摘要
运用数学软件几何画板(TheGeometer'sSketchpad)研究以下的Heilbronn型问题:平面上有n个不同的点,它们之间的最大距离和最小距离的比记作出rn、rn的下确界设为Rn,试求Rn或给出Rn的上下界估计.在文[12]的基础上,笔者运用数学软件几何画板和Mathematica4求得了R10,R11和R12的界,即2.32063…≤R10≤2.79377…以及2.48271…≤R11≤2.90737…,2.6384…≤R12≤2.99941….
A set of n points in the plane determines a total of distances (some of them may be the same ). Let rn be the ratio of the maximum distance to the minimum distance, and Rn be the greatest lower bound for rn . In this paper we get the following results by using mathematical software The Geometer's Sketchpad and Mathemaica 4 : \$2.32063...≤R\-\{10\}≤2.79377.... 2.48271...≤R\-\{11\}≤2.90737.... 2.6384...≤R\-\{12\}≤2.99941....\$
出处
《杭州师范学院学报（自然科学版）》
CAS
2004年第2期81-84,共4页
Journal of Hangzhou Teachers College(Natural Science)
