# Definitions and Synonyms of *hyperbolic geometry* | Another word for *hyperbolic geometry* | What is *hyperbolic geometry? *

*Definition 1: (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 - [noun denoting cognition]*

*Samples where hyperbolic geometry or its synonyms are used according to this definition*

*Karl Gauss pioneered hyperbolic geometry*

*(**hyperbolic geometry* is a kind of ...) (mathematics) geometry based on axioms different from Euclid's

*hyperbolic geometry*is a kind of ...) (mathematics) geometry based on axioms different from Euclid's

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