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- catalog abstract "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.".
- catalog contributor b7114938.
- catalog contributor b7114939.
- catalog created "1995.".
- catalog date "1995".
- catalog date "1995.".
- catalog dateCopyrighted "1995.".
- catalog description "Ch. 1. Axioms for Plane Geometry -- Ch. 2. Some Neutral Theorems of Plane Geometry -- Ch. 3. Qualitative Description of the Hyperbolic Plane -- Ch. 4. H[superscript 3] and Euclidean Approximations in H[superscript 2] -- Ch. 5. Differential Geometry of Surfaces -- Ch. 6. Quantitative Considerations -- Ch. 7. Consistency and Categoricalness of the Hyperbolic Axioms; The Classical Models -- Ch. 8. Matrix Representation of the Isometry Group -- Ch. 9. Differential and Hyperbolic Geometry in More Dimensions -- Ch. 10. Connections with the Lorentz Group of Special Relativity -- Ch. 11. Constructions by Straightedge and Compass in the Hyperbolic Plane.".
- catalog description "Includes bibliographical references and index.".
- catalog description "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.".
- catalog extent "xii, 287 p. :".
- catalog hasFormat "Introduction to hyperbolic geometry.".
- catalog identifier "0387943390".
- catalog isFormatOf "Introduction to hyperbolic geometry.".
- catalog isPartOf "Universitext".
- catalog issued "1995".
- catalog issued "1995.".
- catalog language "eng".
- catalog publisher "New York : Springer-Verlag,".
- catalog relation "Introduction to hyperbolic geometry.".
- catalog subject "516.9 20".
- catalog subject "Geometry, Hyperbolic.".
- catalog subject "Mathematics.".
- catalog subject "QA685 .R18 1994".
- catalog tableOfContents "Ch. 1. Axioms for Plane Geometry -- Ch. 2. Some Neutral Theorems of Plane Geometry -- Ch. 3. Qualitative Description of the Hyperbolic Plane -- Ch. 4. H[superscript 3] and Euclidean Approximations in H[superscript 2] -- Ch. 5. Differential Geometry of Surfaces -- Ch. 6. Quantitative Considerations -- Ch. 7. Consistency and Categoricalness of the Hyperbolic Axioms; The Classical Models -- Ch. 8. Matrix Representation of the Isometry Group -- Ch. 9. Differential and Hyperbolic Geometry in More Dimensions -- Ch. 10. Connections with the Lorentz Group of Special Relativity -- Ch. 11. Constructions by Straightedge and Compass in the Hyperbolic Plane.".
- catalog title "Introduction to hyperbolic geometry / Arlan Ramsay, Robert D. Richtmyer.".
- catalog type "text".