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# non-Euclidean geometry

Any system of geometry not based on the set of axioms of Euclidean geometry, which is based on the three-dimensional space of common experience.

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• non-Euclidean geometry — geometry based upon one or more postulates that differ from those of Euclid, esp. from the postulate that only one line may be drawn through a given point parallel to a given line. [1870 75; NON + EUCLIDEAN] * * * Any theory of the nature of… …   Universalium

• Non-Euclidean geometry — Behavior of lines with a common perpendicular in each of the three types of geometry Non Euclidean geometry is the term used to refer to two specific geometries which are, loosely speaking, obtained by negating the Euclidean parallel postulate,… …   Wikipedia

• non-Euclidean geometry — noun (mathematics) geometry based on axioms different from Euclid s non Euclidean geometries discard or replace one or more of the Euclidean axioms • Topics: ↑mathematics, ↑math, ↑maths • Hypernyms: ↑geometry …   Useful english dictionary

• non-Euclidean geometry — See geometry …   Philosophy dictionary

• Models of non-Euclidean geometry — are mathematical models of geometries in which are non Euclidean in the sense that it is not the case that exactly one line can be drawn parallel to a given line l through a point that is not on l. In hyperbolic geometric models, by contrast,… …   Wikipedia

• Euclidean geometry — geometry based upon the postulates of Euclid, esp. the postulate that only one line may be drawn through a given point parallel to a given line. [1860 65] * * * Study of points, lines, angles, surfaces, and solids based on Euclid s axioms. Its… …   Universalium

• non-Euclidean — non Eu•clid•e•an [[t]ˌnɒn yuˈklɪd i ən[/t]] adj. cvb math. differing from the postulates of Euclid or based upon postulates other than those of Euclid: non Euclidean geometry[/ex] • Etymology: 1870–75 …   From formal English to slang

• Euclidean geometry — A Greek mathematician performing a geometric construction with a compass, from The School of Athens by Raphael. Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his… …   Wikipedia

• Non-Euclidean crystallographic group — In mathematics, a non Euclidean crystallographic group, NEC group or N.E.C. group is a discrete group of isometries of the hyperbolic plane. These symmetry groups correspond to the wallpaper groups in euclidean geometry. A NEC group which… …   Wikipedia

• non-euclidean — adjective Usage: often capitalized E Date: 1872 not assuming or in accordance with all the postulates of Euclid s Elements < non euclidean geometry > …   New Collegiate Dictionary