Enumerating isodiametric and isoperimetric polygons
نویسندگان
چکیده
منابع مشابه
Enumerating isodiametric and isoperimetric polygons
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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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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We survey current work relating to isoperimetric functions and isodiametric functions of finite presentations. §
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This is the first of two papers devoted to connections between asymptotic functions of groups and computational complexity. One of the main results of this paper states that if for every m the first m digits of a real number α ≥ 4 are computable in time ≤ C22Cm for some constant C > 0 then nα is equivalent (“big O”) to the Dehn function of a finitely presented group. The smallest isodiametric f...
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The maximal perimeter of an equilateral convex polygon with unit diameter and n = 2m edges is not known when m ≥ 4. Using experimental methods, we construct improved polygons for m ≥ 4, and prove that the perimeters we obtain cannot be improved for large n by more than c/n4, for a particular constant c.
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2011
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2011.03.004