The Beckman-Quarles Theorem states that every unit-preserving mapping of Rd into Rd is an isometry. A. Tyszka proved that every unit preserving mapping of Q8 into Q8 is an isometry. We extend the last result by showing that every unit-preserving mapping from Q d into Qd is an isometry for all even d of the form d = 4k(k + 1), k ≥ 1, as well as for all odd d of the form 2k2 - 1 which are complete squares, k ≥ 2.
ASJC Scopus subject areas
- Geometry and Topology