Isodiametric Problems for Polygons
نویسندگان
چکیده
منابع مشابه
Isodiametric Problems for Polygons
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/n in the area problem and c2/n in the perimeter problem, for certain con...
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For a positive integer n that is not a power of 2, precisely the same family of convex polygons with n sides is optimal in three different geometric problems. These polygons have maximal perimeter relative to their diameter, maximal width relative to their diameter, and maximal width relative to their perimeter. We study the number of different convex n-gons E(n) that are extremal in these thre...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2006
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-006-1238-y