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Ivan Pavlov's Library tagged math →  View Popular

07 Sep 08

Isoperimetric Polygons of Maximum Width

  • 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.
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