![]() ![]() The appearance of this geometry in the nineteenth century stimulated the development of non-Euclidean geometry generally, including hyperbolic geometry.Įlliptic geometry has a variety of properties that differ from those of classical Euclidean plane geometry. Because of this, the elliptic geometry described in this article is sometimes referred to as single elliptic geometry whereas spherical geometry is sometimes referred to as double elliptic geometry. However, unlike in spherical geometry, two lines are usually assumed to intersect at a single point (rather than two). Instead, as in spherical geometry, there are no parallel lines since any two lines must intersect. Available in 16-mm or video format from The Media Guild, 11722 Sorrento Valley Road, Suite E, San Diego, CA 92121.Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. ![]() Produced by the Open University of Great Britain. Depicts the Poincaré model of the hyperbolic plane. Belmont, CA: Wadsworth.Ī Non-Euclidean Universe (1978 25 min). Higgins (Eds.), Mathematics: People, Problems, Results, Vol. The evolution of mathematics in ancient China. The Development of Mathematics in China and Japan, 2d ed. Higgins (Eds.), Mathematics: People, Problems, Results,Vol. The Ancient Tradition of Geometric Problems. Mathematical Thought from Ancient to Modern Times, pp. The Thirteen Books of Euclid’s Elements, 2d ed. Euclid’s parallel postulate and its modern offspring. The persistence (and futility) of efforts to trisect the angle. An Introduction to the History of Mathematics, 4th ed. Famous Problems of Geometry and How to Solve Them. Englewood Cliffs, NJ: Prentice-Hall.īold, B. (This presentation of both Euclid’s original work and non-Euclidean geometry is interwoven with a nontechnical description of the revolution in mathematics that resulted from the development of non-Euclidean geometry. Bibliography of Non-Euclidean Geometry, 2d ed. (Uses groups and analytic techniques of linear algebra to construct and study models of these geometries. Euclidean and Non-Euclidean Geometry: An Analytic Approach. Steen (Ed.), Mathematics Today: Twelve Informal Essays, pp. (This is a brief elementary introduction that can be used as supplementary material at the high-school level. Deductive Systems: Finite and Non-Euclidean Geometries. (This is an entertaining poetic presentation. New York: Galois Institute of Mathematics and Art. Non-Euclidean Geometry: Or, Three Moons in Mathesis, 2d ed. Princeton, NJ: Princeton University Press. The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Ideas of Space: Euclidean, Non-Euclidean and Relativistic. (This is an easy-to-read and detailed presentation. An Introduction to Non-Euclidean Geometry. ![]() (This is an expository presentation of non-Euclidean geometry.) Lavrent’ev (Eds.), Mathematics: Its Content, Methods and Meaning, Vol. This process is experimental and the keywords may be updated as the learning algorithm improves.Īleksandrov, A.D. These keywords were added by machine and not by the authors. Since the mathematics of the ancient Greeks was primarily geometry, such readings provide an introduction to the history of mathematics in general. ![]() Thus, the study of Euclidean and non-Euclidean geometry as mathematical systems can be greatly enhanced by parallel readings in the history of geometry. An acquaintance with this history and an appreciation for the mathematical and intellectual importance of Euclidean geometry is essential for an understanding of the profound impact of this development on mathematical and philosophical thought. These individual experiences mirror the difficulties mathematicians encountered historically in the development of non-Euclidean geometry. Eventually, however, this encounter should not only produce a deeper understanding of Euclidean geometry but also offer convincing support for the necessity of carefully reasoned proofs for results that may have once seemed obvious. A brief encounter with these “strange” geometries frequently results in initial confusion. Mathematics is not usually considered a source of surprises, but non-Euclidean geometry contains a number of easily obtainable theorems that seem almost “heretical” to anyone grounded in Euclidean geometry. ![]()
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