Abstract
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.
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Farrahi, B. A characterization of isometries of rational Euclidean spaces. J Geom 12, 65–68 (1979). https://doi.org/10.1007/BF01920233
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DOI: https://doi.org/10.1007/BF01920233