Geometry & symmetry:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2011
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 459 S. graph. Darst. |
| ISBN: | 9780470499498 0470499494 |
Staff View
MARC
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| 100 | 1 | |a Kinsey, Laura Christine |e Verfasser |0 (DE-588)113682344 |4 aut | |
| 245 | 1 | 0 | |a Geometry & symmetry |c L. Christine Kinsey ; Teresa E. Moore ; Efstratios Prassidis |
| 246 | 1 | 3 | |a Geometry and symmetry |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2011 | |
| 300 | |a XVII, 459 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Symmetry (Mathematics) | |
| 650 | 4 | |a Geometry | |
| 650 | 4 | |a Mechanics | |
| 650 | 4 | |a Symmetry (Mathematics) | |
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| 700 | 1 | |a Prassidis, Stratos |d 1962- |e Verfasser |0 (DE-588)113951485 |4 aut | |
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Record in the Search Index
| _version_ | 1804141159067418624 |
|---|---|
| adam_text | Contents
Preface
I Euclidean geometry l
1
A brief history of early geometry
3
1.1
Prehellenistic mathematics
....................................................3
1.2
Greek mathematics before Euclid
...............................................5
1.3
Euclid
.......................................................................9
1.4
The Elements
................................................................11
1.5
Projects
.....................................................................14
2
Book I of Euclid s The Elements
15
2.1
Preliminaries
................................................................15
2.2
Propositions I.5-I.26: Triangles
...............................................39
2.3
Propositions
1.27—1.32:
Parallel lines
...........................................54
2.4
Propositions
1.33—1.46:
Area
..................................................59
2.5
The Pythagorean Theorem
...................................................64
2.6
Hubert s axioms for euclidean geometry
.......................................71
2.7
Distance and geometry
.......................................................75
2.8
Projects
.....................................................................78
3
More euclidean geometry
80
3.1
Circle theorems
.............................................................80
3.2
Similarity
...................................................................88
3.3
More triangle theorems
......................................................92
3.4
Inversion in a circle
.........................................................101
3.5
Projects
...................................................................107
4
Constructions
4.1
Straightedge and compass constructions
......................................109
4.2
Trisections
.................................................................
121
4.3
Constructions with compass alone
...........................................124
CONTENTS
4.4
Theoretical
origami
.........................................................129
4.5
Knots and star polygons
.....................................................139
4.6
Linkages
...................................................................144
4.7
Projects
...................................................................153
II Noneuclidean geometries
155
5
Neutral geometry
157
5.1
Views on geometry
.........................................................157
5.2
Neutral geometry
...........................................................159
5.3
Alternate parallel postulates
.................................................169
5.4
Projects
...................................................................176
6
Hyperbolic geometry
178
6.1
The history of hyperbolic geometry
..........................................178
6.2
Strange new universe
.......................................................181
6.3
Models of the hyperbolic plane
..............................................186
6.4
Consistency of geometries
...................................................197
6.5
Asymptotic parallels
........................................................199
6.6
Biangles
...................................................................203
6.7
Divergent parallels
..........................................................208
6.8
Triangles in hyperbolic space
................................................210
6.9
Projects
...................................................................218
7
Other geometries
220
7.1
Exploring the geometry of a sphere
...........................................220
7.2
Elliptic geometry
...........................................................226
7.3
Comparative geometry
......................................................239
7.4
Area and defect
.............................................................242
7.5
Taxicab geometry
...........................................................254
7.6
Finite geometries
...........................................................258
7.7
Projects
...................................................................264
III Symmetry
265
8
Isometries
267
8.1
Transformation geometry
...................................................267
CONTENTS
8.2 Rosette
groups
.............................................................289
8.3
Frieze patterns
