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An elementary proof of the theorem of Beckman and Quarles

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Publication:914156
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zbMath0701.51013MaRDI QIDQ914156

Walter Benz

Publication date: 1987

Published in: Elemente der Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/141394

zbMATH Keywords

Beckman-Quarles theorem


Mathematics Subject Classification ID

Elementary problems in Euclidean geometries (51M04) Euclidean analytic geometry (51N20)


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Maps between buildings that preserve a given Weyl distance., On \(n\)-norm preservers and the Aleksandrov conservative \(n\)-distance problem, The Beckman-Quarles theorem via the triangle inequality, Mappings which preserve regular dodecahedrons, The Beckman-Quarles theorem for mappings from \(\mathbb{R}^2\) of \(\mathbb{F}^2\), where \(\mathbb{F}\) is a subfield of a commutative field extending \(\mathbb{R}\), A characterization of isometries on an open convex set. II, Isometries of Spheres, The Beckman-Quarles theorem in hyperbolic geometry, On diversity and stability of unit bases for the Euclidean metric, A contribution to the Aleksandrov conservative distance problem in two dimensions



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