In geometry, the Beckman–Quarles 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
two vertices that must be that distance apart. According to the Beckman–Quarles theorem, the only plane transformations that preserve all unit distance...
33 KB (4,029 words) - 21:16, 2 July 2025
in Antarctica. Biography portal Beckman–Quarles 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
linear bijection preserving magnitude. See also Quadratic spaces. Beckman–Quarles theorem Conformal map – Mathematical function that preserves angles The...
18 KB (2,425 words) - 22:57, 23 June 2025
Euclidean distance (category Pythagorean theorem)
distances come from points in a Euclidean space. According to the Beckman–Quarles theorem, any transformation of the Euclidean plane or of a higher-dimensional...
26 KB (3,288 words) - 16:41, 30 April 2025
geometry) Beckman–Quarles 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 Beckman–Quarles 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." Beckman–Quarles 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 Beckman–Quarles theorem holds true for the inversive distance: if a bijection of the set...
8 KB (1,083 words) - 18:59, 5 September 2024
extensively. One application of the problem connects it to the Beckman–Quarles 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 Beckman–Quarles theorem. Themistocles M. Rassias posed the following problem: Aleksandrov–Rassias...
4 KB (404 words) - 06:26, 11 June 2024