Papers › Tight bounds on the maximal perimeter of convex equilateral small polygons
Tight bounds on the maximal perimeter of convex equilateral small polygons
Christian Bingane, Charles Audet
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A small polygon is a polygon that has diameter one. The maximal perimeter of a convex equilateral small polygon with n=2ˢ sides is not known when s ≥4. In this paper, we construct a family of convex equilateral small n-gons, n=2ˢ and s ≥4, and show that their perimeters are within O(1/n⁴) of the maximal perimeter and exceed the previously best known values from the literature. In particular, for the first open case n=16, our result proves that Mossinghoff's equilateral hexadecagon is suboptimal.
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