The universe of quadrics:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Springer
[2020]
|
| Schlagworte: | |
| Online-Zugang: | Inhaltstext http://www.springer.com Inhaltsverzeichnis Inhaltsverzeichnis |
| Beschreibung: | viii, 606 Seiten Illustrationen, Diagramme 24 cm, 1392 g |
| ISBN: | 9783662610527 3662610523 |
Internformat
MARC
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| 100 | 1 | |a Odehnal, Boris |d 1973- |0 (DE-588)109677870X |4 aut | |
| 245 | 1 | 0 | |a The universe of quadrics |c Boris Odehnal ; Hellmuth Stachel ; Georg Glaeser |
| 264 | 1 | |a Berlin |b Springer |c [2020] | |
| 300 | |a viii, 606 Seiten |b Illustrationen, Diagramme |c 24 cm, 1392 g | ||
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| 700 | 1 | |a Glaeser, Georg |d 1955- |0 (DE-588)105717746 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-033212224 | ||
Datensatz im Suchindex
| _version_ | 1804183375976595456 |
|---|---|
| adam_text | TABLE
OF
CONTENTS
1
INTRODUCTION
1
2
QUADRICS
IN
EUCLIDEAN
3-SPACE
7
2.1
ELLIPSOIDS
.......................................................................................
11
2.2
HYPERBOLOIDS
.................................................................................
26
2.3
PARABOLOIDS
....................................................................................
52
2.4
SHARED
METRIC
PROPERTIES
............................................................
70
2.5 FLEXIBLE
MODELS
OF
QUADRICS
.........................................................
80
3
LINEAR
ALGEBRAIC
APPROACH
TO
QUADRICS
91
3.1
PRINCIPAL-AXES
TRANSFORMATION
IN
E
N
..........................................
92
3.2
QUADRICS
IN
THE
EUCLIDEAN
PLANE
AND
3-SPACE
...............................
112
4
PROJECTIVE
AND
AFFINE
QUADRICS
119
4.1
THREE-DIMENSIONAL
PROJECTIVE
GEOMETRY
........................................
120
4.2
POLARITIES
...........................................................................................
137
4.3
THE
PROJECTIVE
N-SPACE
...................................................................
157
4.4
PROJECTIVE
MODELS
OF
NON-EUCLIDEAN
GEOMETRIES
.........................
165
5
PENCILS
OF
QUADRICS
177
5.1
DEFINITION
OF
PENCILS,
BASICS,
INVARIANTS
........................................
179
5.2
PRINCIPAL
POINTS
AND
COMMON
POLAR
TETRAHEDRON
.........................
191
5.3
DESARGUES
*
S
INVOLUTION
THEOREM
....................................................
191
5.4
DUAL
PENCILS
.....................................................................................
193
5.5
SPECIAL
PENCILS
..................................................................................
195
6
CUBIC
AND
QUARTIC
SPACE
CURVES
AS
INTERSECTIONS
OF
QUADRICS
205
6.1
STANDARD
CUBIC
..................................................................................
207
6.2
QUADRICS
CONTAINING
A
CUBIC
..........................................................
212
6.3
OSCULATING
PLANES
OF
A
CUBIC
..........................................................
226
6.4
AN
ANALOGUE
TO
STEINER
*
S
GENERATION
..............................................
234
6.5
CHORDS
OF
A
CUBIC
............................................................................
236
6.6
THE
CUBIC
OF
COINCIDENCE
-
POINTS
WITH
COINCIDING
IMAGES
.
.
238
VIII
TABLE
OF
CONTENTS
6.7
PROJECTION
WITH
THE
CHORDS
OF
A
CUBIC
...........................................
241
6.8
CROSS
RATIOS
AND
PROJECTIVE
AUTOMORPHISMS
..................................
245
6.9
QUARTIC
SPACE
CURVES
......................................................................
247
7
CONFOCAL
QUADRICS
279
7.1
THE
FAMILIES
OF
CONFOCAL
QUADRICS
.............................................
280
7.2
IVORY
*
S
THEOREM
AND
BIPARTITE
FRAMEWORKS
..............................
294
7.3
STRING
CONSTRUCTIONS
OF
QUADRICS
................................................
319
8
SPECIAL
PROBLEMS
327
8.1
REFLECTION
IN
QUADRATIC
SURFACES
................................................
328
8.2
MOVING
CONICS
ON
QUADRICS
.........................................................
340
8.3
QUADRICS
ON
SKEW
QUADRILATERALS
................................................
360
8.4
RATIONAL
PARAMETRIZATIONS,
QUADRICS
AS
BEZIER
SURFACES
....
368
9 QUADRICS
AND
DIFFERENTIAL
GEOMETRY
383
9.1
CURVATURE
FUNCTIONS
ON
QUADRICS
....................................................
