The number of different distances determined by a set of points in the Euclidean plane
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- Chung, F.R.K., Szemerédi, E. & Trotter, W.T. Discrete Comput Geom (1992) 7: 1. doi:10.1007/BF02187820
In 1946 P. Erdös posed the problem of determining the minimum numberd(n) of different distances determined by a set ofn points in the Euclidean plane. Erdös provedd(n) ≥cn1/2 and conjectured thatd(n)≥cn/ √logn. If true, this inequality is best possible as is shown by the lattice points in the plane. We showd(n)≥n4/5/(logn)c.