منابع مشابه
A Linear-time Construction of Reuleaux Polygons
The relation between planar geometric graphs which are full equi-intersectors and Reuleaux polygons is studied. It is shown that there is a one-to-one correspondence between these objects. This is used to present exhaustive constructions of Reuleaux polygons of arbitrary (odd) order n. The obvious construction is running in quadratic time, but more careful investigations lead to a reened versio...
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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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It is shown that if C is an n-dimensional convex body then there is an affine image C of C for which |∂ C| | C| n−1 n is no larger than the corresponding expression for a regular n-dimensional " tetrahedron ". It is also shown that among n-dimensional subspaces of L p (for each p ∈ [1, ∞]), ℓ n p has maximal volume ratio.
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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.
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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...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1960
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1960.10.823