385
9.2
QUADRICS
AS
RULED
SURFACES
.............................................................
398
9.3
LIE S
OSCULATING
QUADRIC
...................................................................
413
9.4
NORMALS
TO
A
QUADRIC
......................................................................
417
9.5
CURVES
OF
CONSTANT
SLOPE
ON
QUADRICS
...........................................
457
9.6
GEODESICS
ON
QUADRICS
......................................................................
467
10 LINE GEOMETRY,
SPHERE
GEOMETRY,
KINEMATICS
475
10.1
LINE
GEOMETRY
..................................................................................477
10.2
SPHERE
GEOMETRY
............................................................................
519
10.3
KINEMATICS
........................................................................................
533
11
SOME
GENERALIZATIONS
OF
QUADRICS
561
11.1
MULLER
*
S
CUBIC
SURFACE
......................................................................
563
11.2
SUPERQUADRICS
..................................................................................
567
11.3
SURFACES
OF
OSCULATING
CIRCLES
..........................................................
574
11.4
PLUCKER
*
S
CONOID
...............................................................................
577
11.5
SUM
AND
PRODUCT
OF
DISTANCES
TO
FIXED
POINTS
............................
579
REFERENCES
587
INDEX
595
|
| adam_txt |
TABLE
OF
CONTENTS
1
INTRODUCTION
1
2
QUADRICS
IN
EUCLIDEAN
3-SPACE
7
2.1
ELLIPSOIDS
.
11
2.2
HYPERBOLOIDS
.
26
2.3
PARABOLOIDS
.
52
2.4
SHARED
METRIC
PROPERTIES
.
70
2.5 FLEXIBLE
MODELS
OF
QUADRICS
.
80
3
LINEAR
ALGEBRAIC
APPROACH
TO
QUADRICS
91
3.1
PRINCIPAL-AXES
TRANSFORMATION
IN
E
N
.
92
3.2
QUADRICS
IN
THE
EUCLIDEAN
PLANE
AND
3-SPACE
.
112
4
PROJECTIVE
AND
AFFINE
QUADRICS
119
4.1
THREE-DIMENSIONAL
PROJECTIVE
GEOMETRY
.
120
4.2
POLARITIES
.
137
4.3
THE
PROJECTIVE
N-SPACE
.
157
4.4
PROJECTIVE
MODELS
OF
NON-EUCLIDEAN
GEOMETRIES
.
165
5
PENCILS
OF
QUADRICS
177
5.1
DEFINITION
OF
PENCILS,
BASICS,
INVARIANTS
.
179
5.2
PRINCIPAL
POINTS
AND
COMMON
POLAR
TETRAHEDRON
.
191
5.3
DESARGUES
*
S
INVOLUTION
THEOREM
.
191
5.4
DUAL
PENCILS
.
193
5.5
SPECIAL
PENCILS
.
195
6
CUBIC
AND
QUARTIC
SPACE
CURVES
AS
INTERSECTIONS
OF
QUADRICS
205
6.1
STANDARD
CUBIC
.
207
6.2
QUADRICS
CONTAINING
A
CUBIC
.
212
6.3
OSCULATING
PLANES
OF
A
CUBIC
.
226
6.4
AN
ANALOGUE
TO
STEINER
*
S
GENERATION
.
234
6.5
CHORDS
OF
A
CUBIC
.
236
6.6
THE
CUBIC
OF
COINCIDENCE
-
POINTS
WITH
COINCIDING
IMAGES
.
.
238
VIII
TABLE
OF
CONTENTS
6.7
PROJECTION
WITH
THE
CHORDS
OF
A
CUBIC
.
241
6.8
CROSS
RATIOS
AND
PROJECTIVE
AUTOMORPHISMS
.
245
6.9
QUARTIC
SPACE
CURVES
.
247
7
CONFOCAL
QUADRICS
279
7.1
THE
FAMILIES
OF
CONFOCAL
QUADRICS
.
280
7.2
IVORY
*
S
THEOREM
AND
BIPARTITE
FRAMEWORKS
.
294
7.3
STRING
CONSTRUCTIONS
OF
QUADRICS
.
319
8
SPECIAL
PROBLEMS
327
8.1
REFLECTION
IN
QUADRATIC
SURFACES
.
328
8.2
MOVING
CONICS
ON
QUADRICS
.
340
8.3
QUADRICS
ON
SKEW
QUADRILATERALS
.
360
8.4
RATIONAL
PARAMETRIZATIONS,
QUADRICS
AS
BEZIER
SURFACES
.
368
9 QUADRICS
AND
DIFFERENTIAL
GEOMETRY
383
9.1
CURVATURE
FUNCTIONS
ON
QUADRICS
.
