Beckman–Quarles Theorem

(Theory)

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Theory
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What is Beckman–Quarles theorem?

In geometry, the Beckman–Quarles theorem, named after F. S. Beckman and D. A. Quarles, Jr., states that if a transformation of the Euclidean plane or a higher-dimensional Euclidean space preserves unit distances, then it preserves all distances. Equivalently, every automorphism of the unit distance graph of the plane must be an isometry of the plane.Beckman and Quarles published this result in 1953; it was later rediscovered by other authors.

Technology Types

euclidean geometrymathematical theoremmetric geometrypropositionstatementtheoremtheorems in geometrytheory

Synonyms

Beckman-Quarles theorem

Translations

Satz von Beckman und Quarles (de)

Tech Info


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