Journal of Geometry

, Volume 82, Issue 1, pp 195–203

On mappings of \(\mathbb{Q}^d \) to \(\mathbb{Q}^d \) that preserve distances 1 and \(\sqrt 2 \) and the Beckman-Quarles Theorem

Authors

    • Department of MathematicsUniversity of Haifa
Original Paper

DOI: 10.1007/s00022-004-1660-3

Cite this article as:
Zaks, J. J. geom. (2005) 82: 195. doi:10.1007/s00022-004-1660-3

Abstract.

Benz proved that every mapping \(f:\mathbb{Q}^d \to \mathbb{Q}^d \) that preserves the distances 1 and 2 is an isometry, provided d ≥ 5. We prove that every mapping \(f:\mathbb{Q}^d \to \mathbb{Q}^d \) that preserves the distances 1 and \(\sqrt 2 \) is an isometry, provided d ≥ 5.

Mathematics Subject Classification (2000).

51M0546B04

Key words.

Distance preserving mappingsisometryBeckman-Quarles Theorem

Copyright information

© Birkhäuser Verlag, Basel 2005