385
9.2
QUADRICS
AS
RULED
SURFACES
.
398
9.3
LIE'S
OSCULATING
QUADRIC
.
413
9.4
NORMALS
TO
A
QUADRIC
.
417
9.5
CURVES
OF
CONSTANT
SLOPE
ON
QUADRICS
.
457
9.6
GEODESICS
ON
QUADRICS
.
467
10 LINE GEOMETRY,
SPHERE
GEOMETRY,
KINEMATICS
475
10.1
LINE
GEOMETRY
.477
10.2
SPHERE
GEOMETRY
.
519
10.3
KINEMATICS
.
533
11
SOME
GENERALIZATIONS
OF
QUADRICS
561
11.1
MULLER
*
S
CUBIC
SURFACE
.
563
11.2
SUPERQUADRICS
.
567
11.3
SURFACES
OF
OSCULATING
CIRCLES
.
574
11.4
PLUCKER
*
S
CONOID
.
577
11.5
SUM
AND
PRODUCT
OF
DISTANCES
TO
FIXED
POINTS
.
579
REFERENCES
587
INDEX
595 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Odehnal, Boris 1973- Stachel, Hellmuth 1942- Glaeser, Georg 1955- |
| author_GND | (DE-588)109677870X (DE-588)1027861474 (DE-588)105717746 |
| author_facet | Odehnal, Boris 1973- Stachel, Hellmuth 1942- Glaeser, Georg 1955- |
| author_role | aut aut aut |
| author_sort | Odehnal, Boris 1973- |
| author_variant | b o bo h s hs g g gg |
| building | Verbundindex |
| bvnumber | BV047828951 |
| ctrlnum | (OCoLC)1199699491 (DE-599)DNB1202083714 |
| dewey-full | 516.36 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.36 |
| dewey-search | 516.36 |
| dewey-sort | 3516.36 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV047828951 |
| illustrated | Illustrated |
| index_date | 2024-07-03T19:08:48Z |
| indexdate | 2024-07-10T09:22:27Z |
| institution | BVB |
| isbn | 9783662610527 3662610523 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-033212224 |
| oclc_num | 1199699491 |
| open_access_boolean | |
| owner | DE-83 |
| owner_facet | DE-83 |
| physical | viii, 606 Seiten Illustrationen, Diagramme 24 cm, 1392 g |
| publishDate | 2020 |
| publishDateSearch | 2020 |
| publishDateSort | 2020 |
| publisher | Springer |
| record_format | marc |
| spelling | Odehnal, Boris 1973- (DE-588)109677870X aut The universe of quadrics Boris Odehnal ; Hellmuth Stachel ; Georg Glaeser Berlin Springer [2020] viii, 606 Seiten Illustrationen, Diagramme 24 cm, 1392 g txt rdacontent n rdamedia nc rdacarrier Quadrik (DE-588)4291376-7 gnd rswk-swf Quadrik (DE-588)4291376-7 s DE-604 Stachel, Hellmuth 1942- (DE-588)1027861474 aut Glaeser, Georg 1955- (DE-588)105717746 aut Erscheint auch als Online-Ausgabe Odehnal, Boris, 1973- The Universe of Quadrics 1st edition 2020 Berlin : Springer Berlin Heidelberg, 2020 Online-Ressource Erscheint auch als Druck-Ausgabe 9783662610558 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=72d349bc3bd849f3a13f40e39ded89c2&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com B:DE-101 application/pdf https://d-nb.info/1202083714/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033212224&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Odehnal, Boris 1973- Stachel, Hellmuth 1942- Glaeser, Georg 1955- The universe of quadrics Quadrik (DE-588)4291376-7 gnd |
| subject_GND | (DE-588)4291376-7 |
| title | The universe of quadrics |
| title_auth | The universe of quadrics |
| title_exact_search | The universe of quadrics |
| title_exact_search_txtP | The universe of quadrics |
| title_full | The universe of quadrics Boris Odehnal ; Hellmuth Stachel ; Georg Glaeser |
| title_fullStr | The universe of quadrics Boris Odehnal ; Hellmuth Stachel ; Georg Glaeser |
| title_full_unstemmed | The universe of quadrics Boris Odehnal ; Hellmuth Stachel ; Georg Glaeser |
| title_short | The universe of quadrics |
| title_sort | the universe of quadrics |
| topic | Quadrik (DE-588)4291376-7 gnd |
| topic_facet | Quadrik |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=72d349bc3bd849f3a13f40e39ded89c2&prov=M&dok_var=1&dok_ext=htm http://www.springer.com https://d-nb.info/1202083714/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033212224&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT odehnalboris theuniverseofquadrics AT stachelhellmuth theuniverseofquadrics AT glaesergeorg theuniverseofquadrics |