Geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English French |
| Published: |
Berlin [u.a.]
Springer
2003
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | VI, 357 S. graph. Darst. |
| ISBN: | 3540434984 9783540434986 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometry |c Michèle Audin |
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Record in the Search Index
| _version_ | 1808226750633607168 |
|---|---|
| adam_text |
CONTENTS
INTRODUCTION
.
1
1.
THIS
IS
A
BOOK
.
1
2.
HOW
TO
USE
THIS
BOOK
.
2
3.
ABOUT
THE
ENGLISH
EDITION
.
3
4.
ACKNOWLEDGEMENTS
.
3
I.
AFFINE
GEOMETRY
.
7
1.
AFFINE
SPACES
.
7
2.
AFFINE
MAPPINGS
.
14
3.
USING
AFFINE
MAPPINGS:
THREE
THEOREMS
IN
PLANE
GEOMETRY
.
23
4.
APPENDIX:
A
FEW
WORDS
ON
BARYCENTERS
.
26
5.
APPENDIX:
THE
NOTION
OF
CONVEXITY
.
28
6.
APPENDIX:
CARTESIAN
COORDINATES
IN
AFFINE
GEOMETRY
.
30
EXERCISES
AND
PROBLEMS
.
32
II.
EUCLIDEAN
GEOMETRY,
GENERALITIES
.
43
1.
EUCLIDEAN
VECTOR
SPACES,
EUCLIDEAN
AFFINE
SPACES
.
43
2.
THE
STRUCTURE
OF
ISOMETRIES
.
46
3.
THE
GROUP
OF
LINEAR
ISOMETRIES
.
52
EXERCISES
AND
PROBLEMS
.
58
III.
EUCLIDEAN
GEOMETRY
IN
THE
PLANE
.
65
1.
ANGLES
.
65
2.
ISOMETRIES
AND
RIGID
MOTIONS
IN
THE
PLANE
.
76
3.
PLANE
SIMILARITIES
.
79
4.
INVERSIONS
AND
PENCILS
OF
CIRCLES
.
83
EXERCISES
AND
PROBLEMS
.
98
IV.
EUCLIDEAN
GEOMETRY
IN
SPACE
.
113
1.
ISOMETRIES
AND
RIGID
MOTIONS
IN
SPACE
.
113
2.
THE
VECTOR
PRODUCT,
WITH
AREA
COMPUTATIONS
.
116
3.
SPHERES,
SPHERICAL
TRIANGLES
.
120
4.
POLYHEDRA,
EULER
FORMULA
.
122
5.
REGULAR
POLYHEDRA
.
126
EXERCISES
AND
PROBLEMS
.
130
V.
PROJECTIVE
GEOMETRY
.
143
1.
PROJECTIVE
SPACES
.
143
2.
PROJECTIVE
SUBSPACES
.
145
VI
CONTENTS
3.
AFFINE
VS
PROJECTIVE
.
147
4.
PROJECTIVE
DUALITY
.
153
5.
PROJECTIVE
TRANSFORMATIONS
.
155
6.
THE
CROSS-RATIO
.
161
7.
THE
COMPLEX
PROJECTIVE
LINE
AND
THE
CIRCULAR
GROUP
.
164
EXERCISES
AND
PROBLEMS
.
170
VI.
CONICS
AND
QUADRICS
.
183
1.
AFFINE
QUADRICS
AND
CONICS,
GENERALITIES
.
184
2.
CLASSIFICATION
AND
PROPERTIES
OF
AFFINE
CONICS
.
189
3.
PROJECTIVE
QUADRICS
AND
CONICS
.
200
4.
THE
CROSS-RATIO
OF
FOUR
POINTS
ON
A
CONIC
AND
PASCAL
'
S
THEOREM
.
208
5.
AFFINE
QUADRICS,
VIA
PROJECTIVE
GEOMETRY
.
210
6.
EUCLIDEAN
CONICS,
VIA
PROJECTIVE
GEOMETRY
.
215
7.
CIRCLES,
INVERSIONS,
PENCILS
OF
CIRCLES
.
219
8.
