Non-Euclidean Geometry - Elliptic Non-euclidean Geometry
york publications dover geometries
A later development following that of Bolyai's and Lobachevsky's hyperbolic non-Euclidean geometry was that of elliptic non-Euclidian geometry. The rudiments of elliptic non-Euclidean geometry were developed by Georg Friedrich Bernhard Riemann. His introduction to his foundations of spherical geometry apparently was used as the basis for his elliptic geometry which made use of the postulate that the sum of the angles of a triangle in space are greater than 180°. Based on the foundations that Riemann had introduced, Klein was able to further develop elliptic non-Euclidean geometry and was actually the mathematician who defined this new field as Elliptic non-Euclidian geometry. Klein's Erlanger Program made a significant contribution in providing major distinguishing features among parabolic (Euclidean geometry), hyperbolic, and elliptic geometries.
Resources
Books
Bonola, R. Non-Euclidean Geometry. New York: Dover Publications, 1911.
Greenberg, M.J. Euclidean and Non-Euclidean Geometries. San Francisco: W. H. Freeman and Co., 1974.
Krause, E.F. Taxicab Geometry. New York: Dover Publications, 1986.
Rosenfeld, B.A. A History of Non-Euclidean Geometry. New York: Springer-Verlag, 1988.
Stillwell, J. Mathematics and Its History. New York: Springer-Verlag, 1989.
Trudeau, R.J. The Non-Euclidean Revolution. Boston: Birkhauser, 1987.
G.H. Miller
User Comments