Szemerédi–Trotter theorem
= Szemerédi–Trotter theorem
{c}
{wiki}
For $m$ lines and $n$ points in the real plane, the number of point-line incidences is
$$
O(m+n+m^{2/3}n^{2/3}).
$$
Connecting consecutive incidence points on each line and applying the <Crossing lemma> proves the bound.