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Author Ramirez Galarza, Ana Irene.
Title Introducción a la geometría avanzada. English
Introduction to classical geometries / Ana Irene Ramirez Galarza, Jose Seade.
Imprint Basel ; Boston : Birkhauser, 2007.

View online
Subject Geometry.
Alt Name Seade, J. (José)
View online
Subject Geometry.
Alt Name Seade, J. (José)
Description 1 online resource (viii, 219 pages) : illustrations
Bibliography Note Includes bibliographical references (pages 211-213) and index.
Contents Euclidean geometry -- Affine geometry -- Projective geometry -- Hyperbolic geometry -- Appendices.
Summary This book follows Felix 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 fundamental ideas of the classical geometries are presented in a clear and elementary way, making them accessible to a wide audience, and relating them to more advanced topics in modern geometry, such as manifolds, Lie groups, the Gaussian curvature, group actions, and foliations. The book appeals to, and develops, the geometric intuition of the reader. The only prerequisites are calculus, linear algebra and basic analytic geometry. After studying the material, the reader will have a good understanding of basic geometry as well as a clear picture of the relations of this beautiful subject to other branches of mathematics. This is supported by more than 100 carefully chosen illustrations and a large number of exercises. While mainly addressed to students at advanced undergraduate level, the text can be of interest to anyone wanting to learn classical geometry.
Note Print version record.
ISBN 9783764375188
9780817675172 (alk. paper)
0817675175 (alk. paper)
ISBN/ISSN 10.1007/978-3-7643-7518-8
OCLC # 184984578
Additional Format Print version: Ramirez Galarza, Ana Irene. Introduccion a la geometria avanzada. English. Introduction to classical geometries. Basel ; Boston : Birkhauser, 2007 9780817675172 0817675175 (DLC) 2007922251 (OCoLC)75714153