Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century / Edition 1

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2006 Trade paperback Edition. ed. Very Good. The book has been read, but is in excellent condition. Pages are intact and not marred by notes or highlighting. The spine remains ... undamaged. Trade paperback (US). Glued binding. 376 p. Contains: Illustrations. Springer Undergraduate Mathematics. *****PLEASE NOTE: This item is shipping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** Read more Show Less

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Overview

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?
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Editorial Reviews

From the Publisher
From the reviews:

"Gray’s new book will become both a classic reference and a model on how to write a useful course text. With original source material woven in with historical context, this book is a fun read as it examines geometry historically as a connected sequence of diverse ideas … . it includes a useful index and extensive bibliography. If you enjoy mathematics, buy this and read it! Summing Up: Highly recommended. General readers; lower-division undergraduates through faculty." (J. Johnson, CHOICE, Vol. 44 (11), July, 2007)

"Gray (Open Univ., UK) does it again. Complementing his works on Jinos Bolyai or the world of different geometries, Gray's new book will become both a classic reference and a model on how to write a useful course text. With original source material in with historical context, this book is a fun read as it examines geometry historically as a connected sequence of diverse ideas: duality in projective geometry, the problem of parallels in non-Euclidean geometries, the nature of surfaces in differential geometry, and concern for geometry as a true "measure" of space (physical or philosophical). Documenting mathematicians' contributions within this historical sequence, the book becomes a fascinating Who's Who: Poncelet, Desargues, Pascal, Gergonne, Saccheri, Lambert, Legendre, Gauss, Bolyai, Lobachevski, Möbius, Plücker, Beltrami, Klein, Poincaré, Hilbert, and Einstein. Finally, the book's unusual twist is its inclusion of three chapters on writing and critical reading about the history of mathematics; these chapters alone make the book valuable to those helping students improve as writers of mathematics. An offshoot of a University of Warwick course, it includes a useful index and extensive bibliography. If you enjoy mathematics, but this and read it! Summing up: Highly recommended. General readers; lower-division undergraduates through faculty."- J. Johnson, Western Washington University

"This is an outstanding text for the well-prepared student who has a basic knowledge of linear algebra, matrix theory, calculus of several variables, and geometry. … an important addition to the mathematical and historical literature. Albeit primarily a textbook for a one-semester upper level or graduate course in the history of mathematics, it will be appreciated and enjoyed by those interested in geometry, history, philosophy, and pedagogy. … The book contains an excellent bibliography. … it provides a useful reference for anyone interested in geometry." (James J. Tattersall, Mathematical Reviews, Issue 2008 b)

"The 19th century was certainly an exciting time in geometry. To chronicle all of that excitement in one place is a monumental task; to have done so with real clarity and attention to detail, as Jeremy Gray has done, is an impressive achievement. … Gray has succeeded on several levels: as a historical chronicler, as a mathematical scholar, and as an advisor to teachers. Worlds Out Of Nothing is a first-rate addition to the geometry enthusiast’s bookshelf." (Mark Bollman, MathDL, January, 2008)

“The book under review provides a course on the history of geometry in the 19th century. … In the book the emphasis is put on understanding the historical significance of the new geometry. In this way it can fill the gap between what is usually taught today in geometry … and the historical considerations, it can provide the historical and philosophical background of the geometry developed in the 19th century.” (Roman Murawski, Zentralblatt MATH, Vol. 1205, 2011)

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Product Details

  • ISBN-13: 9781846286322
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 11/17/2006
  • Series: Springer Undergraduate Mathematics Series
  • Edition number: 1
  • Pages: 376
  • Product dimensions: 7.00 (w) x 9.20 (h) x 0.80 (d)

Meet the Author

Jeremy Gray is Professor of the History of Mathematics and Director of the Centre for the History of the Mathematical Sciences at the Open University in England, and is an Honorary Professor in the Mathematics Department at the University of Warwick. He is the author, co-author, or editor of 14 books on the history of mathematics in the 19th and 20th Centuries and is internationally recognised as an authority on the subject. His book, Ideas of Space, is a standard text on the history of geometry (see competitive literature).

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Table of Contents

1 Mathematics in the French revolution 1
2 Poncelet (and pole and polar) 11
3 Theorems in projective geometry 25
4 Poncelet's Traite 43
5 Duality and the duality controversy 53
6 Poncelet and Chasles 63
7 Lambert and legendre 79
8 Gauss 89
9 Janos Bolyai 99
10 Lobachevskii 113
11 To 1855 123
12 Writing 131
13 Mobius 143
14 The duality paradox 155
15 The Plucker formulae 165
16 Higher plane curves 171
17 Complex curves 183
18 Riemann 187
19 Differential geometry of surfaces 203
20 Non-euclidean geometry accepted 219
21 Writing 233
22 Fundamental geometry 239
23 Hilbert 251
24 Italian foundations 261
25 The disc model 273
26 The geometry of space 291
27 Summary : geometry to 1900 301
28 The formal side 305
29 The physical side 313
30 Is geometry true? 325
31 Writing 333
A Von Staudt and his influence 337
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