A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. ...A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. By using the mathematical software Mathematica,the author gets the following results in this paper.R 12 ≤2.99496..., R 13 ≤cscπ10.展开更多
The problem of “strung balls”, which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in R^n(n ≥ 3). Higher dimensional versions of the results given on ...The problem of “strung balls”, which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in R^n(n ≥ 3). Higher dimensional versions of the results given on a plane are obtained.展开更多
文摘A set of n points in the plane determines a total C 2 n distances (some of them may be the same).Let r n be the ratio of the maximum distance to the minimum distance, and R n be the greatest lower bound for r n. By using the mathematical software Mathematica,the author gets the following results in this paper.R 12 ≤2.99496..., R 13 ≤cscπ10.
基金This research is supported by NSFC(China) Grant, TRAPOYT and China MOE Research Grant.
文摘The problem of “strung balls”, which considers how many circles in a given family of circles can be intersected by a line in a plane, is discussed in R^n(n ≥ 3). Higher dimensional versions of the results given on a plane are obtained.
