maximal perimeter and maximal width of a convex small polygon},
author={Christian Bingane},
year={2021}
}
A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with n = 2s sides are unknown when s ≥ 4. In this paper, we construct a family of convex small n-gons, n = 2s with s ≥ 4, and show that their perimeters and their widths are within O(1/n8) and O(1/n5) of the maximal perimeter and the maximal width, respectively. From this result, it follows that Mossinghoff’s conjecture on the diameter graph of a convex small 2s-gon with maximal…
5 Citations
Tight Bounds on the Maximal Area of Small Polygons: Improved Mossinghoff Polygons
• Christian Bingane
• Mathematics, Computer Science
Discrete &amp; Computational Geometry
• 2022
It is shown that, for all even n ≥ 6, the area obtained improves by O (1 /n 5 ) that of the best prior small n -gon constructed by Mossinghoﬀ, and in particular, for n = 6 , the small 6-gon constructed has maximal area.
The equilateral small octagon of maximal width
• Mathematics
• 2022
A small polygon is a polygon of unit diameter. The maximal width of an equilateral small polygon with n = 2 s vertices is not known when s ≥ 3 . This paper solves the ﬁrst open case and ﬁnds the
A note on the maximal perimeter and maximal width of a convex small polygon
• Mathematics
• 2021
The polygon P is small if its diameter equals one. When n = 2, it is still an open problem to find the maximum perimeter or the maximum width of a small n-gon. Motivated by Bingane’s series of works,
Tight bounds on the maximal perimeter of convex equilateral small polygons
• Mathematics
Archiv der Mathematik
• 2022
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