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- W3092123050 abstract "A small polygon is a polygon of unit diameter. The maximal perimeter and the maximal width of a convex small polygon with $$n=2^s$$ vertices are not known when $$s ge 4$$ . In this paper, we construct a family of convex small n-gons, $$n=2^s$$ and $$sge 3$$ , and show that the perimeters and the widths obtained cannot be improved for large n by more than $$a/n^6$$ and $$b/n^4$$ respectively, for certain positive constants a and b. In addition, assuming that a conjecture of Mossinghoff is true, we formulate the maximal perimeter problem as a nonlinear optimization problem involving trigonometric functions and, for $$n=2^s$$ with $$3 le sle 7$$ , we provide global optimal solutions." @default.
- W3092123050 created "2020-10-15" @default.
- W3092123050 creator A5033875337 @default.
- W3092123050 date "2022-06-02" @default.
- W3092123050 modified "2023-10-05" @default.
- W3092123050 title "Tight bounds on the maximal perimeter and the maximal width of convex small polygons" @default.
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- W3092123050 doi "https://doi.org/10.1007/s10898-022-01181-9" @default.
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