Verfügbarkeit: Continuous symmetry | Technische Universität München

Continuous symmetry: from Euclid to Klein

Gespeichert in:

Bibliographische Detailangaben
Beteiligte Personen:	Barker, William H. 1946- (VerfasserIn), Howe, Roger 1945- (VerfasserIn)
Format:	Buch
Sprache:	Englisch
Veröffentlicht:	Providence, Rhode Island American Mathematical Society [2007]
Schlagwörter:	Geometry, Plane Group theory Symmetry groups Euklidische Geometrie
Links:	http://www.loc.gov/catdir/toc/fy0803/2007060795.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016770100&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	xxi, 546 Seiten Diagramme
ISBN:	9780821839003 0821839004

Internformat

MARC


LEADER	00000nam a2200000 c 4500
001	BV035102132
003	DE-604
005	20230824
007	t\|
008	081015s2007 xxu\|\|\|\| \|\|\|\| 00\|\|\| eng d
010			\|a 2007060795
020			\|a 9780821839003 \|9 978-0-8218-3900-3
020			\|a 0821839004 \|9 0-8218-3900-4
035			\|a (OCoLC)150256520
035			\|a (DE-599)BVBBV035102132
040			\|a DE-604 \|b ger \|e rda
041	0		\|a eng
044			\|a xxu \|c US
049			\|a DE-19 \|a DE-634 \|a DE-824 \|a DE-11 \|a DE-384
050		0	\|a QA455
082	0		\|a 516.22 \|2 22
084			\|a SK 380 \|0 (DE-625)143235: \|2 rvk
100	1		\|a Barker, William H. \|d 1946- \|e Verfasser \|0 (DE-588)141066091 \|4 aut
245	1	0	\|a Continuous symmetry \|b from Euclid to Klein \|c William Barker, Roger Howe
264		1	\|a Providence, Rhode Island \|b American Mathematical Society \|c [2007]
264		4	\|c © 2007
300			\|a xxi, 546 Seiten \|b Diagramme
336			\|b txt \|2 rdacontent
337			\|b n \|2 rdamedia
338			\|b nc \|2 rdacarrier
650		4	\|a Geometry, Plane
650		4	\|a Group theory
650		4	\|a Symmetry groups
650	0	7	\|a Euklidische Geometrie \|0 (DE-588)4137555-5 \|2 gnd \|9 rswk-swf
689	0	0	\|a Euklidische Geometrie \|0 (DE-588)4137555-5 \|D s
689	0		\|5 DE-604
700	1		\|a Howe, Roger \|d 1945- \|e Verfasser \|0 (DE-588)171158407 \|4 aut
776	0	8	\|i Erscheint auch als \|n Online-Ausgabe \|z 978-1-4704-1197-8
856	4		\|u http://www.loc.gov/catdir/toc/fy0803/2007060795.html \|3 Table of contents
856	4	2	\|m GBV Datenaustausch \|q application/pdf \|u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016770100&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA \|3 Inhaltsverzeichnis
943	1		\|a oai:aleph.bib-bvb.de:BVB01-016770100

