The Foundations of Geometry and the Non-Euclidean Plane

  • George E. Martin

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. George E. Martin
      Pages 2-9
    3. George E. Martin
      Pages 10-19
    4. George E. Martin
      Pages 20-33
    5. George E. Martin
      Pages 34-47
  3. Absolute Geometry

    1. Front Matter
      Pages 49-49
    2. George E. Martin
      Pages 50-64
    3. George E. Martin
      Pages 65-72
    4. George E. Martin
      Pages 73-83
    5. George E. Martin
      Pages 84-94
    6. George E. Martin
      Pages 95-110
    7. George E. Martin
      Pages 111-120
    8. George E. Martin
      Pages 121-130
    9. George E. Martin
      Pages 144-154
    10. George E. Martin
      Pages 155-171
    11. George E. Martin
      Pages 172-181
    12. George E. Martin
      Pages 182-191
    13. George E. Martin
      Pages 192-203

About this book

Introduction

This book is a text for junior, senior, or first-year graduate courses traditionally titled Foundations of Geometry and/or Non­ Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap­ ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for in-service teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 -20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 -30). The text is self-contained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 -34). There are over 650 exercises, 30 of which are 10-part true-or-false questions. A rigorous ruler-and-protractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten­ sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three­ and four-dimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 -4) is to be read as quickly as possible and then used for ref­ erence if necessary.

Keywords

Absolute Geometrie Area Congruence Geometry Martin Nichteuklidische Geometrie Non-Euclidean Geometry Plane

Authors and affiliations

  • George E. Martin
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-5725-7
  • Copyright Information Springer-Verlag New York 1975
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-5727-1
  • Online ISBN 978-1-4612-5725-7
  • Series Print ISSN 0172-6056
  • About this book