The Beckman-Quarles theorem via the triangle inequality

DOI10.1515/ADVGEOM-2020-0024zbMath1477.51013OpenAlexW3173362264MaRDI QIDQ2238258

Vilmos Totik

Publication date: 1 November 2021

Published in: Advances in Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/advgeom-2020-0024

zbMATH Keywords

triangle inequalityBeckman-Quarles theoremisometries in \(\mathbb{R}^n \)

Mathematics Subject Classification ID

Elementary problems in Euclidean geometries (51M04)

Cites Work

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• Another proof of the Beckman-Quarles theorem
• An elementary proof of the theorem of Beckman and Quarles
• The Beckman-Quarles theorem in Minkowski space for a spacelike square- distance
• Functions That Preserve Unit Distance
• A Discrete Form of the Beckman-Quarles Theorem
• Congruence-Preserving Mappings
• Characterizing Motions by Unit Distance Invariance
• On Isometries of Euclidean Spaces

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