@article{Szemerdi1983ExtremalPI,
title={Extremal problems in discrete geometry},
author={Endre Szemer{\'e}di and William T. Trotter},
journal={Combinatorica},
year={1983},
volume={3},
pages={381-392}
}

In this paper, we establish several theorems involving configurations of points and lines in the Euclidean plane. Our results answer questions and settle conjectures of P. Erd6s, G. Purdy, and G. Dirac. The principal result is that there exists an absolute constant cl so that wlaen V'n<=t~_[T], the number of incidences between n points and t lines is less than c~n~/3t ""/3. Using this restllt, it follows immediately that there exists an absolute constant c2 so that if k -< ]/~, then the number… CONTINUE READING