An improved bound for the affine sylvester problem

Abstract

In 2006, Lenchner and Brönnimann showed that in the affine plane, given n lines, not all parallel and not all passing through a common point, there had to be at least n/6 ordinary points. The present paper improves on this result to show that there must be at least 2n-3/7 ordinary points, except for a single arrangement of 6 lines with one ordinary point.