摘要
本文给出Ｈｅｉｌｂｒｏｎｎ型问题的结果．设Ｓ是Ｒ~３中六点组成的集合．直径为Ｄ．若ｄ表示Ｓ中任意两点距离的最小值，则Ｄ≥２ｄ．等号当且仅当Ｓ是由正八面体的六个顶点或多面体面△×△１的六个顶点组成时才成立（△１，△２分别表示一维、二维正则单形，且其棱长相等）．
In this paper, the following result of a Heilbroon's problem is proved. Let S be a set consists of six points in R^3, its diameter being D. By d denote the minimum distance between any two points in S, then D≥ 2d. The equility holds if and only if S consists of the six venices of an octahedron or the six venices of the polygron △2 x △1, where by △1, △2 we denote the regular 1- and 2- simplex, with the same length of edges.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
2000年第5期797-806,共10页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金!(19771039)
广东省科学基金资助项目(960179)
