Translated by Philip G. Spain
Softcover ISBN:  9780821843475 
Product Code:  STML/43 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421526 
Product Code:  STML/43.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821843475 
eBook: ISBN:  9781470421526 
Product Code:  STML/43.B 
List Price:  $108.00 $83.50 
Translated by Philip G. Spain
Softcover ISBN:  9780821843475 
Product Code:  STML/43 
List Price:  $59.00 
Individual Price:  $47.20 
eBook ISBN:  9781470421526 
Product Code:  STML/43.E 
List Price:  $49.00 
Individual Price:  $39.20 
Softcover ISBN:  9780821843475 
eBook ISBN:  9781470421526 
Product Code:  STML/43.B 
List Price:  $108.00 $83.50 

Book DetailsStudent Mathematical LibraryVolume: 43; 2008; 243 ppMSC: Primary 51
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 selfcontained book provides a much deeper understanding of familiar topics, as well as an introduction to new topics that complete the picture of twodimensional 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 onesemester course in geometry for undergraduates, particularly for mathematics majors and future secondary school teachers.
ReadershipUndergraduate students interested in plane geometry.

Table of Contents

Chapters

Chapter 1. Introduction: Euclidean space

Chapter 2. Elementary geometrical figures and their properties

Chapter 3. Symmetries of the plane and of space

Chapter 4. Hyperbolic geometry

Chapter 5. Spherical geometry


Additional Material

Reviews

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


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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 selfcontained book provides a much deeper understanding of familiar topics, as well as an introduction to new topics that complete the picture of twodimensional 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 onesemester course in geometry for undergraduates, particularly for mathematics majors and future secondary school teachers.
Undergraduate students interested in plane geometry.

Chapters

Chapter 1. Introduction: Euclidean space

Chapter 2. Elementary geometrical figures and their properties

Chapter 3. Symmetries of the plane and of space

Chapter 4. Hyperbolic geometry

Chapter 5. Spherical geometry

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