A good example of a non-Euclidian space is the surface of the earth. The lines of longitude all intersect the equator at right angles. They are all therefore parallel with respect to one another, and, according to Euclid, should never cross. However, they all meet at the north pole! In a curved space, Euclidian geometry must be modified to account for this occurrence, as well as the fact that the sum of the angles of a triangle on a curved space do not add to 180 degrees.