# Transformation Geometry

## An Introduction to Symmetry

Textbook

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

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

### 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

1. 1.Department of Mathematics and StatisticsState University of New York at AlbanyAlbanyUSA

### 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
• Copyright Information Springer-Verlag New York 1982
• Publisher Name Springer, New York, NY
• eBook Packages
• Hardcover ISBN 978-0-387-90636-2
• Softcover ISBN 978-1-4612-5682-3
• eBook ISBN 978-1-4612-5680-9
• Series ISSN 0172-6056
• Edition Number 1
• Number of Pages XII, 240
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site