Elliptic Geometry

A constant curvature Non-Euclidean Geometry which replaces the Parallel Postulate with the statement ``through any point in the plane, there exist no lines Parallel to a given line.'' Elliptic geometry is sometimes also called Riemannian Geometry. It can be visualized as the surface of a Sphere on which ``lines'' are taken as Great Circles. In elliptic geometry, the sum of angles of a Triangle is $>180^\circ$.

See also Euclidean Geometry, Hyperbolic Geometry, Non-Euclidean Geometry