Items related to Geometry from a Differentiable Viewpoint
Synopsis
The development of geometry from Euclid to Euler to Lobachevsky, Bolyai, Gauss and Riemann is a story that is often broken into parts – axiomatic geometry, non-Euclidean geometry and differential geometry. This poses a problem for undergraduates: Which part is geometry? What is the big picture to which these parts belong? In this introduction to differential geometry, the parts are united with all of their interrelations, motivated by the history of the parallel postulate. Beginning with the ancient sources, the author first explores synthetic methods in Euclidean and non-Euclidean geometry and then introduces differential geometry in its classical formulation, leading to the modern formulation on manifolds such as space-time. The presentation is enlivened by historical diversions such as Huygens's clock and the mathematics of cartography. The intertwined approaches will help undergraduates understand the role of elementary ideas in the more general, differential setting. This thoroughly revised second edition includes numerous new exercises and a new solution key. New topics include Clairaut's relation for geodesics and the use of transformations such as the reflections of the Beltrami disk.
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Review
Review of the first edition: '... an unusual and interesting account of two subjects and their close historical interrelation.' The Mathematical Gazette
'... the author has succeeded in making differential geometry an approachable subject for advanced undergraduates.' Andrej Bucki, Mathematical Reviews
Book Description
This text, for a first course in differential or modern geometry, introduces methods within a historical context that is familiar to students from high school. The thoroughly revised second edition has been reorganized for greater clarity and includes numerous new exercises and topics such as Euclid's geometry of space.
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- PublisherCambridge University Press
- Publication date2012
- ISBN 10 0521133114
- ISBN 13 9780521133111
- BindingPaperback
- LanguageEnglish
- Edition number2
- Number of pages374
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Geometry from a Differentiable Viewpoint
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Geometry from a Differentiable Viewpoint
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