000 02815nam a22004335i 4500
001 978-3-7643-7518-8
003 DE-He213
005 20161121231131.0
007 cr nn 008mamaa
008 100301s2007 sz | s |||| 0|eng d
020 _a9783764375188
_9978-3-7643-7518-8
024 7 _a10.1007/978-3-7643-7518-8
_2doi
050 4 _aQA440-699
072 7 _aPBM
_2bicssc
072 7 _aMAT012000
_2bisacsh
082 0 4 _a516
_223
100 1 _aGalarza, Ana Irene Ramírez.
_eauthor.
245 1 0 _aIntroduction to Classical Geometries
_h[electronic resource] /
_cby Ana Irene Ramírez Galarza, José Seade.
264 1 _aBasel :
_bBirkhäuser Basel,
_c2007.
300 _aX, 220 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aEuclidean geometry -- Affine geometry -- Projective geometry -- Hyperbolic geometry -- Appendices.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aGeometry.
650 1 4 _aMathematics.
650 2 4 _aGeometry.
650 2 4 _aMathematics, general.
700 1 _aSeade, José.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783764375171
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-7643-7518-8
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509073
_d509073