caa a22 4500 469075201 CHVBK 20180323132933.0 cr unu---uuuuu 170328e19920101xx s 000 0 eng 10.1007/BF02187820 doi (NATIONALLICENCE)springer-10.1007/BF02187820 The number of different distances determined by a set of points in the Euclidean plane [Elektronische Daten] [Fan Chung, E. Szemerédi, W. Trotter] 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) ≥cn 1/2 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)≥n 4/5/(logn) c . Springer-Verlag New York Inc., 1992 Chung Fan Bell Communications Research, 445 South Street, 07962, Morristown, NJ, USA aut Szemerédi E. Mathematics Institute of the Hungarian Academy of Sciences, Budapest, Hungary aut Trotter W. Bell Communications Research, 445 South Street, 07962, Morristown, NJ, USA aut Discrete & Computational Geometry Springer New York 7/1(1992-01-01), 1-11 0179-5376 7:1<1 1992 7 454 https://doi.org/10.1007/BF02187820 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02187820 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Chung Fan Bell Communications Research, 445 South Street, 07962, Morristown, NJ, USA aut NATIONALLICENCE 700 1- Szemerédi E. Mathematics Institute of the Hungarian Academy of Sciences, Budapest, Hungary aut NATIONALLICENCE 700 1- Trotter W. Bell Communications Research, 445 South Street, 07962, Morristown, NJ, USA aut NATIONALLICENCE 773 0- Discrete & Computational Geometry Springer New York 7/1(1992-01-01), 1-11 0179-5376 7:1<1 1992 7 454 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer