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25 Remote Warehouse Mathematics- Geometry General

Introduction to Hyperbolic Geometry

by

Introduction to Hyperbolic Geometry Cover

 

Synopses & Reviews

Publisher Comments:

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.

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

Product Details

ISBN:
9780387943398
Author:
Ramsay, Arlan
Publisher:
Springer
Author:
Richtmyer, Robert D.
Location:
New York :
Subject:
Geometry, Hyperbolic
Subject:
Geometry - Non-Euclidean
Subject:
Mathematics-Geometry - General
Subject:
General Mathematics
Subject:
Mathematics - General
Edition Description:
Book
Series:
Universitext
Series Volume:
2631
Publication Date:
19951231
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
302
Dimensions:
235 x 155 mm 431 gr

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Related Subjects

Children's » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Differential Geometry
Science and Mathematics » Mathematics » Geometry » General

Introduction to Hyperbolic Geometry New Trade Paper
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Product details 302 pages Springer-Verlag New York, Incorporated - English 9780387943398 Reviews:
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