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008			150903s2005 xxu| o |||| 0|eng d
020			_a9780387290522 _99780387290522
024	7		_a10.1007/0387290524 _2doi
035			_avtls000330696
039		9	_a201509030724 _bVLOAD _c201404120519 _dVLOAD _c201404090300 _dVLOAD _c201401311348 _dstaff _y201401301152 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA440-699
100	1		_aStillwell, John. _eautor _9302354
245	1	4	_aThe Four Pillars of Geometry / _cby John Stillwell ; edited by S. Axler, K.A. Ribet.
264		1	_aNew York, NY : _bSpringer New York, _c2005.
300			_axii, 229 páginas, 138 ilustraciones _brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aUndergraduate Texts in Mathematics, _x0172-6056
500			_aSpringer eBooks
505	0		_aStraightedge and compass -- Euclid’s approach to geometry -- Coordinates -- Vectors and Euclidean spaces -- Perspective -- Projective planes -- Transformations -- Non-Euclidean geometry.
520			_aFor two millennia the right way to teach geometry was the Euclidean approach, and in many respects, this is still the case. But in the 1950s the cry "Down with triangles!" was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new right approach? Or was the right approach still something else, perhaps transformation groups? The Four Pillars of Geometry approaches geometry in four different ways, spending two chapters on each. This makes the subject accessible to readers of all mathematical tastes, from the visual to the algebraic. Not only does each approach offer a different view; the combination of viewpoints yields insights not available in most books at this level. For example, it is shown how algebra emerges from projective geometry, and how the hyperbolic plane emerges from the real projective line. The author begins with Euclid-style construction and axiomatics, then proceeds to linear algebra when it becomes convenient to replace tortuous arguments with simple calculations. Next, he uses projective geometry to explain why objects look the way they do, as well as to explain why geometry is entangled with algebra. And lastly, the author introduces transformation groups---not only to clarify the differences between geometries, but also to exhibit geometries that are unexpectedly the same. All readers are sure to find something new in this attractive text, which is abundantly supplemented with figures and exercises. This book will be useful for an undergraduate geometry course, a capstone course, or a course aimed at future high school teachers. John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer, including Elements of Number Theory (2003), Mathematics and Its History (Second Edition, 2002), Numbers and Geometry (1998) and Elements of Algebra (1994).
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aAxler, S. _eeditor. _9302355
700	1		_aRibet, K.A. _eeditor. _9302356
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9780387255309
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/0-387-29052-4 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c278615 _d278615