Introduction to Hyperbolic Geometry / by Arlan Ramsay, Robert D. Richtmyer.
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 establ...
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| Online Access: |
Full Text (via Springer) |
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| Format: | eBook |
| Language: | English |
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New York, NY :
Springer New York,
1995.
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| Series: | Universitext.
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| Subjects: |
| Summary: | 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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| Physical Description: | 1 online resource (xii, 289 pages) |
| ISBN: | 9781475755855 1475755856 |
| ISSN: | 0172-5939. |