non-Euclidean geometry

Definitions of non-Euclidean geometry

1. noun

   (mathematics) geometry based on axioms different from Euclid's
   “non-Euclidean geometries discard or replace one or more of the Euclidean axioms”

   types:

   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

   Riemannian geometry, elliptic geometry

   (mathematics) a non-Euclidean geometry that regards space as like a sphere and a line as like a great circle

   type of:

   geometry

   the pure mathematics of points and lines and curves and surfaces