On mappings of ℚd to ℚd that preserve distances 1 and √2 and the Beckman-Quarles Theorem

Joseph Zaks

doi:10.1007/s00022-004-1660-3

On mappings of ℚ^d to ℚ^d that preserve distances 1 and √2 and the Beckman-Quarles Theorem

Joseph Zaks

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Benz proved that every mapping f : ℚ^d → ℚ^d that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping f : ℚ^d → ℚ^d that preserves the distances 1 and √2 is an isometry, provided d ≥ 5.

Original language	English
Pages (from-to)	195-203
Number of pages	9
Journal	Journal of Geometry
Volume	82
Issue number	1-2
DOIs	https://doi.org/10.1007/s00022-004-1660-3
State	Published - Aug 2005

Keywords

Beckman-Quarles Theorem
Distance preserving mappings
Isometry

ASJC Scopus subject areas

Geometry and Topology

Access to Document

10.1007/s00022-004-1660-3

Cite this

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abstract = "Benz proved that every mapping f : ℚd → ℚd that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping f : ℚd → ℚd that preserves the distances 1 and √2 is an isometry, provided d ≥ 5.",

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