Journal of Geometry

, Volume 64, Issue 1, pp 89–94

Triangles in arrangements of lines

  • Haiwei Gu
Article

DOI: 10.1007/BF01229215

Cite this article as:
Gu, H. J Geom (1999) 64: 89. doi:10.1007/BF01229215
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Abstract

Givenn lines in the real projective plane, Grünbaum conjectures that, for n≥16, the numberp3 of triangular regions determined by the lines is at most 1/3n(n−1). We show that ifn≥7 thenp3 ≤8/21n(n−1)+2/7, we also point out that if no vertex is a point of intersection of exactly three of the lines, thenp3≤1/3n(n−1).

Copyright information

© BirkhÄuser Verlag 1999

Authors and Affiliations

  • Haiwei Gu
    • 1
  1. 1.Department of MathematicsQufu Normal UniversityQufu, ShandongPeople's Republic of China