Name
Title | ||
|---|---|---|
On the relative distances of nine or ten points in the boundary of a plane convex body |
Abstract | ||
|---|---|---|
Let C be a plane convex body. The relative distance of points a,b@?C is the ratio of the Euclidean distance of a and b to the half of the Euclidean distance of a"1,b"1@?C such that a"1b"1 is a longest chord of C parallel to the line-segment ab. It was conjectured that there exists no plane convex body whose boundary contains ten points at pairwise relative distances greater than 23. In this paper we disprove this conjecture. And we construct a nonagon whose relative distances of arbitrary two consecutive vertices are equal to 3-1. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1016/j.dam.2011.10.006 | Discrete Applied Mathematics |
Keywords | Field | DocType |
c parallel,relative distance,euclidean distance,consecutive vertex,pairwise relative distance,longest chord,plane convex body,line-segment ab | Discrete mathematics,Combinatorics,Vertex (geometry),Distance from a point to a plane,Convex body,Convex combination,Euclidean distance,Convex hull,Convex set,Convex curve,Mathematics | Journal |
Volume | Issue | ISSN |
160 | 3 | 0166-218X |
Citations | PageRank | References |
1 | 0.48 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Zhanjun Su | 1 | 1 | 1.83 |
| Sipeng Li | 2 | 1 | 0.82 |
| Jian Shen | 3 | 92 | 14.67 |
| Liping Yuan | 4 | 21 | 5.07 |