Erdős’s Unit Distance Problem

Endre Szemerédi ()
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Endre Szemerédi: Renyi Alfred Mathematical Institute of the Hungarian Academy of Sciences

A chapter in Open Problems in Mathematics, 2016, pp 459-477 from Springer

Abstract: Abstract We survey some problems and results around one of Paul Erdős’s favorite questions, first published 70 years ago: What is the maximum number of times that the unit distance can occur among n points in the plane? This simple and beautiful question has generated a lot of important research in discrete geometry, in extremal combinatorics, in additive number theory, in Fourier analysis, in algebra, and in other fields, but we still do not seem to be close to a satisfactory answer.

Keywords: Unit Circle; Unit Distance; Geometric Graph; Combinatorial Geometry; Diameter Graph (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-32162-2_15

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DOI: 10.1007/978-3-319-32162-2_15

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