Overview

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.

Full Product Details

Author:   Arlan Ramsay ,  Robert D. Richtmyer
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1995 ed.
Dimensions:   Width: 21.00cm , Height: 1.90cm , Length: 27.90cm
Weight:   0.753kg
ISBN:  

9780387943398

ISBN 10:   0387943390
Pages:   289
Publication Date:   16 December 1995
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Replaced By:   9780387745329
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

Preface; Introduction; 1. Axioms for Plane Geometry; 2. Some Neutral Theorems of Plane Geometry; 3. Qualitative Description of the Hyperbolic Plane; 4. H3 and Euclidean Approximations in H2; 5. Differential Geometry of Surface; 6. Quantitative Considerations; 7. Consistency and Categoricalness of the Hyperbolic Axioms- the Classical Models; 8. Matrix Representation of the Isometry Group; 9. Differential and Hyperbolic Geometry in More Dimensions; 10. Connections with the Lorentz Group of Special Relativity; 11. Constructions by Straightedge and Compass in the Hyperbolic Plane; Index

Reviews

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

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