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＜電子ブック＞
Introduction to Classical Geometries / by Ana Irene Ramírez Galarza, José Seade

版	1st ed. 2007.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2007
本文言語	英語
大きさ	X, 220 p : online resource
著者標目	*Ramírez Galarza, Ana Irene author Seade, José author SpringerLink (Online service)
件　名	LCSH:Geometry LCSH:Mathematics FREE:Geometry FREE:Mathematics
一般注記	Euclidean geometry -- Affine geometry -- Projective geometry -- Hyperbolic geometry -- Appendices 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 HTTP:URL=https://doi.org/10.1007/978-3-7643-7518-8

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