Plane geometry and its groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
San Francisco [u.a.]
Holden-Day
1967
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 288 S. graph. Darst. |
Internformat
MARC
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Datensatz im Suchindex
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CONTENTS
Preface vii
Chapter I. AXIOMS
1. Sets in the Plane 1
2. Reflections 7
3. Congruence Theorems 17
4. Isometry 22
5. The Triangle 23
Chapter II. PRODUCTS OF REFLECTIONS
1. Pencils 25
2. Rotations 29
3. Po/«? Reflections 35
4. Translations 41
5. G7/ofe Reflections 52
6. Products of Rotations 55
Chapter III. GROUPS
1. Groups and Homomorphisms 59
2. Homogeneous Spaces 65
3. Crystallographic Groups 73
Chapter IV. CIRCLES
1. C/rc/es 85
2. rfe Fundamental Theorem 89
3. Theorems of Pappus, Desargues, and Pascal 98
Chapter V. METRIC GEOMETRY
1. ^rea 107
2. 77;e Pythagorean Theorem 119
3. 77ze Proportionality Theorem 126
4. The Theorems of Menelaus and Ceva 137
5. Power 146
xi
xii Contents
Chapter VI. SIMILITUDE
1. Homothety 152
2. Similitude 158
3. The Triangle 165
4. Three Circles 171
Chapter VII. GEOMETRIC INEQUALITIES
1. The Triangle Inequality 174
2. The Billiard Ball Problem 179
3. The Erdos Mordell Inequality 186
4. The Isoperimetric Inequality 189
Chapter VIII. CIRCULAR TRANSFORMATIONS
1. Circle Preserving Maps 198
2. Inversion 200
3. 77ze Grow/? o/ Circular Transformations 208
4. Geometry of the Circle 213
5. Applications to Metric Geometry 220
Chapter IX. HYPERBOLIC GEOMETRY
1. 77ie Hyperbolic Group 223
2. Products of Reflections 231
3. Area and Length 236
4. The Field of Ends 241
5. ^ Iwear Mode/ 249
6. Elliptic Geometry 251
Appendix. A NON ARCHIMEDEAN PLANE 260
References for Further Study 266
Solutions for Exercises 269
Index of Notations 280
Index of Groups 282
Lw? of Axioms 283
/Aufex 285 |
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| indexdate | 2024-10-03T16:00:09Z |
| institution | BVB |
| language | English |
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| physical | XII, 288 S. graph. Darst. |
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| spelling | Guggenheimer, Heinrich W. 1924-2021 Verfasser (DE-588)114374066 aut Plane geometry and its groups Heinrich W. Guggenheimer San Francisco [u.a.] Holden-Day 1967 XII, 288 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometry, Plane Group theory Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 Gruppentheorie (DE-588)4072157-7 s HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003852027&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Guggenheimer, Heinrich W. 1924-2021 Plane geometry and its groups Geometry, Plane Group theory Gruppentheorie (DE-588)4072157-7 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4072157-7 (DE-588)4020236-7 |
| title | Plane geometry and its groups |
| title_auth | Plane geometry and its groups |
| title_exact_search | Plane geometry and its groups |
| title_full | Plane geometry and its groups Heinrich W. Guggenheimer |
| title_fullStr | Plane geometry and its groups Heinrich W. Guggenheimer |
| title_full_unstemmed | Plane geometry and its groups Heinrich W. Guggenheimer |
| title_short | Plane geometry and its groups |
| title_sort | plane geometry and its groups |
| topic | Geometry, Plane Group theory Gruppentheorie (DE-588)4072157-7 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometry, Plane Group theory Gruppentheorie Geometrie |
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