Distinct distances in the plane

被引：47
|
作者：
Solymosi, J [1 ]
Tóth, CD [1 ]
机构：
[1] Swiss Fed Inst Technol, Inst Theoret Informat, CH-8092 Zurich, Switzerland
来源：
DISCRETE & COMPUTATIONAL GEOMETRY | 2001年 / 25卷 / 04期
关键词：
D O I：
10.1007/s00454-001-0009-z
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
It is shown that every set of n points in the plane has an element from which there are at least cn(6/7) other elements at distinct distances, where c > 0 is a constant. This improves earlier results of Erdos, Moser, Beck, Chung, Szemeredi, Trotter, and Szekely.
引用
收藏
页码：629 / 634
页数：6
相关论文
共 50 条
  • [1] Distinct Distances in the Plane
    J. Solymosi
    Cs. D. Tóth
    Discrete & Computational Geometry, 2001, 25 : 629 - 634
  • [2] On Bipartite Distinct Distances in the Plane
    Mathialagan, Surya
    ELECTRONIC JOURNAL OF COMBINATORICS, 2021, 28 (04):
  • [3] DISTINCT DISTANCES IN THE COMPLEX PLANE
    Sheffer, Adam
    Zahl, Joshua
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 374 (09) : 6691 - 6725
  • [4] Three distinct distances in the plane
    Harborth, H
    Piepmeyer, L
    GEOMETRIAE DEDICATA, 1996, 61 (03) : 315 - 327
  • [5] On the Erdos distinct distances problem in the plane
    Guth, Larry
    Katz, Nets Hawk
    ANNALS OF MATHEMATICS, 2015, 181 (01) : 155 - 190
  • [6] Distinct Distances on Algebraic Curves in the Plane
    Pach, Janos
    De Zeeuw, Frank
    COMBINATORICS PROBABILITY & COMPUTING, 2017, 26 (01): : 99 - 117
  • [7] Incidences in Three Dimensions and Distinct Distances in the Plane
    Elekes, Gyoergy
    Sharir, Micha
    COMBINATORICS PROBABILITY & COMPUTING, 2011, 20 (04): : 571 - 608
  • [8] A NOTE ON THE DISTINCT DISTANCES PROBLEM IN THE HYPERBOLIC PLANE
    Lu, Zhipeng
    Meng, Xianchang
    PACIFIC JOURNAL OF MATHEMATICS, 2023, 327 (01) : 129 - 137
  • [9] Incidences in Three Dimensions and Distinct Distances in the Plane [Extended Abstract]
    Elekes, Gyoergy
    Sharir, Micha
    PROCEEDINGS OF THE TWENTY-SIXTH ANNUAL SYMPOSIUM ON COMPUTATIONAL GEOMETRY (SCG'10), 2010, : 413 - 422
  • [10] N-POINTS IN THE PLANE, EPISILON-N DISTINCT DISTANCES
    COPPERSMITH, D
    ERDOS, P
    AMERICAN MATHEMATICAL MONTHLY, 1982, 89 (08): : 604 - 605
12345