Elementary geometry in hyperbolic space:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
de Gruyter
1989
|
| Series: | De Gruyter studies in mathematics
11 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 225 S. |
| ISBN: | 3110117347 0899254934 |
Staff View
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS /. PRELIMINARIES 1 1. QUATERNIONS 1 2. THE HYPERBOLIC FUNCTIONS
3 3. TRACE RELATIONS 8 4. THE FRACTIONAL LINEAR GROUP AND THE CROSS
RATIO 10 NOTES TO CHAPTER I 16 II. THE MOBIUS GROUP 17 1. SIMILARITY
TRANSFORMATIONS 17 2. THE EXTENDED SPACE. ORIENTATION. ANGULAR MEASURE
18 3. INVERSION 20 4. CIRCLE- AND SPHERE-PRESERVING TRANSFORMATIONS 22
5. THE MOBIUS GROUP OF THE UPPER HALF-SPACE 24 NOTES TO CHAPTER II 27
III. THE BASIC NOTIONS OF HYPERBOLIC GEOMETRY 28 1. LINES AND PLANES.
CONVEXITY 28 2. ORTHOGONALITY 31 3. THE INVARIANT RIEMANNIAN METRIC 34
4. THE HYPERBOLIC METRIC 36 5. TRANSFORMATION TO THE UNIT BALL 40 NOTES
TO CHAPTER III. 42 IV. THE ISOMETRY GROUP OF HYPERBOLIC SPACE 44 1.
CHARACTERIZATION OF THE ISOMETRY GROUP 44 2. CLASSIFICATION OF THE
MOTIONS 45 3. REVERSALS 48 4. THE ISOMETRY GROUP OF A PLANE 54 5. THE
SPHERICAL AND CYLINDRIC SURFACES 56 NOTES TO CHAPTER IV 60 V LINES 61 1.
LINE MATRICES 61 2. ORIENTED LINES 63 3. DOUBLE CROSSES 67 4.
TRANSVERSALS 70 5. PENCILS AND BUNDLES OF LINES 72 NOTES TO CHAPTER V 78
VI. RIGHT-ANGLED HEXAGONS 79 1. RIGHT-ANGLED HEXAGONS AND PENTAGONS 79
2. TRIGONOMETRIC RELATIONS FOR RIGHT-ANGLED HEXAGONS 81 3. TRIGONOMETRIC
RELATIONS FOR POLYGONS IN A PLANE 85 4. DETERMINATION OF A HEXAGON BY
THREE OF ITS SIDES 93 5. THE AMPLITUDES OF A RIGHT-ANGLED HEXAGON 102 6.
TRANSVERSALS OF A RIGHT-ANGLED HEXAGON 107 7. THE BISECTORS AND RADII OF
A RIGHT-ANGLED HEXAGON ILL 8. THE MEDIANS OF A RIGHT-ANGLED HEXAGON 123
9. THE ALTITUDES OF A RIGHT-ANGLED HEXAGON 127 NOTES TO CHAPTER VI 138
VII. POINTS AND PLANES 140 1. POINT AND PLANE MATRICES 140 2. INCIDENCE
AND ORTHOGONALITY 144 3. DISTANCES AND ANGLES 148 4. PENCILS OF POINTS
AND PLANES 155 5. BUNDLES OF POINTS AND PLANES 159 6. TETRAHEDRA 164
NOTES TO CHAPTER VII 174 VIII. SPHERICAL SURFACES 175 1. EQUATIONS OF
SPHERICAL SURFACES 175 2. AN INVARIANT OF A PAIR OF SPHERICAL SURFACES
177 3. THE POWER OF A POINT WITH RESPECT TO A SPHERICAL SURFACE 182 4.
THE RADICAL PLANE OF A PAIR OF SPHERICAL SURFACES 185 5. LINEAR FAMILIES
OF SPHERICAL SURFACES 191 NOTES TO CHAPTER VIII 201 IX. AREA AND VOLUME
202 1. VARIOUS COORDINATE SYSTEMS 202 2. AREA 206 3. VOLUME OF SOME
BODIES OF REVOLUTION 209 4. VOLUME OF POLYHEDRA 213 NOTES TO CHAPTER IX
220 REFERENCES 221 INDEX 223
|
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| institution | BVB |
| isbn | 3110117347 0899254934 |
| language | English |
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| physical | XI, 225 S. |
| publishDate | 1989 |
| publishDateSearch | 1989 |
| publishDateSort | 1989 |
| publisher | de Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| spelling | Fenchel, Werner 1905-1988 Verfasser (DE-588)117709980 aut Elementary geometry in hyperbolic space Berlin u.a. de Gruyter 1989 XI, 225 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 11 Hyperbolische Geometrie Hyperbolische Geometrie (DE-588)4161041-6 gnd rswk-swf Hyperbolische Geometrie (DE-588)4161041-6 s DE-604 De Gruyter studies in mathematics 11 (DE-604)BV000005407 11 OEBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001207156&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fenchel, Werner 1905-1988 Elementary geometry in hyperbolic space De Gruyter studies in mathematics Hyperbolische Geometrie Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| subject_GND | (DE-588)4161041-6 |
| title | Elementary geometry in hyperbolic space |
| title_auth | Elementary geometry in hyperbolic space |
| title_exact_search | Elementary geometry in hyperbolic space |
| title_full | Elementary geometry in hyperbolic space |
| title_fullStr | Elementary geometry in hyperbolic space |
| title_full_unstemmed | Elementary geometry in hyperbolic space |
| title_short | Elementary geometry in hyperbolic space |
| title_sort | elementary geometry in hyperbolic space |
| topic | Hyperbolische Geometrie Hyperbolische Geometrie (DE-588)4161041-6 gnd |
| topic_facet | Hyperbolische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001207156&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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| work_keys_str_mv | AT fenchelwerner elementarygeometryinhyperbolicspace |