The product of the distances of a point inside a regular polytope to its vertices

被引：0

作者：

Chakerian, Gulbank D. ^{[1
]}

Klamkin, Murray S. ^{[2
]}

机构：

[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA

[2] Univ Alberta, Math, Edmonton, AB, Canada

来源：

JOURNAL OF GEOMETRY | 2007年 / 86卷 / 1-2期

关键词：

Regular polytope; simplex; cube; cross-polytope; product of distances;

D O I：

10.1007/s00022-006-1813-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the maximum of the product of the distances from a point inside an n-dimensional regular simplex, cross-polytope or cube to the vertices is attained at the midpoint of an edge for small n, but is attained at symmetrically placed pairs on an edge for sufficiently high dimensions. We also examine the problem for regular polygons and general triangles in the plane.

引用

页码：31 / 41

页数：11

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