Given an arrangement of points, a line containing just two of them is called an ordinary line. Dirac conjectured that every sufficiently set of n noncollinear points contains at least n/2 ordinary lines. Csima and Sawyer proved that for an n>=3 arrangement of points, at least 6n/13 lines must be ordinary. Only two exceptions are known for Dirac's conjecture: the Kelly-Moser configuration (7 points, 3 ordinary lines; cf. Fano plane) and McKee's configuration (13 points, 6 ordinary lines).

collinear | general position | incident | near-pencil | ordinary point | special point | Sylvester graph