# non-Euclidean geometry

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Related to non-Euclidean geometry: hyperbolic geometry

## non-Euclidean geometry

*n*

(Mathematics) the branch of modern geometry in which certain axioms of Euclidean geometry are restated. It introduces fundamental changes into the concept of space

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Noun | 1. | non-Euclidean geometry - (mathematics) geometry based on axioms different from Euclid's; "non-Euclidean geometries discard or replace one or more of the Euclidean axioms"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement geometry - the pure mathematics of points and lines and curves and surfaces hyperbolic geometry - (mathematics) a non-Euclidean geometry in which the parallel axiom is replaced by the assumption that through any point in a plane there are two or more lines that do not intersect a given line in the plane; "Karl Gauss pioneered hyperbolic geometry" elliptic geometry, Riemannian geometry - (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle; "Bernhard Riemann pioneered elliptic geometry" |

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