Distinct distances on two lines

Micha Sharir*, Adam Sheffer, József Solymosi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Let P1 and P2 be two finite sets of points in the plane, so that P1 is contained in a line ℓ1, P2 is contained in a line ℓ2, and ℓ1 and ℓ2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs of P1×P2 isΩ(min{|P1|2/3|P2|2/3,|P1|2,|P2|2}). In particular, if |P1|=|P2|=m, then the number of these distinct distances is Ω(m4/3), improving upon the previous bound Ω(m5/4) of Elekes (1999) [3].

Original languageEnglish
Pages (from-to)1732-1736
Number of pages5
JournalJournal of Combinatorial Theory - Series A
Issue number7
StatePublished - Sep 2013


  • Combinatorial geometry
  • Distinct distances
  • Incidences


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