While the Sylvester–Gallai theorem states that an arrangement of points, not all collinear, must determine an ordinary line, it does not say how many must be determined. Let formula_4 be the minimum number of ordinary lines determined over every set of formula_1 non-collinear points. Melchior's proof showed that formula_69. raised the question of whether formula_4 approaches infinity with formula_1. confirmed that it does by proving that formula_72. conjectured that formula_73, for all values of formula_1, a conjecture that still stands . This is often referred to as the Dirac–Motzkin conjecture; see for example . proved that formula_75.