The number of different distances determined by a set of points in the Euclidean plane

DOI10.1007/BF02187820zbMath0755.52005OpenAlexW2145670890WikidataQ102185077 ScholiaQ102185077MaRDI QIDQ1186077

William T. jun. Trotter, Fan R. K. Chung, Endre Szemerédi

Publication date: 28 June 1992

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131176

zbMATH Keywords

Euclidean planenumber of different distancesset of points

Mathematics Subject Classification ID

Erd?s problems and related topics of discrete geometry (52C10)

Related Items (21)

On the geometric structures with \(n\) points and \(k\) distances ⋮ On Erd\H{o}s Chains in the Plane ⋮ On distinct distances between a variety and a point set ⋮ On the Erdös-diameter of sets ⋮ The exact fitting problem in higher dimensions ⋮ Maximum planar sets that determine \(k\) distances ⋮ On bipartite distinct distances in the plane ⋮ Pinned algebraic distances determined by Cartesian products in 𝔽_{𝕡}² ⋮ Finite point configurations in the plane, rigidity and Erdős problems ⋮ On distinct sums and distinct distances. ⋮ Smoothness of projections, Bernoulli convolutions, and the dimension of exceptions ⋮ On the Erdős distinct distances problem in the plane ⋮ Near optimal bounds for the Erdős distinct distances problem in high dimensions ⋮ The grid revisited ⋮ The second and the third smallest distances on the sphere ⋮ A note on the number of different inner products generated by a finite set of vectors ⋮ Incidences in Three Dimensions and Distinct Distances in the Plane ⋮ Cardinalities of \(k\)-distance sets in Minkowski spaces ⋮ On distinct distances among points in general position and other related problems ⋮ Distinct distances in the complex plane ⋮ Distinct distances determined by subsets of a point set in space

Cites Work

• Unnamed Item
• The number of different distances determined by n points in the plane
• A combinatorial distinction between the Euclidean and projective planes
• Extremal problems in discrete geometry
• On the Different Distances Determined by n Points
• On Sets of Distances of n Points

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