Transformation Geometry

An Introduction to Symmetry

  • George E. Martin

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

Table of contents

  1. Front Matter
    Pages i-xii
  2. George E. Martin
    Pages 1-6
  3. George E. Martin
    Pages 7-13
  4. George E. Martin
    Pages 14-22
  5. George E. Martin
    Pages 23-32
  6. George E. Martin
    Pages 33-42
  7. George E. Martin
    Pages 43-51
  8. George E. Martin
    Pages 52-61
  9. George E. Martin
    Pages 62-70
  10. George E. Martin
    Pages 71-77
  11. George E. Martin
    Pages 78-87
  12. George E. Martin
    Pages 88-116
  13. George E. Martin
    Pages 117-135
  14. George E. Martin
    Pages 136-146
  15. George E. Martin
    Pages 147-166
  16. George E. Martin
    Pages 167-181
  17. George E. Martin
    Pages 182-197
  18. George E. Martin
    Pages 198-224
  19. Back Matter
    Pages 225-239

About this book

Introduction

Transformation geometry is a relatively recent expression of the successful venture of bringing together geometry and algebra. The name describes an approach as much as the content. Our subject is Euclidean geometry. Essential to the study of the plane or any mathematical system is an under­ standing of the transformations on that system that preserve designated features of the system. Our study of the automorphisms of the plane and of space is based on only the most elementary high-school geometry. In particular, group theory is not a prerequisite here. On the contrary, this modern approach to Euclidean geometry gives the concrete examples that are necessary to appreciate an introduction to group theory. Therefore, a course based on this text is an excellent prerequisite to the standard course in abstract algebra taken by every undergraduate mathematics major. An advantage of having nb college mathematics prerequisite to our study is that the text is then useful for graduate mathematics courses designed for secondary teachers. Many of the students in these classes either have never taken linear algebra or else have taken it too long ago to recall even the basic ideas. It turns out that very little is lost here by not assuming linear algebra. A preliminary version of the text was written for and used in two courses-one was a graduate course for teachers and the other a sophomore course designed for the prospective teacher and the general mathematics major taking one course in geometry.

Keywords

Abbildungsgeometrie Congruence Euclidean geometry Geometry Martin

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/10.1007/978-1-4612-5680-9
  • Copyright Information Springer-Verlag New York 1982
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-5682-3
  • Online ISBN 978-1-4612-5680-9
  • Series Print ISSN 0172-6056
  • About this book