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Mathematics Non-euclidean

Non-Euclidean Geometry

Fifth Edition

by (author) H.S.M. Coxeter

University of Toronto Press, Scholarly Publishing Division
Initial publish date
Dec 2018
Non-Euclidean, General, General
  • eBook

    Publish Date
    Dec 2018
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The name non-Euclidean was used by Gauss to describe a system of geometry which differs from Euclid's in its properties of parallelism. Such a system was developed independently by Bolyai in Hungary and Lobatschewsky in Russia, about 120 years ago. Another system, differing more radically from Euclid's, was suggested later by Riemann in Germany and Cayley in England. The subject was unified in 1871 by Klein, who gave the names of parabolic, hyperbolic, and elliptic to the respective systems of Euclid-Bolyai-Lobatschewsky, and Riemann-Cayley. Since then, a vast literature has accumulated.


The Fifth edition adds a new chapter, which includes a description of the two families of 'mid-lines' between two given lines, an elementary derivation of the basic formulae of spherical trigonometry and hyperbolic trigonometry, a computation of the Gaussian curvature of the elliptic and hyperbolic planes, and a proof of Schlafli's remarkable formula for the differential of the volume of a tetrahedron.

About the author

H.S.M. Coxeter (1907-2003) was Professor of Mathematics at the University of Toronto.

H.S.M. Coxeter's profile page

Editorial Reviews

"Professor Coxeter's textbook presents the fundamental principles in a clear, readable manner. It should be the standard textbook on non-Euclidean geometry for a long time to come."

Mathematical Gazette

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