# Definitions and Synonyms of *non-euclidean geometry* | Another word for *non-euclidean geometry* | What is *non-euclidean geometry? *

*Definition 1: (mathematics) geometry based on axioms different from Euclid's - [noun denoting cognition]*

*Samples where non-euclidean geometry or its synonyms are used according to this definition*

*non-Euclidean geometries discard or replace one or more of the Euclidean axioms*

*(**non-euclidean geometry* is a kind of ...) the pure mathematics of points and lines and curves and surfaces

*non-euclidean geometry*is a kind of ...) the pure mathematics of points and lines and curves and surfaces

*(... is a kind of **non-euclidean 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

*non-euclidean 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

### (... is a kind of

*"Karl Gauss pioneered hyperbolic geometry"*### (... is a kind of *non-euclidean 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"*