Beck's Theorem (Geometry)

In discrete geometry, Beck's theorem refers to any of several related results proved by Jozsef Beck in a 1983 paper published in Combinatorica, establishing lower bounds on the number of lines determined by a finite set of points in the plane, where a line counts as determined if it passes through at least two of the points. The theorem's original proof used a constant later shown to be far from optimal, and the true best possible constants remain unknown. A related and stronger result, the Erdos-Beck theorem, implies Beck's theorem though it was not stated in Beck's own paper.