Journal of Geometry

, Volume 12, Issue 1, pp 65–68 | Cite as

A characterization of isometries of rational Euclidean spaces

  • Bijan Farrahi


We show that an injection of the rational Euclidean n-space, n≥5, which preserves the distances e, 1/2e, e an arbitrary non-zero rational number, is necessarily an isometry. Further, we show that the above characterization fails in case n=3 or 4.


Euclidean Space Rational Number 
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Copyright information

© Birkhäuser Verlag 1979

Authors and Affiliations

  • Bijan Farrahi
    • 1
  1. 1.Arya-Mehr UniversityTehranIran

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