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Transformation Geometry

An Introduction to Symmetry

  • Textbook
  • © 1982

Overview

Authors:
  1. George E. Martin

    1. Department of Mathematics and Statistics, State University of New York at Albany, Albany, USA

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

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • George E. Martin
    Pages 1-6

  3. Properties of Transformations

    • George E. Martin
    Pages 7-13

  4. Translations and Halfturns

    • George E. Martin
    Pages 14-22

  5. Reflections

    • George E. Martin
    Pages 23-32

  6. Congruence

    • George E. Martin
    Pages 33-42

  7. The Product of Two Reflections

    • George E. Martin
    Pages 43-51

  8. Even Isometries

    • George E. Martin
    Pages 52-61

  9. Classification of Plane Isometries

    • George E. Martin
    Pages 62-70

  10. Equations for Isometries

    • George E. Martin
    Pages 71-77

  11. The Seven Frieze Groups

    • George E. Martin
    Pages 78-87

  12. The Seventeen Wallpaper Groups

    • George E. Martin
    Pages 88-116

  13. Tessellations

    • George E. Martin
    Pages 117-135

  14. Similarities on the Plane

    • George E. Martin
    Pages 136-146

  15. Classical Theorems

    • George E. Martin
    Pages 147-166

  16. Affine Transformations

    • George E. Martin
    Pages 167-181

  17. Transformations on Three-space

    • George E. Martin
    Pages 182-197

  18. Space and Symmetry

    • George E. Martin
    Pages 198-224

  19. Back Matter

    Pages 225-239
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics and Statistics, State University of New York at Albany, Albany, USA

    George E. Martin

Bibliographic Information

  • Book Title: Transformation Geometry

  • Book Subtitle: An Introduction to Symmetry

  • Authors: George E. Martin

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-5680-9

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York Inc. 1982

  • Hardcover ISBN: 978-0-387-90636-2Published: 13 April 1982

  • Softcover ISBN: 978-1-4612-5682-3Published: 14 October 2011

  • eBook ISBN: 978-1-4612-5680-9Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: XII, 240

  • Topics: Geometry

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