000			02037nam a2200205 4500
001			15004212
010			_a 2007060844
020			_a9781470454791
082	0	0	_a516 _bAGR/E
100	1		_aAgricola, Ilka
240	1	0	_aElementargeometrie
245	1	0	_aElementary geometry
260			_aProvidence, R.I. : _bAmerican Mathematical Society, _c2008.
300			_axi, 243 p. _bill. (some col.) ;
500			_a"Originally published in German by Friedr. Vieweg & Sohn Verlag, ... c2005"--T.p. verso.
520			_aElementary geometry provides the foundation of modern geometry. For the most part, the standard introductions end at the formal Euclidean geometry of high school. Agricola and Friedrich revisit geometry, but from the higher viewpoint of university mathematics. Plane geometry is developed from its basic objects and their properties and then moves to conics and basic solids, including the Platonic solids and a proof of Euler's polytope formula. Particular care is taken to explain symmetry groups, including the description of ornaments and the classification of isometries by their number of fixed points. Complex numbers are introduced to provide an alternative, very elegant approach to plane geometry. The authors then treat spherical and hyperbolic geometries, with special emphasis on their basic geometric properties. This largely self-contained book provides a much deeper understanding of familiar topics, as well as an introduction to new topics that complete the picture of two-dimensional geometries. For undergraduate mathematics students the book will be an excellent introduction to an advanced point of view on geometry. For mathematics teachers it will be a valuable reference and a source book for topics for projects. The book contains over 100 figures and scores of exercises. It is suitable for a one-semester course in geometry for undergraduates, particularly for mathematics majors and future secondary school teachers.
650		0	_aGeometry
700	1		_aFriedrich, Thomas
942			_cBK
999			_c67052 _d67052