**Student Mathematical Library**

Volume: 43;
2008;
243 pp;
Softcover

MSC: Primary 51;

Print ISBN: 978-0-8218-4347-5

Product Code: STML/43

List Price: $42.00

Individual Price: $33.60

**Electronic ISBN: 978-1-4704-2152-6
Product Code: STML/43.E**

List Price: $42.00

Individual Price: $33.60

#### Supplemental Materials

# Elementary Geometry

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*Ilka Agricola; Thomas Friedrich*

*Translated by: Philip G. Spain*

Translated by Philip G. Spain

Elementary geometry provides the foundation of modern geometry. For the most part, the standard introductions end at the formal Euclidean geometry of high school. Agricola and Friedrich revisit geometry, but from the higher viewpoint of university mathematics. Plane geometry is developed from its basic objects and their properties and then moves to conics and basic solids, including the Platonic solids and a proof of Euler's polytope formula. Particular care is taken to explain symmetry groups, including the description of ornaments and the classification of isometries by their number of fixed points. Complex numbers are introduced to provide an alternative, very elegant approach to plane geometry. The authors then treat spherical and hyperbolic geometries, with special emphasis on their basic geometric properties.

This largely self-contained book provides a much deeper understanding of familiar topics, as well as an introduction to new topics that complete the picture of two-dimensional geometries. For undergraduate mathematics students the book will be an excellent introduction to an advanced point of view on geometry. For mathematics teachers it will be a valuable reference and a source book for topics for projects.

The book contains over 100 figures and scores of exercises. It is suitable for a one-semester course in geometry for undergraduates, particularly for mathematics majors and future secondary school teachers.

#### Table of Contents

# Table of Contents

## Elementary Geometry

- Cover Cover11 free
- Title i2 free
- Copyright ii3 free
- Contents iii4 free
- Preface to the English Edition v6 free
- Preface to the German Edition vii8 free
- Chapter 1. Introduction: Euclidean space 114 free
- Exercises 619 free

- Chapter 2. Elementary geometrical figures and their properties 922
- Chapter 3. Symmetries of the plane and of space 99112
- §3.1. Affine mappings and centroids 99112
- §3.2. Projections and their properties 105118
- §3.3. Central dilations and translations 108121
- §3.4. Plane isometries and similarity transforms 114127
- §3.5. Complex description of plane transformations 127140
- §3.6. Elementary transformations of the space E[sup(3)] 131144
- §3.7. Discrete subgroups of the plane transformation group 139152
- §3.8. Finite subgroups of the spatial transformation group 151164
- Exercises 156169

- Chapter 4. Hyperbolic geometry 167180
- Chapter 5. Spherical geometry 209222
- Bibliography 229242
- List of Symbols 235248
- Index 237250
- Back Cover Back Cover1257

#### Readership

Undergraduate students interested in plane geometry.

#### Reviews

...comprehensive in scope, uncovering key ideas ranging from Euclidean geometry to transformations to affine systems to non-Euclidean geometries. ...The authors neither cut corners nor 'wave' at neat ideas; rather, they try to connect everything via a quite rigorous development, complete with well-chosen exercises.

-- CHOICE Reviews

The book is nicely written, with numerous figures, and the material in the book is organized systematically. It can be widely used by university students and teachers.

-- EMS Newsletter