# There exist 6*n*/13 ordinary points

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DOI: 10.1007/BF02189318

- Cite this article as:
- Csima, J. & Sawyer, E.T. Discrete Comput Geom (1993) 9: 187. doi:10.1007/BF02189318

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## Abstract

In 1958 L. M. Kelly and W. O. J. Moser showed that apart from a pencil, any configuration of*n* lines in the real projective plane has at least 3*n*/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 to*n*/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 leaving*n*/2 open, and we improve the 3*n*/7 estimate to 6*n*/13 (apart from pencils and the Kelly-Moser example), with equality in the McKee example. Our result applies also to arrangements of pseudolines.