Distances from the Vertices of a Regular Simplex

被引：1

作者：

Hajja, Mowaffaq ^{[1
]}

Hayajneh, Mostafa ^{[2
]}

Bach Nguyen ^{[3
]}

Shaqaqha, Shadi ^{[2
]}

机构：

[1] Philadelphia Univ, POB 1, Amman 19392, Jordan

[2] Yarmouk Univ, Irbid, Jordan

[3] Louisiana State Univ, Baton Rouge, LA 70803 USA

来源：

RESULTS IN MATHEMATICS | 2017年 / 72卷 / 1-2期

关键词：

Algebraic dependence; Cayley-Menger determinant; Germ; Height of an ideal; Integral domain; Krull dimension; Pompeiu's theorem; Principal ideal; Real analytic function; Regular simplex; Soddy circles; Transcendence degree;

D O I：

10.1007/s00025-017-0689-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

If S is a given regular d-simplex of edge length a in the d-dimensional Euclidean space epsilon, then the distances t(1), ... , t(d+1) of an arbitrary point in epsilon to the vertices of S are related by the elegant relation (d + 1) (a(4) + t(1)(4) + ... + t(d+1)(4)) = (a(2) + t(1)(2) + ... + t(2)(d+1)) The purpose of this paper is to prove that this is essentially the only relation that exists among t(1),..., t(d+1). The proof uses tools from analysis, algebra, and geometry.

引用

页码：633 / 648

页数：16

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