On a Triangle with the Maximum Area in a Planar Point Set

  • Kiyoshi Hosono
  • Ferran Hurtado
  • Masatsugu Urabe
  • Jorge Urrutia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3330)

Abstract

For a planar point set P in general position, we study the ratio between the maximum area of an empty triangle with vertices in P and the area of the convex hull of P.

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References

  1. 1.
    Fleischer, R., Mehlhorn, V., Rote, G., Welzl, E., Yap, C.: Simultaneous inner and outer approximation of shapes. Algorithmica 8, 365–389 (1992)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Harborth, H.: Konvexe Funfecke in Ebenen Punktmengen. Elem. Math. 33, 116–118 (1978)MATHMathSciNetGoogle Scholar
  3. 3.
    Komlós, J., Pintz, J., Szeméredi, E.: On Heilbronn’s triangle problem. J. London Mathematical Society 24(2), 385–396 (1981)MATHCrossRefGoogle Scholar
  4. 4.
    Komlós, J., Pintz, J., Szeméredi, E.: A lower bound for Heilbronn’s problem. J. London Mathematical Society 25(2), 13–24 (1982)MATHCrossRefGoogle Scholar
  5. 5.
    Sás, E.: On a certain extremum-property of the ellipse (in Hungarian, English summary). Mat. Fiz. Lapok 48, 533–542 (1941)MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Kiyoshi Hosono
    • 1
  • Ferran Hurtado
    • 2
  • Masatsugu Urabe
    • 1
  • Jorge Urrutia
    • 3
  1. 1.Department of MathematicsTokai UniversityShizuokaJapan
  2. 2.Departament de Matemàtica Aplicada IIUniversitat Politècnica de CatalunyaBarcelonaEspaña
  3. 3.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMéxico D.F.México

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