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A History of Non-Euclidean Geometry

Evolution of the Concept of a Geometric Space

  • Book
  • © 1988

Overview

Authors:
  1. B. A. Rosenfeld

    1. Institute for the History of Science and Technology, Moscow, U.S.S.R.

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Part of the book series: Studies in the History of Mathematics and Physical Sciences (HISTORY, volume 12)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xi
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  2. Spherical Geometry

    • B. A. Rosenfeld
    Pages 1-34

  3. The Theory of Parallels

    • B. A. Rosenfeld
    Pages 35-109

  4. Geometric Transformations

    • B. A. Rosenfeld
    Pages 110-151

  5. Geometric Algebra and the Prehistory of Multidimensional Geometry

    • B. A. Rosenfeld
    Pages 152-180

  6. Philosophy of Space

    • B. A. Rosenfeld
    Pages 181-205

  7. Lobačevskian Geometry

    • B. A. Rosenfeld
    Pages 206-246

  8. Multidimensional Spaces

    • B. A. Rosenfeld
    Pages 247-279

  9. The Curvature of Space

    • B. A. Rosenfeld
    Pages 280-326

  10. Groups of Transformations

    • B. A. Rosenfeld
    Pages 327-381

  11. Application of Algebras

    • B. A. Rosenfeld
    Pages 382-427

  12. Back Matter

    Pages 428-471
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Keywords

About this book

The Russian edition of this book appeared in 1976 on the hundred-and-fiftieth anniversary of the historic day of February 23, 1826, when LobaeevskiI delivered his famous lecture on his discovery of non-Euclidean geometry. The importance of the discovery of non-Euclidean geometry goes far beyond the limits of geometry itself. It is safe to say that it was a turning point in the history of all mathematics. The scientific revolution of the seventeenth century marked the transition from "mathematics of constant magnitudes" to "mathematics of variable magnitudes. " During the seventies of the last century there occurred another scientific revolution. By that time mathematicians had become familiar with the ideas of non-Euclidean geometry and the algebraic ideas of group and field (all of which appeared at about the same time), and the (later) ideas of set theory. This gave rise to many geometries in addition to the Euclidean geometry previously regarded as the only conceivable possibility,to the arithmetics and algebras of many groups and fields in addition to the arith­ metic and algebra of real and complex numbers, and, finally, to new mathe­ matical systems, i. e. , sets furnished with various structures having no classical analogues. Thus in the 1870's there began a new mathematical era usually called, until the middle of the twentieth century, the era of modern mathe­ matics.

Authors and Affiliations

  • Institute for the History of Science and Technology, Moscow, U.S.S.R.

    B. A. Rosenfeld

Bibliographic Information

  • Book Title: A History of Non-Euclidean Geometry

  • Book Subtitle: Evolution of the Concept of a Geometric Space

  • Authors: B. A. Rosenfeld

  • Series Title: Studies in the History of Mathematics and Physical Sciences

  • DOI: https://doi.org/10.1007/978-1-4419-8680-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1988

  • Hardcover ISBN: 978-0-387-96458-4Published: 07 September 1988

  • Softcover ISBN: 978-1-4612-6449-1Published: 05 September 2012

  • eBook ISBN: 978-1-4419-8680-1Published: 08 September 2012

  • Series ISSN: 0172-570X

  • Edition Number: 1

  • Number of Pages: XI, 471

  • Additional Information: Title of the original Russian edition: Istorija neevklidovoj geometrii

  • Topics: Geometry

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