Non-Euclidean geometry

Summary

A non-Euclidean geometry is a geometry that keeps the other basic assumptions of Euclidean geometry but drops the parallel postulate. The two classical ones are hyperbolic geometry, where a line has many parallels through an outside point, and elliptic geometry, where it has none. Their discovery showed that the parallel postulate cannot be proved from the other axioms. They also became models for curved space in differential geometry and physics.