.............................................................294
8.4
Wallpaper patterns
.........................................................30
1
8.5
Isometries in hyperbolic geometry
...........................................314
8.6
Projects
...................................................................319
9
Tilings
320
9.1
Tilings on the plane
.........................................................320
9.2
Tilings by irregular tiles
.....................................................327
9.3
Tilings of noneuclidean spaces
...............................................341
9.4
Penrose tilings
.............................................................345
9.5
Projects
...................................................................355
10
Geometry in three dimensions
357
10.1
Euclidean geometry in three dimensions
....................................357
10.2
Polyhedra
...............................................................369
10.3
Volume
.................................................................387
10.4
Infinite polyhedra
........................................................393
10.5
Isometries in three dimensions
............................................397
10.6
Symmetries of polyhedra
..................................................406
10.7
Four-dimensional figures
.................................................412
10.8
Projects
.................................................................417
Appendix A Logic and proofs
419
A.I Mathematical systems
.....................................................419
A.2 Logic
....................................................................420
A.3 Structuring proofs
........................................................424
A.4 Inventing proofs
..........................................................427
A.5 Writing proofs
............................................................428
A.6 Geometric diagrams
.......................................................429
A.7 Using geometric software
..................................................431
A.8 Van
Hiele
levels of geometric thought
.......................................431
Appendix
В
Postulates and theorems
434
B.I Postulates
................................................................
434
B.2 Book I of Euclid s The Elements
.............................................436
B.3 More euclidean geometry
..................................................439
CONTENTS
B.4
Constructions
............................................................441
B.5 Neutral
geometry
.........................................................442
B.6
Hyperbolic geometry
......................................................443
B.7 Other geometries
.........................................................445
B.8 Isometries
................................................................446
B.9 Tilings
...................................................................448
B.10 Geometry in three dimensions
..............................................448
Bibliography
450
Index
455
|
| any_adam_object | 1 |
| author | Kinsey, Laura Christine Moore, Teresa E. Prassidis, Stratos 1962- |
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| ctrlnum | (OCoLC)699525089 (DE-599)HBZHT016534893 |
| 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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| illustrated | Illustrated |
| indexdate | 2024-07-09T22:11:26Z |
| institution | BVB |
| isbn | 9780470499498 0470499494 |
| language | English |
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| physical | XVII, 459 S. graph. Darst. |
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| publisher | Wiley |
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| spelling | Kinsey, Laura Christine Verfasser (DE-588)113682344 aut Geometry & symmetry L. Christine Kinsey ; Teresa E. Moore ; Efstratios Prassidis Geometry and symmetry Hoboken, NJ Wiley 2011 XVII, 459 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mechanics Geometry Symmetry (Mathematics) Symmetrie (DE-588)4058724-1 gnd rswk-swf Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s Symmetrie (DE-588)4058724-1 s DE-604 Moore, Teresa E. Verfasser (DE-588)139623159 aut Prassidis, Stratos 1962- Verfasser (DE-588)113951485 aut Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018984793&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kinsey, Laura Christine Moore, Teresa E. Prassidis, Stratos 1962- Geometry & symmetry Mechanics Geometry Symmetry (Mathematics) Symmetrie (DE-588)4058724-1 gnd Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4020236-7 |
| title | Geometry & symmetry |
| title_alt | Geometry and symmetry |
| title_auth | Geometry & symmetry |
| title_exact_search | Geometry & symmetry |
| title_full | Geometry & symmetry L. Christine Kinsey ; Teresa E. Moore ; Efstratios Prassidis |
| title_fullStr | Geometry & symmetry L. Christine Kinsey ; Teresa E. Moore ; Efstratios Prassidis |
| title_full_unstemmed | Geometry & symmetry L. Christine Kinsey ; Teresa E. Moore ; Efstratios Prassidis |
| title_short | Geometry & symmetry |
| title_sort | geometry symmetry |
| topic | Mechanics Geometry Symmetry (Mathematics) Symmetrie (DE-588)4058724-1 gnd Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Mechanics Geometry Symmetry (Mathematics) Symmetrie Geometrie |
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