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  3. Geometry from a Differentiable Viewpoint
  • Cited by 17
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 June 2012
      27 January 1995
      ISBN:
      9781139173926
      DOI:
      https://doi.org/10.1017/CBO9781139173926
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      • Subjects:
      Mathematics, Geometry and Topology
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    Subjects:
    Mathematics, Geometry and Topology
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    Book description

    Differential geometry has developed in many directions since its beginnings with Euler and Gauss. This often poses a problem for undergraduates: which direction should be followed? What do these ideas have to do with geometry? This book is designed to make differential geometry an approachable subject for advanced undergraduates. The text serves as both an introduction to the classical differential geometry of curves and surfaces and as a history of the non-Euclidean plane. The book begins with the theorems of non-Euclidean geometry, then introduces the methods of differential geometry and develops them towards the goal of constructing models of the hyperbolic plane. Interesting diversions are offered, such as Huygens' pendulum clock and mathematical cartography; however, the focus of the book is on the models of non-Euclidean geometry and the modern ideas of abstract surfaces and manifolds. Although the main use of this text is as an advanced undergraduate course book, the historical aspect of the text should appeal to most mathematicians.

    Reviews

    ‘ … this is an unusual and interesting account of two subjects and their close historical interrelation.’

    Source: The Mathematical Gazette

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