Introduction to hyperbolic geometry:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
1995
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Klappentext Inhaltsverzeichnis |
| Physical Description: | XII, 287 S. graph. Darst. |
| ISBN: | 0387943390 3540943390 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to hyperbolic geometry |c Arlan Ramsay ; Robert D. Richtmyer |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1995 | |
| 300 | |a XII, 287 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804124205915045888 |
|---|---|
| adam_text | 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 prop¬
erties of the real number system so the time and effort needed to
develop the real number system from geometric axioms can be
used instead for geometry itself. The first four chapters together
with selections from the rest provide a convenient text for a stan¬
dard one semester course in non-Euclidean geometry. The
development includes properties of the ¡sometry group of the hyper¬
bolic plane, tilings, and applications to special relativity. Elementary
techniques from complex analysis, matrix theory, and group the¬
ory are used in later chapters, and some mathematical sophistication
on the part of students is thus required, but a formal course in these
topics is not a prerequisite.
Contents
Preface v
Introduction
A Bit of History
What Are Axioms For?
What Are Models For? (Consistency and Categoricalness)
What Is Geometry? (The Problem of Visualization)
The Role of Analysis in Geometry (Differential Geometry)
Outline of the Following Chapters
Chapter
Axioms for Plane Geometry
1.1
1.2
1.3
Appendix: The Real Number System
A.1 Axioms of an Ordered Field
A.2 The Rational Subfield
A.3 The Completeness Axiom
A.4 Categoricalness of the Axioms
A.5 Some Models of R
A.6 Categoricalness and the
Chapter
Some Neutral Theorems of Plane Geometry
2.1
2.2
2.3
2.4
2.5
2-6
x Contents
2.7
2.8
2.9
2.10
Chapter
Qualitative Description of the Hyperbolic Plane
3.1
3.2
3.3
3.4
3.5 Ultraparallel
3.6
3.7
3.8
3.9
3.10
3.11
3.12
3.13
3.14
and Quadrilaterals
3.15
of a Circular Sector
3.16
Chapter
H3 and Euclidean Approximations in H2
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
Chapter
Differential Geometry of Surfaces
5.1
in Three Dimensions
Contents xi
5 2
53
in the Hyperbolic Plane
5.4
5.5
5 6
5 7 Approximate Laws for Very Small Right Triangles
¿& Area 170
5.9
5.10
5.11
5.12
Chapter
Quantitative Considerations
6.1
6.2
6.3
6.4
6.5
6.6
Chapter
Consistency and Categoricalness of the Hyperbolic Axioms;
The Classical Models
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
Chapter
Matrix Representation of the Isometry Group
8.1
8.2
8.3
8.4
xii Contents
Chapter
Differential and Hyperbolic Geometry in More Dimensions
9.1
9.2
9.3
9.4
9.5
9.6
Chapter
Connections with the Lorentz Group of Special Relativity
10.1
10.2
10.3
Two Space Variables and Time with the Direct Isometry
Group of the Hyperbolic Plane
10.4
10.5
10.6
Chapter
Constructions by Straightedge and Compass 25a
in the Hyperbolic Plane
11.1
11.2
11.3
11.4
11.5
11.6
Quadratic-Surd Fields
11.7
11.8
11.9
11.10
Index
|
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| ctrlnum | (OCoLC)30594494 (DE-599)BVBBV009850961 |
| dewey-full | 516.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.9 |
| dewey-search | 516.9 |
| dewey-sort | 3516.9 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T17:41:58Z |
| institution | BVB |
| isbn | 0387943390 3540943390 |
| language | English |
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| physical | XII, 287 S. graph. Darst. |
| publishDate | 1995 |
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| spelling | Ramsay, Arlan Verfasser aut Introduction to hyperbolic geometry Arlan Ramsay ; Robert D. Richtmyer New York [u.a.] Springer 1995 XII, 287 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Géométrie hyperbolique ram Hyperbolische meetkunde gtt Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Hyperbolische Geometrie (DE-588)4161041-6 s DE-604 Richtmyer, Robert D. Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006521235&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UBPassau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006521235&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ramsay, Arlan Richtmyer, Robert D. Introduction to hyperbolic geometry Géométrie hyperbolique ram Hyperbolische meetkunde gtt Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 (DE-588)4151278-9 |
| title | Introduction to hyperbolic geometry |
| title_auth | Introduction to hyperbolic geometry |
| title_exact_search | Introduction to hyperbolic geometry |
| title_full | Introduction to hyperbolic geometry Arlan Ramsay ; Robert D. Richtmyer |
| title_fullStr | Introduction to hyperbolic geometry Arlan Ramsay ; Robert D. Richtmyer |
| title_full_unstemmed | Introduction to hyperbolic geometry Arlan Ramsay ; Robert D. Richtmyer |
| title_short | Introduction to hyperbolic geometry |
| title_sort | introduction to hyperbolic geometry |
| topic | Géométrie hyperbolique ram Hyperbolische meetkunde gtt Geometry, Hyperbolic Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Géométrie hyperbolique Hyperbolische meetkunde Geometry, Hyperbolic Hyperbolische Geometrie Einführung |
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