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- Beckman–Quarles_theorem abstract "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.".
- Beckman–Quarles_theorem wikiPageID "7580572".
- Beckman–Quarles_theorem wikiPageLength "9118".
- Beckman–Quarles_theorem wikiPageOutDegree "36".
- Beckman–Quarles_theorem wikiPageRevisionID "641702220".
- Beckman–Quarles_theorem wikiPageWikiLink Algebraic_number.
- Beckman–Quarles_theorem wikiPageWikiLink Cartesian_coordinate_system.
- Beckman–Quarles_theorem wikiPageWikiLink Category:Euclidean_geometry.
- Beckman–Quarles_theorem wikiPageWikiLink Category:Metric_geometry.
- Beckman–Quarles_theorem wikiPageWikiLink Category:Theorems_in_geometry.
- Beckman–Quarles_theorem wikiPageWikiLink Characteristic_(algebra).
- Beckman–Quarles_theorem wikiPageWikiLink Continuous_function.
- Beckman–Quarles_theorem wikiPageWikiLink Countable_set.
- Beckman–Quarles_theorem wikiPageWikiLink Dense_set.
- Beckman–Quarles_theorem wikiPageWikiLink Euclidean_space.
- Beckman–Quarles_theorem wikiPageWikiLink Field_(mathematics).
- Beckman–Quarles_theorem wikiPageWikiLink Function_(mathematics).
- Beckman–Quarles_theorem wikiPageWikiLink Function_composition.
- Beckman–Quarles_theorem wikiPageWikiLink Geometry.
- Beckman–Quarles_theorem wikiPageWikiLink Graph_automorphism.
- Beckman–Quarles_theorem wikiPageWikiLink Hilbert_space.
- Beckman–Quarles_theorem wikiPageWikiLink Injective_function.
- Beckman–Quarles_theorem wikiPageWikiLink Inversive_distance.
- Beckman–Quarles_theorem wikiPageWikiLink Isometry.
- Beckman–Quarles_theorem wikiPageWikiLink Lorentz_transformation.
- Beckman–Quarles_theorem wikiPageWikiLink Minkowski_space.
- Beckman–Quarles_theorem wikiPageWikiLink Multivalued_function.
- Beckman–Quarles_theorem wikiPageWikiLink Möbius_plane.
- Beckman–Quarles_theorem wikiPageWikiLink Projective_plane.
- Beckman–Quarles_theorem wikiPageWikiLink Quadratic_form.
- Beckman–Quarles_theorem wikiPageWikiLink Rational_number.
- Beckman–Quarles_theorem wikiPageWikiLink Real_line.
- Beckman–Quarles_theorem wikiPageWikiLink Simplex.
- Beckman–Quarles_theorem wikiPageWikiLink Square_root_of_2.
- Beckman–Quarles_theorem wikiPageWikiLink Structural_rigidity.
- Beckman–Quarles_theorem wikiPageWikiLink Two-dimensional_space.
- Beckman–Quarles_theorem wikiPageWikiLink Unit_distance_graph.
- Beckman–Quarles_theorem wikiPageWikiLinkText "Beckman–Quarles theorem".
- Beckman–Quarles_theorem wikiPageUsesTemplate Template:Math.
- Beckman–Quarles_theorem wikiPageUsesTemplate Template:Mvar.
- Beckman–Quarles_theorem wikiPageUsesTemplate Template:Reflist.
- Beckman–Quarles_theorem subject Category:Euclidean_geometry.
- Beckman–Quarles_theorem subject Category:Metric_geometry.
- Beckman–Quarles_theorem subject Category:Theorems_in_geometry.
- Beckman–Quarles_theorem type Redirect.
- Beckman–Quarles_theorem type Theorem.
- Beckman–Quarles_theorem comment "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.".
- Beckman–Quarles_theorem label "Beckman–Quarles theorem".
- Beckman–Quarles_theorem sameAs Q2226606.
- Beckman–Quarles_theorem sameAs Satz_von_Beckman_und_Quarles.
- Beckman–Quarles_theorem sameAs m.0265w3g.
- Beckman–Quarles_theorem sameAs Q2226606.
- Beckman–Quarles_theorem wasDerivedFrom Beckman–Quarles_theorem?oldid=641702220.
- Beckman–Quarles_theorem isPrimaryTopicOf Beckman–Quarles_theorem.