Beckman-Quarles theorem

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In geometry, the Beckman-Quarles theorem states that for a Euclidean space E of dimension d at least 2, any mapping f from E to itself that preserves the property of being at a unit distance apart must be an isometry.

[edit] References

  • F. S. Beckman and D. A. Quarles, Jr., On isometries of Euclidean space, Proc. Amer. Math. Soc., 4 (1953) 810-815.
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