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

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

by Jeremy Gray
     
 

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… See more details below

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?

Product Details

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

Table of Contents

1Mathematics in the French revolution1
2Poncelet (and pole and polar)11
3Theorems in projective geometry25
4Poncelet's Traite43
5Duality and the duality controversy53
6Poncelet and Chasles63
7Lambert and legendre79
8Gauss89
9Janos Bolyai99
10Lobachevskii113
11To 1855123
12Writing131
13Mobius143
14The duality paradox155
15The Plucker formulae165
16Higher plane curves171
17Complex curves183
18Riemann187
19Differential geometry of surfaces203
20Non-euclidean geometry accepted219
21Writing233
22Fundamental geometry239
23Hilbert251
24Italian foundations261
25The disc model273
26The geometry of space291
27Summary : geometry to 1900301
28The formal side305
29The physical side313
30Is geometry true?325
31Writing333
AVon Staudt and his influence337

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