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Elementary Geometry
 
Ilka Agricola Humboldt-Universität zu Berlin, Berlin, Germany
Thomas Friedrich Humboldt-Universität zu Berlin, Berlin, Germany

Translated by Philip G. Spain

Elementary Geometry
Softcover ISBN:  978-0-8218-4347-5
Product Code:  STML/43
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2152-6
Product Code:  STML/43.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-4347-5
eBook: ISBN:  978-1-4704-2152-6
Product Code:  STML/43.B
List Price: $108.00 $83.50
Elementary Geometry
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Elementary Geometry
Ilka Agricola Humboldt-Universität zu Berlin, Berlin, Germany
Thomas Friedrich Humboldt-Universität zu Berlin, Berlin, Germany

Translated by Philip G. Spain

Softcover ISBN:  978-0-8218-4347-5
Product Code:  STML/43
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2152-6
Product Code:  STML/43.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-4347-5
eBook ISBN:  978-1-4704-2152-6
Product Code:  STML/43.B
List Price: $108.00 $83.50
  • Book Details
     
     
    Student Mathematical Library
    Volume: 432008; 243 pp
    MSC: 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 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.

  • 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
  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 432008; 243 pp
MSC: 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 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.

  • 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 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.