Isodiametric Problems for Polygons |
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Authors: | Michael J Mossinghoff |
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Institution: | (1) Department of Mathematics, Davidson College, Davidson, NC 28035-6996, USA |
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Abstract: | The maximal area of a polygon with n = 2m edges and unit diameter is not known when m ≥ 5, nor is the maximal perimeter of
a convex polygon with n = 2m edges and unit diameter known when m ≥ 4. We construct improved polygons in both problems, and show that the values we obtain
cannot be improved for large n by more than c1/n3 in the area problem and c2/n5 in the perimeter problem, for certain constants c1 and c2. |
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Keywords: | |
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