---

Csima and Sawyer prove that $f(n)\ge 6n/13$ for every $n\ge 8$: $n$ points in the real plane, not all on one line, determine at least $6n/13$ ordinary lines, lines through exactly two of the points. The paper is written in the dual language of ordinary points in an arrangement of lines. This improves the constant $3/7$ of Kelly and Moser for Problem 210; the exception $n=7$ is the configuration where $3n/7$ is attained.

Covers. A linear lower bound with the constant $6/13$ for every $n\ge 8$. It does not reach the sharp constant $1/2$, which Green and Tao later prove for large $n$.

The result is refereed: J. Csima and E. T. Sawyer, There exist $6n/13$ ordinary points, Discrete Comput. Geom. 9 (1993), no. 2, 187-202. The site's page credits this paper with the bound $6n/13$ for $n\ge 8$; its label, proved, rests on the later result of Green and Tao, so the acceptance here stands on the refereed publication. The paper is not held.