Euclidean And Non Euclidean. The term non-Euclidean sounds very fancy, but it really just means any type of geometry that's not Euclidean—i.e., that doesn't exist in a flat world There are several applications of non-Euclidean geometry; one is that it helps describe the picture of the universe painted by Einstein's Theory of Relativity

The first thread started with the search to understand the movement of stars and planets in the apparently hemispherical sky Non-Euclidean geometry is a branch of geometry that explores geometrical systems that differ from classical Euclidean geometry, which is based on the postulates of the ancient Greek mathematician Euclid

David Hilbert (1862-1943), in his book Gundlagen der Geometrie (Foundations of Geometry), published in 1899 a list of axioms for Euclidean geometry, which are axioms for a synthetic geometry. The non-Euclidean geometries developed along two different historical threads In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry.As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises by either replacing the parallel postulate with an alternative, or relaxing the metric requirement.

. Consider directed segments (also called "arrows") between points of the plane. While many of Euclid's findings had been previously stated by earlier Greek mathematicians, Euclid

. Euclidean and Non-Euclidean Geometry Euclidean Geometry Euclidean Geometry is the study of geometry based on definitions, undefined terms (point, line and plane) and the assumptions of the mathematician Euclid (330 B.C.) Euclid's text Elements was the first systematic discussion of geometry In Non-Euclidean geometry, these traditional postulates are altered or replaced, leading to different mathematical consequences.