Introduction to Classical Geometries
(Sprache: Englisch)
This book develops the geometric intuition of the reader by examining the symmetries of the space in question. This approach introduces in turn all the classical geometries: Euclidean, affine, elliptic, projective and hyperbolic. Pre-requisites are...
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This book develops the geometric intuition of the reader by examining the symmetries of the space in question. This approach introduces in turn all the classical geometries: Euclidean, affine, elliptic, projective and hyperbolic. Pre-requisites are calculus, linear algebra and basic analytic geometry.
Klappentext zu „Introduction to Classical Geometries “
This book develops the geometric intuition of the reader by examining the symmetries (or rigid motions) of the space in question. This approach introduces in turn all the classical geometries: Euclidean, affine, elliptic, projective and hyperbolic. The main focus is on the mathematically rich two-dimensional case, although some aspects of 3- or $n$-dimensional geometries are included. Basic notions of algebra and analysis are used to convey better understanding of various concepts and results. Concepts of geometry are presented in a very simple way, so that they become easily accessible: the only pre-requisites are calculus, linear algebra and basic analytic geometry.
This book follows Klein's proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3 or $n$-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions.
The book appeals to, and develops, the geometric intuition of the reader. Some basic notions of algebra and analysis are also used to get better understandings of various concepts and results.
The book appeals to, and develops, the geometric intuition of the reader. Some basic notions of algebra and analysis are also used to get better understandings of various concepts and results.
Inhaltsverzeichnis zu „Introduction to Classical Geometries “
- Preface.1. Euclidean Geometry.
2. Affine Geometry.
3. Projective Geometry.
4. Hyperbolic Geometry.
- Appendices.
- Bibliography.
- Index.
Bibliographische Angaben
- Autoren: Ana Irene Ramírez Galarza , José Seade
- 2007, 2007, 220 Seiten, Maße: 17 x 24,1 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3764375175
- ISBN-13: 9783764375171
- Erscheinungsdatum: 20.03.2007
Sprache:
Englisch
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