G-2021-45
The equilateral small octagon of maximal width
et référence BibTeX
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 \(s \ge 3\)
. This paper solves the first open case and finds the optimal equilateral small octagon. Its width is approximatively 3.24 % larger than the width of the regular octagon: \(\cos(\pi/8)\)
. In addition, the paper proposes a family of equilateral small \(n\)
-gons, for \(n=2^s\)
with \(s\ge 4\)
, whose widths are within \(O(1/n^4)\)
of the maximal width.
Paru en août 2021 , 14 pages
Axe de recherche
Publication
juil. 2022
et
Mathematics of Computation, 91(336), 2027–2040, 2022
référence BibTeX