Isoperimetric Polygons of Maximum Width
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...
متن کاملAn isoperimetric inequality for logarithmic capacity of polygons
We verify an old conjecture of G. Pólya and G. Szegő saying that the regular n-gon minimizes the logarithmic capacity among all n-gons with a fixed area.
متن کاملThe Poincaré Metric and Isoperimetric Inequalities for Hyperbolic Polygons
We prove several isoperimetric inequalities for the conformal radius (or equivalently for the Poincaré density) of polygons on the hyperbolic plane. Our results include, as limit cases, the isoperimetric inequality for the conformal radius of Euclidean n-gons conjectured by G. Pólya and G. Szegö in 1951 and a similar inequality for the hyperbolic n-gons of the maximal hyperbolic area conjecture...
متن کاملAsymmetric polygons with maximum area
We say that a polygon inscribed in the circle is asymmetric if it contains no two antipodal points being the endpoints of a diameter. Given n diameters of a circle and a positive integer k < n, this paper addresses the problem of computing a maximum area asymmetric k-gon having as vertices k < n endpoints of the given diameters. The study of this type of polygons is motivated by ethnomusiciolog...
متن کاملIsoperimetric Inequalities and the Width Parameters of Graphs
We relate the isoperimetric inequalities with many width parameters of graphs: treewidth, pathwidth and the carving width. Using these relations, we deduce 1. A lower bound for the treewidth in terms of girth and average degree 2. The exact values of the pathwidth and carving width of the d– dimensional hypercube, Hd 3. That treewidth (Hd) = Θ (
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 2008
ISSN: 0179-5376,1432-0444
DOI: 10.1007/s00454-008-9103-9