• In geometry, the BeckmanQuarles theorem states that if a transformation of the Euclidean plane or a higher-dimensional Euclidean space preserves unit...
    22 KB (2,473 words) - 22:29, 20 March 2025
  • Thumbnail for Unit distance graph
    two vertices that must be that distance apart. According to the BeckmanQuarles theorem, the only plane transformations that preserve all unit distance...
    33 KB (4,029 words) - 21:16, 2 July 2025
  • Thumbnail for Donald A. Quarles
    in Antarctica. Biography portal BeckmanQuarles theorem, discovered by and named after Quarles's son, Donald A. Quarles Jr. United States Air Force senior...
    11 KB (939 words) - 02:41, 1 April 2025
  • Thumbnail for Isometry
    linear bijection preserving magnitude. See also Quadratic spaces. BeckmanQuarles theorem Conformal map – Mathematical function that preserves angles The...
    18 KB (2,425 words) - 22:57, 23 June 2025
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    Euclidean distance (category Pythagorean theorem)
    distances come from points in a Euclidean space. According to the BeckmanQuarles theorem, any transformation of the Euclidean plane or of a higher-dimensional...
    26 KB (3,288 words) - 16:41, 30 April 2025
  • geometry) BeckmanQuarles theorem (Euclidean geometry) Beer's theorem (metric geometry) Brahmagupta theorem (Euclidean geometry) Brianchon's theorem (conics)...
    78 KB (6,292 words) - 23:25, 29 June 2025
  • each of these graphs is the two-vertex complete graph K2. By the BeckmanQuarles theorem, the infinite unit distance graph on all points of the Euclidean...
    3 KB (399 words) - 10:41, 13 October 2022
  • Cederberg, "A direct isometry is either a rotation or a translation." BeckmanQuarles theorem, a characterization of isometries as the transformations that preserve...
    23 KB (3,411 words) - 05:58, 24 September 2024
  • both pairs have the same inversive distance. An analogue of the BeckmanQuarles theorem holds true for the inversive distance: if a bijection of the set...
    8 KB (1,083 words) - 18:59, 5 September 2024
  • Thumbnail for Hadwiger–Nelson problem
    extensively. One application of the problem connects it to the BeckmanQuarles theorem, according to which any mapping of the Euclidean plane (or any...
    16 KB (1,860 words) - 12:34, 6 July 2025
  • that it is an isometry, as it does for Euclidean spaces by the BeckmanQuarles theorem. Themistocles M. Rassias posed the following problem: Aleksandrov–Rassias...
    4 KB (404 words) - 06:26, 11 June 2024