Items related to Introduction to Hyperbolic Geometry (Universitext)
Synopsis
This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes properties of the isometry group of the hyperbolic plane, tilings, and applications to special relativity. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite.
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Review
"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical Society
"About this title" may belong to another edition of this title.
- PublisherSpringer-Verlag Berlin and Heidelberg GmbH & Co. K
- Publication date1995
- ISBN 10 3540943390
- ISBN 13 9783540943396
- BindingPaperback
- LanguageEnglish
- Number of pages299
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