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Catalogue Information
Field name	Details
Dewey Class	510.9
Title	Worlds Out of Nothing ([Ebook]) : A Course in the History of Geometry in the 19th Century / by Jeremy Gray.
Author	Gray, Jeremy J. , 1947-
Other name(s)	SpringerLink (Online service)
Publication	London : Springer , 2010.
Physical Details	XXIV, 400 pages, 71 illus. : online resource.
Series	Springer undergraduate mathematics series 1615-2085
ISBN	9780857290601
Summary Note	Worlds 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 (PlÃ¼ckerâs equations) and their role in resolving a paradox in the theory of duality; to Riemannâs work on differential geometry; and to Beltramiâs 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 Kleinâs Erlangen Program, rose to prominence, and looks at PoincarÃ©âs 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 Hilbertâs Foundations of Geometry; geometry and physics, with a look at some of Einsteinâs 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.:
Contents note	Mathematics in the French Revolution -- Poncelet (and Pole and Polar) -- Theorems in Projective Geometry -- Ponceletâs TraitÃ© -- Duality and the Duality Controversy -- Poncelet and Chasles -- Lambert and Legendre -- Gauss -- Janos Bolyai -- Lobachevskii -- To 1855 -- Writing -- MÃ¶bius -- The Duality Paradox -- The PlÃ¼cker Formulae -- Higher Plane Curves -- Complex Curves -- Riemann -- Differential Geometry of Surfaces -- Non-Euclidean Geometry Accepted -- Writing -- Fundamental Geometry -- Hilbert -- Italian Foundations -- The Disc Model -- The Geometry of Space -- Summary: Geometry to 1900 -- The Formal Side -- The Physical Side -- Is Geometry True?- Writing -- Appendix: Von Staudt and his Influence -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-0-85729-060-1
Links to Related Works	Subject References: Geometry . Geometry - History . History of mathematics . Mathematics . Mathematics - History . Authors: Gray, Jeremy J. 1947- . Corporate Authors: SpringerLink (Online service) . Series: Springer undergraduate mathematics series . Classification: 510.9 . 510.9 (DDC 23) .

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Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century

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