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

• Main Author: Gray, Jeremy. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: London : Springer London, 2010.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Geometry.; Mathematics_$xHistory.; History of Mathematics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-85729-060-1

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 his...

Table of Contents:

• Mathematics in the French Revolution
• Poncelet (and Pole and Polar)
• Theorems in Projective Geometry
• Poncelet<U+0019>s Trait ̌
• Duality and the Duality Controversy
• Poncelet and Chasles
• Lambert and Legendre
• Gauss
• Janos Bolyai
• Lobachevskii
• To 1855
• Writing
• Mb̲ius
• The Duality Paradox
• The Pl<U+00fc>cker 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.