Discrete & Computational Geometry

, Volume 35, Issue 4, pp 537–549 | Cite as

Distinct Distances in Homogeneous Sets in Euclidean Space

  • Jozsef Solymosi
  • Csaba D. Toth


It is shown that every homogeneous set of n points in d-dimensional Euclidean space determines at least \(\Omega(n^{2d/(d^2+1)} / \log^{c(d)} n)\) distinct distances for a constant c(d) > 0. In three-space the above general bound is slightly improved and it is shown that every homogeneous set of n points determines at least \(\Omega(n^{0.6091})\) distinct distances.


Computational Mathematic Euclidean Space Distinct Distance 
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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Department of Mathematics, University of British Columbia, Vancouver, British Columbia, V6T 1Z2Canada
  2. 2.Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139USA

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