Discrete & Computational Geometry
, Volume 9, Issue 2, pp 187202
First online:
There exist 6n/13 ordinary points
 J. CsimaAffiliated withDepartment of Mathematics and Statistics, McMaster University
 , E. T. SawyerAffiliated withDepartment of Mathematics and Statistics, McMaster University
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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 KellyMoser example (a complete quadrilateral with its three diagonal lines). In 1981 S. Hansen claimed to have improved this ton/2 (apart from pencils, the KellyMoser 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 KellyMoser example), with equality in the McKee example. Our result applies also to arrangements of pseudolines.
 Title
 There exist 6n/13 ordinary points
 Journal

Discrete & Computational Geometry
Volume 9, Issue 2 , pp 187202
 Cover Date
 199302
 DOI
 10.1007/BF02189318
 Print ISSN
 01795376
 Online ISSN
 14320444
 Publisher
 Springer New York
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 Authors

 J. Csima ^{(1)}
 E. T. Sawyer ^{(1)}
 Author Affiliations

 1. Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada