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020			_a9780857290601 _99780857290601
024	7		_a10.1007/9780857290601 _2doi
035			_avtls000333790
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040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA21-27
100	1		_aGray, Jeremy. _eautor _9306473
245	1	0	_aWorlds Out of Nothing : _bA Course in the History of Geometry in the 19th Century / _cby Jeremy Gray.
264		1	_aLondon : _bSpringer London, _c2010.
300			_axxiv, 400 páginas 71 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		_aSpringer Undergraduate Mathematics Series, _x1615-2085
500			_aSpringer eBooks
505	0		_aMathematics in the French Revolution -- Poncelet (and Pole and Polar) -- Theorems in Projective Geometry -- Poncelet’s Traité -- Duality and the Duality Controversy -- Poncelet, Chasles, and the Early Years of Projective Geometry -- Euclidean Geometry, the Parallel Postulate, and the Work of Lambert and Legendre -- Gauss (Schweikart and Taurinus) and Gauss’s Differential Geometry -- János Bolyai -- Lobachevskii -- Publication and Non-Reception up to 1855 -- On Writing the History of Geometry – 1 -- Across the Rhine – Möbius’s Algebraic Version of Projective Geometry -- Plücker, Hesse, Higher Plane Curves, and the Resolution of the Duality Paradox -- The Plücker Formulae -- The Mathematical Theory of Plane Curves -- Complex Curves -- Riemann: Geometry and Physics -- Differential Geometry of Surfaces -- Beltrami, Klein, and the Acceptance of Non-Euclidean Geometry -- On Writing the History of Geometry – 2 -- Projective Geometry as the Fundamental Geometry -- Hilbert and his Grundlagen der Geometrie -- The Foundations of Projective Geometry in Italy -- Henri Poincaré and the Disc Model of non-Euclidean Geometry -- Is the Geometry of Space Euclidean or Non-Euclidean? -- Summary: Geometry to 1900 -- What is Geometry? The Formal Side -- What is Geometry? The Physical Side -- What is Geometry? Is it True? Why is it Important? -- On Writing the History of Geometry – 3.
520			_aWorlds Out of Nothing is the first book to provide a course on the history of geometry in the 19th century. Based on the latest historical research, the book is aimed primarily at undergraduate and graduate students in mathematics but will also appeal to the reader with a general interest in the history of mathematics. Emphasis is placed on understanding the historical significance of the new mathematics: Why was it done? How - if at all - was it appreciated? What new questions did it generate? Topics covered in the first part of the book are projective geometry, especially the concept of duality, and non-Euclidean geometry. The book then moves on to the study of the singular points of algebraic curves (Plücker’s equations) and their role in resolving a paradox in the theory of duality; to Riemann’s work on differential geometry; and to Beltrami’s role in successfully establishing non-Euclidean geometry as a rigorous mathematical subject. The final part of the book considers how projective geometry, as exemplified by Klein’s Erlangen Program, rose to prominence, and looks at Poincaré’s ideas about non-Euclidean geometry and their physical and philosophical significance. It then concludes with discussions on geometry and formalism, examining the Italian contribution and Hilbert’s Foundations of Geometry; geometry and physics, with a look at some of Einstein’s ideas; and geometry and truth. Three chapters are devoted to writing and assessing work in the history of mathematics, with examples of sample questions in the subject, advice on how to write essays, and comments on what instructors should be looking for.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9780857290595
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-85729-060-1 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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