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- W2022387986 abstract "The value $frac{1}{2n}cot(frac{pi}{2n})$is shown to be an upper bound on the width of any n-sided polygon with unit perimeter. This bound is reached when n is not a power of 2, and the corresponding optimal solutions are the regular polygons when n is odd and clipped regular Reuleaux polygons when n is even but not a power of 2. Using a global optimization algorithm, we show that the optimal width for the quadrilateral is $frac{1}{4}sqrt{2(3sqrt{3}-3)}$with a precision of 10−4. We propose two mathematical programs to determine the maximum width when n=2s with s≥3 and provide approximate, but near-optimal, solutions obtained by various heuristics and local optimization for n=8, 16, and 32." @default.
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- W2022387986 date "2008-08-22" @default.
- W2022387986 modified "2023-09-30" @default.
- W2022387986 title "Isoperimetric Polygons of Maximum Width" @default.
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- W2022387986 doi "https://doi.org/10.1007/s00454-008-9103-9" @default.
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