Non-Euclidean geometry

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On a sphere, the sum of the angles of a triangle is not equal to 180°. The surface of a sphere is not a Euclidean space, but locally the laws of the Euclidean geometry are good approximations. In a small triangle on the face of the earth, the sum of the angles is very nearly 180°.

In mathematics, non-Euclidean geometry is a small set of geometries based on axioms closely related to those specifying Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geometry arises when either the metric requirement is relaxed, or the parallel postulate is set aside. In the latter case one obtains hyperbolic geometry and elliptic geometry, the traditional non-Euclidean geometries. When the metric requirement is relaxed, then there are affine planes associated with the planar algebras which give rise to kinematic geometries that have also been called non-Euclidean geometry.

• See also: Wikipedia

• Related: Hyperbolic space, Projective geometry

MacTutor Archive article on non-Euclidean geometry MacTutor Archive article on non-Euclidean geometry www-groups.dcs.st-and.ac.uk/.../Non-Euclidean_geometry.html - Web

Non-Euclidean geometries Non-Euclidean geometries www.encyclopediaofmath.org/index.php/Non-Euclidean_geometries - Web

Synthetic Spacetime Synthetic Spacetime www.webcitation.org/5koAax8ct - Web

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