000 | 02815nam a22004335i 4500 | ||
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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 |
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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 |