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Discrete & Computational Geometry

, Volume 9, Issue 2, pp 187–202 | Cite as

There exist 6n/13 ordinary points

  • J. Csima
  • E. T. Sawyer
Article

Abstract

In 1958 L. M. Kelly and W. O. J. Moser showed that apart from a pencil, any configuration ofn lines in the real projective plane has at least 3n/7 ordinary or simple points of intersection, with equality in the Kelly-Moser example (a complete quadrilateral with its three diagonal lines). In 1981 S. Hansen claimed to have improved this ton/2 (apart from pencils, the Kelly-Moser example and the McKee example). In this paper we show that one of the main theorems used by Hansen is false, thus leavingn/2 open, and we improve the 3n/7 estimate to 6n/13 (apart from pencils and the Kelly-Moser example), with equality in the McKee example. Our result applies also to arrangements of pseudolines.

Keywords

Additional Line Discrete Comput Geom Euclidean Plane Open Segment Ordinary Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1993

Authors and Affiliations

  • J. Csima
    • 1
  • E. T. Sawyer
    • 1
  1. 1.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada

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