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# The equilateral small octagon of maximal width

## Christian Bingane et Charles Audet

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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.

, 14 pages

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À paraître dans : Mathematics of Computation, 2022 référence BibTeX