The Eightfold Way: The Beauty of Klein's Quartic Curve
by Silvio Levy
Publisher: Cambridge University Press 1999
Number of pages: 331
The German mathematician Felix Klein discovered in 1879 that the surface that we now call the Klein quartic has many remarkable properties, including an incredible 336-fold symmetry, the maximum possible degree of symmetry for any surface of its type. This volume explores the rich tangle of properties and theories surrounding this multiform object.
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by Roberto Bonola - Open Court Publishing Company
Examines various attempts to prove Euclid's parallel postulate - by the Greeks, Arabs and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky.
by Julian Lowell Coolidge - Oxford At The Clarendon Press
Chapters include: Foundation For Metrical Geometry In A Limited Region; Congruent Transformations; Introduction Of Trigonometric Formulae; Analytic Formulae; Consistency And Significance Of The Axioms; Geometric And Analytic Extension Of Space; etc.
by D.M.Y. Sommerville - G.Bell & Sons Ltd.
Renowned for its lucid yet meticulous exposition, this text follows the development of non-Euclidean geometry from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations.
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These notes are intended as a relatively quick introduction to hyperbolic geometry. They review the wonderful history of non-Euclidean geometry. They develop a number of the properties that are particularly important in topology and group theory.