Elliptical Geometry

In elliptic geometry there are no parallels to a given line L through an external point P, and the sum of the angles of a triangle is greater than 180°. Consider the geometry on the surface of a sphere, the shortest distance between two points on a sphere is an arc of a great circle dividing the sphere in exactly two halves. Since any two great circles always meet, no parallel lines are possible. The angles of a triangle formed by arcs of three great circles always add up to more than 180°. To better understand this, imagine a triangle on the earth's surface bounded by a portion of the equator and two meridians of longitude connecting its end points to one of the poles. Since the two angles at the equator are each 90°, the sum of the angles is determined by the angle at which the meridians meet at the pole and is most certainly greater than 180.
Reference: (2009). Non-Euclidean geometry. Columbia Electronic Encyclopedia, 6th Edition, 1. http://search.ebscohost.com/
n.d., n.t., google image, retrieved on 4/11/2009
http://www.gap-system.org/~john/geometry/Diagrams/x25-1.gif