APPENDIX:
A
SUMMARY
OF
QUADRATIC
FORMS
.
225
EXERCISES
AND
PROBLEMS
.
233
VII.
CURVES,
ENVELOPES,
EVOLUTES
.
247
1.
THE
ENVELOPE
OF
A
FAMILY
OF
LINES
IN
THE
PLANE
.
248
2.
THE
CURVATURE
OF
A
PLANE
CURVE
.
254
3.
EVOLUTES
.
256
4.
APPENDIX:
A
FEW
WORDS
ON
PARAMETRIZED
CURVES
.
258
EXERCISES
AND
PROBLEMS
.
261
VIII.
SURFACES
IN
3-DIMENSIONAL
SPACE
.
269
1.
EXAMPLES
OF
SURFACES
IN
3-DIMENSIONAL
SPACE
.
269
2.
DIFFERENTIAL
GEOMETRY
OF
SURFACES
IN
SPACE
.
271
3.
METRIC
PROPERTIES
OF
SURFACES
IN
THE
EUCLIDEAN
SPACE
.
284
4.
APPENDIX:
A
FEW
FORMULAS
.
294
EXERCISES
AND
PROBLEMS
.
296
A
FEW
HINTS
AND
SOLUTIONS
TO
EXERCISES
.
301
CHAPTER
I
.
301
CHAPTER
II
.
304
CHAPTER
III
.
306
CHAPTER
IV
.
314
CHAPTER
V
.
321
CHAPTER
VI
.
326
CHAPTER
VII
.
332
CHAPTER
VIII
.
336
BIBLIOGRAPHY
.
343
INDEX
.
347 |
| any_adam_object | 1 |
| author | Audin, Michèle 1954- |
| author_GND | (DE-588)14151552X |
| author_facet | Audin, Michèle 1954- |
| author_role | aut |
| author_sort | Audin, Michèle 1954- |
| author_variant | m a ma |
| building | Verbundindex |
| bvnumber | BV014605587 |
| callnumber-first | Q - Science |
| callnumber-label | QA445 |
| callnumber-raw | QA445 |
| callnumber-search | QA445 |
| callnumber-sort | QA 3445 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| classification_tum | MAT 500f |
| ctrlnum | (OCoLC)248915808 (DE-599)BVBBV014605587 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| genre_facet | Lehrbuch |
| id | DE-604.BV014605587 |
| illustrated | Illustrated |
| indexdate | 2024-08-24T00:30:09Z |
| institution | BVB |
| isbn | 3540434984 9783540434986 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009928563 |
| oclc_num | 248915808 |
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| physical | VI, 357 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
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| spelling | Audin, Michèle 1954- Verfasser (DE-588)14151552X aut Géométrie Geometry Michèle Audin Berlin [u.a.] Springer 2003 VI, 357 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Differentialgeometrie - Lehrbuch Geometrie - Lehrbuch Geometry Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Geometrie (DE-588)4020236-7 s DE-604 Differentialgeometrie (DE-588)4012248-7 s http://www3.ub.tu-berlin.de/ihv/000861767.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009928563&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Audin, Michèle 1954- Geometry Differentialgeometrie - Lehrbuch Geometrie - Lehrbuch Geometry Differentialgeometrie (DE-588)4012248-7 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4020236-7 (DE-588)4123623-3 |
| title | Geometry |
| title_alt | Géométrie |
| title_auth | Geometry |
| title_exact_search | Geometry |
| title_full | Geometry Michèle Audin |
| title_fullStr | Geometry Michèle Audin |
| title_full_unstemmed | Geometry Michèle Audin |
| title_short | Geometry |
| title_sort | geometry |
| topic | Differentialgeometrie - Lehrbuch Geometrie - Lehrbuch Geometry Differentialgeometrie (DE-588)4012248-7 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Differentialgeometrie - Lehrbuch Geometrie - Lehrbuch Geometry Differentialgeometrie Geometrie Lehrbuch |
| url | http://www3.ub.tu-berlin.de/ihv/000861767.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009928563&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT audinmichele geometrie AT audinmichele geometry |
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