**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: $45.00

Individual Price: $36.00

**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

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.

#### Readership

Undergraduate students interested in plane geometry.

#### Reviews & Endorsements

...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

#### 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