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  3. Hyperbolic Geometry
  • Cited by 46
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
1992
Online ISBN:
9780511569333
DOI:
https://doi.org/10.1017/CBO9780511569333
Subjects:
Mathematics (general), Mathematics, Geometry and Topology
Series:
London Mathematical Society Student Texts (25)
Information

Book description

Although it arose from purely theoretical considerations of the underlying axioms of geometry, the work of Einstein and Dirac has demonstrated that hyperbolic geometry is a fundamental aspect of modern physics. In this book, the rich geometry of the hyperbolic plane is studied in detail, leading to the focal point of the book, Poincare's polygon theorem and the relationship between hyperbolic geometries and discrete groups of isometries. Hyperbolic 3-space is also discussed, and the directions that current research in this field is taking are sketched. This will be an excellent introduction to hyperbolic geometry for students new to the subject, and for experts in other fields.

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