Lattice embeddings of planar point sets

DOI10.1007/s00454-016-9812-4zbMath1353.52012OpenAlexW2517476140MaRDI QIDQ331380

Mohammad Hasan, M. Dambrine

Publication date: 27 October 2016

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

Full work available at URL: https://doi.org/10.1007/s00454-016-9812-4

zbMATH Keywords

lattice embeddingmaximal orderring of integers\(n\)-clusterHeronian triangleimaginary quadratic extension

Mathematics Subject Classification ID

Quadratic extensions (11R11) Miscellaneous applications of number theory (11Z05) Erd?s problems and related topics of discrete geometry (52C10) Algebraic numbers; rings of algebraic integers (11R04) Lattices and convex bodies in (2) dimensions (aspects of discrete geometry) (52C05)

Related Items (1)

On the number of points with pairwise integral distances on a circle

Cites Work

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• On a question of Erdős and Ulam
• There are integral heptagons, no three points on a line, no four on a circle
• On angles whose squared trigonometric functions are rational
• On the `gap' in a theorem of Heegner
• Heronian Triangles Are Lattice Triangles
• Research Problems in Discrete Geometry
• Constructing $7$-clusters
• Triangles with Vertices on Lattice Points
• Heronian Tetrahedra Are Lattice Tetrahedra
• Exponents of the class groups of complex quadratic fields
• Unsolved problems in number theory

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