Geometry by Its History

  • Alexander Ostermann
  • Gerhard Wanner
Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Classical Geometry

    1. Front Matter
      Pages 1-2
    2. Alexander Ostermann, Gerhard Wanner
      Pages 3-26
    3. Alexander Ostermann, Gerhard Wanner
      Pages 27-59
    4. Alexander Ostermann, Gerhard Wanner
      Pages 61-78
    5. Alexander Ostermann, Gerhard Wanner
      Pages 79-112
    6. Alexander Ostermann, Gerhard Wanner
      Pages 113-155
  3. Analytic Geometry

    1. Front Matter
      Pages 157-158
    2. Alexander Ostermann, Gerhard Wanner
      Pages 159-184
    3. Alexander Ostermann, Gerhard Wanner
      Pages 185-240
    4. Alexander Ostermann, Gerhard Wanner
      Pages 241-257
    5. Alexander Ostermann, Gerhard Wanner
      Pages 259-290
    6. Alexander Ostermann, Gerhard Wanner
      Pages 291-317
    7. Alexander Ostermann, Gerhard Wanner
      Pages 319-344
    8. Alexander Ostermann, Gerhard Wanner
      Pages 345-401
  4. Back Matter
    Pages 403-437

About this book

Introduction

In this textbook the authors present first-year geometry roughly in the order in which it was discovered. The first five chapters show how the ancient Greeks established geometry, together with its numerous practical applications, while more recent findings on Euclidian geometry are discussed as well. The following three chapters explain the revolution in  geometry due to the progress made in the field of algebra by Descartes, Euler and Gauss. Spatial geometry, vector algebra and matrices are treated in chapters 9 and 10. The last chapter offers an introduction to projective geometry, which emerged in the 19th century.

Complemented by numerous examples, exercises, figures and pictures, the book offers both motivation and insightful explanations, and provides stimulating and enjoyable reading for students and teachers alike.

Keywords

51-01, 51-03, 01-01 Euclidian geometry analytic geometry geometry history projective Geometry

Authors and affiliations

  • Alexander Ostermann
    • 1
  • Gerhard Wanner
    • 2
  1. 1.Department of MathematicsUniversity of InnsbruckInnsbruckAustria
  2. 2.Section de mathématiquesUniversité de GenèveGenève 4Switzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-29163-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-29162-3
  • Online ISBN 978-3-642-29163-0
  • Series Print ISSN 0172-6056
  • About this book