On a Heilbronn-type problem

Hansheng Diao, Leng Gangsong, Si Lin

Research output: Contribution to journalArticle


Let F be a convex figure with area | F | and let G (n, F) denote the smallest number such that from any n points of F we can get G (n, F) triangles with areas less than or equal to | F | / 4. In this article, to generalize some results of Soifer, we will prove that for any triangle T, G (5, T) = 3; for any parallelogram P, G (5, P) = 2; for any convex figure F, if S (F) = 6, then G (6, F) = 4.

Original languageEnglish (US)
Pages (from-to)3960-3981
Number of pages22
JournalDiscrete Mathematics
Issue number17
StatePublished - Sep 6 2008

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


  • Area
  • Convex figure
  • Heilbronn's problem
  • Parallelogram
  • Soifer's problem
  • Triangle

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  • Cite this

    Diao, H., Gangsong, L., & Lin, S. (2008). On a Heilbronn-type problem. Discrete Mathematics, 308(17), 3960-3981. https://doi.org/10.1016/j.disc.2007.07.101