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An Expedition to Geometry
S. Kumaresan, University of Mumbai, India, and G. Santhanam, Indian Institute of Technology, Kanpur, India
A publication of Hindustan Book Agency.
Hindustan Book Agency
2005; 242 pp; hardcover
ISBN-10: 81-85931-50-X
ISBN-13: 978-81-85931-50-0
List Price: US$49
Member Price: US$39.20
Order Code: HIN/21
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This book uses a holistic view of geometry to introduce axiomatic, algebraic, analytic, and differential geometry.

Starting with an informal introduction to non-Euclidean plane geometries, the book develops the theory of these geometries to put them on a rigorous footing. It can be considered an explanation of the Kleinian view a la Erlangen Programme. The treatment, however, goes beyond the Kleinian view of geometry.

Some noteworthy topics presented include ...

  • various results about triangles (including results on areas of geodesic triangles) in Euclidean, hyperbolic, and spherical planes
  • affine and projective classification of conics
  • twopoint homogeneity of the three planes and
  • the fact that the set of distance preserving maps (isometries) are essentially the same as the set of lengths preserving maps of these planes.

Geometric intuition is emphasized throughout the book. Figures are included wherever needed. The book has several exercises varying from computational problems to investigative or explorative open questions.

A publication of Hindustan Book Agency; distributed within the Americas by the American Mathematical Society. Maximum discount of 20% for all commercial channels.

Readership

Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

  • Introduction
  • Affine geometry
  • Projective geometry
  • Classification of conics
  • Euclidean geometry
  • Hyperbolic plane geometry
  • Spherical plane geometry
  • Theory of surfaces
  • A group action
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