Non-Euclidean Geometry : Fifth Edition / H.S.M. Coxeter.

Format:

Book

Author/Creator:

Coxeter, H.S.M., author.

Series:

Mathematical expositions ; Number 2.

Heritage

Language:

English

Subjects (All):

Geometry, Non-Euclidean.

Physical Description:

1 online resource (326 pages) : illustrations.

Edition:

Fifth edition.

Place of Publication:

Toronto : University of Toronto Press, [2019]

Language Note:

In English.

Summary:

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.

Contents:

Frontmatter

PREFACE

CONTENTS

I. THE HISTORICAL DEVELOPMENT OF NON-EUCLIDEAN GEOMETRY

II. REAL PROJECTIVE GEOMETRY: FOUNDATIONS

III. REAL PROJECTIVE GEOMETRY: POLARITIES, CONICS AND QUADRICS

IV. HOMOGENEOUS COORDINATES

V. ELLIPTIC GEOMETRY IN ONE DIMENSION

VI. ELLIPTIC GEOMETRY IN TWO DIMENSIONS

VII. ELLIPTIC GEOMETRY IN THREE DIMENSIONS

VIII. DESCRIPTIVE GEOMETRY

IX. EUCLIDEAN AND HYPERBOLIC GEOMETRY

X. HYPERBOLIC GEOMETRY IN TWO DIMENSIONS

XI. CIRCLES AND TRIANGLES

XII. THE USE OF A GENERAL TRIANGLE OF REFERENCE

XIII. AREA

XIV. EUCLIDEAN MODELS

XV. CONCLUDING REMARKS

BIBLIOGRAPHY

INDEX

Notes:

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 19. Feb 2019)

ISBN:

9781442637740

1442637749

9781442653207

1442653205

OCLC:

1088930940