Verfügbarkeit: Geometry & symmetry

Geometry & symmetry:

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Bibliographische Detailangaben
Hauptverfasser:	Kinsey, Laura Christine (VerfasserIn), Moore, Teresa E. (VerfasserIn), Prassidis, Stratos 1962- (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Hoboken, NJ Wiley 2011
Schlagworte:	Mechanics Geometry Symmetry (Mathematics) Symmetrie Geometrie
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XVII, 459 S. graph. Darst.
ISBN:	9780470499498 0470499494

Internformat

MARC


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Datensatz im Suchindex

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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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isbn	9780470499498 0470499494
language	English
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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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