Datensatz im Suchindex

_version_	1819263240344961024
adam_text	CONTINUOUS SYMMETRY FROM EUCLID TO KLEIN WILLIAM BARKER ROGER HOWE »AMS AMERICAN MATHEMATICAL SOCIETY CONTENTS INSTRUCTOR PREFACE IX STUDENT PREFACE XIII ACKNOWLEDGMENTS XIX I. FOUNDATIONS OF GEOMETRY IN THE PLANE 1.1. THE REAL NUMBERS 1 1.2. THE INCIDENCE AXIOMS 6 1.3. DISTANCE AND THE RULER AXIOM 17 1.4. BETWEENNESS 22 1.5. THE PLANE SEPARATION AXIOM 27 1.6. THE ANGULAR MEASURE AXIOMS 34 1.7. TRIANGLES AND THE SAS AXIOM 46 1.8. GEOMETRIC INEQUALITIES 56 1.9. PARALLELISM 62 1.10. THE PARALLEL POSTULATE 70 1.11. DIRECTED ANGLE MEASURE AND RAY TRANSLATION 84 1.12. SIMILARITY 94 1.13. CIRCLES 110 1.14. BOLZANO S THEOREM 115 1.15. AXIOMS FOR THE EUCLIDEAN PLANE 119 II. ISOMETRIES IN THE PLANE: PRODUCTS OF REFLECTIONS 11.1. TRANSFORMATIONS IN THE PLANE 121 11.2. ISOMETRIES IN THE PLANE 135 11.3. COMPOSITION AND INVERSION 146 11.4. FIXED POINTS AND THE FIRST STRUCTURE THEOREM 156 11.5. TRIANGLE CONGRUENCE AND ISOMETRIES 161 III. ISOMETRIES IN THE PLANE: CLASSIFICATION AND STRUCTURE 111.1. TWO REFLECTIONS: TRANSLATIONS AND ROTATIONS 165 111.2. GLIDE REFLECTIONS 181 111.3. THE CLASSIFICATION THEOREM 188 111.4. ORIENTATION 191 111.5. GROUPS OF TRANSFORMATIONS 199 111.6. THE SECOND STRUCTURE THEOREM 206 111.7. ROTATION ANGLES 211 III CONTENTS IV. SIMILARITIES IN THE PLANE IV. 1. ELEMENTARY PROPERTIES OF SIMILARITIES 217 IV.2. DILATIONS AS SIMILARITIES 224 IV.3. THE STRUCTURE OF SIMILARITIES 231 IV.4. ORIENTATION AND ROTATION ANGLES 235 IV.5. FIXED POINTS FOR SIMILARITIES 240 V. CONJUGACY AND GEOMETRIC EQUIVALENCE V.I. CONGRUENCE AND GEOMETRIC EQUIVALENCE 251 V.2. GEOMETRIC EQUIVALENCE OF TRANSFORMATIONS: CONJUGACY 256 V.3. GEOMETRIC EQUIVALENCE UNDER SIMILARITIES 266 V.4. EUCLIDEAN GEOMETRY DERIVED FROM TRANSFORMATIONS 276 VI. APPLICATIONS TO PLANE GEOMETRY VI. 1. SYMMETRY IN EARLY GEOMETRY 287 VI.2. THE CLASSICAL COINCIDENCES 292 VI.3. DILATION BY MINUS TWO AROUND THE CENTROID 298 VI.4. REFLECTIONS, LIGHT, AND DISTANCE 309 VI.5. FAGNANO S PROBLEM AND THE ORTHIC TRIANGLE 315 VI.6. THE FERMAT PROBLEM 322 VI.7. THE CIRCLE OF APOLLONIUS 340 VII. SYMMETRIC FIGURES IN THE PLANE VII. 1. SYMMETRY GROUPS 347 VII.2. INVARIANT SETS AND ORBITS 356 VII.3. BOUNDED FIGURES IN THE PLANE 363 VIII. FRIEZE AND WALLPAPER GROUPS VIII. 1. POINT GROUPS AND TRANSLATION SUBGROUPS 376 VIII.2. FRIEZE GROUPS 399 VIII.3. TWO-DIMENSIONAL TRANSLATION LATTICES 416 VIII.4. WALLPAPER GROUPS 439 IX. AREA, VOLUME, AND SCALING IX. 1. LENGTH OF CURVES , 459 IX.2. AREA OF POLYGONAL REGIONS: BASIC PROPERTIES 467 IX.3. AREA AND EQUIDECOMPOSABILITY 482 IX.4. AREA BY APPROXIMATION 487 IX.5. AREA AND SIMILARITY 505 IX.6. SCALING AND DIMENSION 520 REFERENCES 531 INDEX 533
any_adam_object	1
author	Barker, William H. 1946- Howe, Roger 1945-
author_GND	(DE-588)141066091 (DE-588)171158407
author_facet	Barker, William H. 1946- Howe, Roger 1945-
author_role	aut aut
author_sort	Barker, William H. 1946-
author_variant	w h b wh whb r h rh
building	Verbundindex
bvnumber	BV035102132
callnumber-first	Q - Science
callnumber-label	QA455
callnumber-raw	QA455
callnumber-search	QA455
callnumber-sort	QA 3455
callnumber-subject	QA - Mathematics
classification_rvk	SK 380
ctrlnum	(OCoLC)150256520 (DE-599)BVBBV035102132
dewey-full	516.22
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	516 - Geometry
dewey-raw	516.22
dewey-search	516.22
dewey-sort	3516.22
dewey-tens	510 - Mathematics
discipline	Mathematik
format	Book
fullrecord	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01755nam a2200457 c 4500</leader><controlfield tag="001">BV035102132</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20230824 </controlfield><controlfield tag="007">t\|</controlfield><controlfield tag="008">081015s2007 xxu\|\|\|\| \|\|\|\| 00\|\|\| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2007060795</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780821839003</subfield><subfield code="9">978-0-8218-3900-3</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0821839004</subfield><subfield code="9">0-8218-3900-4</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)150256520</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035102132</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rda</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-19</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-824</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA455</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.22</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 380</subfield><subfield code="0">(DE-625)143235:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Barker, William H.</subfield><subfield code="d">1946-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)141066091</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Continuous symmetry</subfield><subfield code="b">from Euclid to Klein</subfield><subfield code="c">William Barker, Roger Howe</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Providence, Rhode Island</subfield><subfield code="b">American Mathematical Society</subfield><subfield code="c">[2007]</subfield></datafield><datafield tag="264" ind1=" " ind2="4"><subfield code="c">© 2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xxi, 546 Seiten</subfield><subfield code="b">Diagramme</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Geometry, Plane</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Group theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetry groups</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Euklidische Geometrie</subfield><subfield code="0">(DE-588)4137555-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Euklidische Geometrie</subfield><subfield code="0">(DE-588)4137555-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Howe, Roger</subfield><subfield code="d">1945-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)171158407</subfield><subfield code="4">aut</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Online-Ausgabe</subfield><subfield code="z">978-1-4704-1197-8</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/toc/fy0803/2007060795.html</subfield><subfield code="3">Table of contents</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016770100&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-016770100</subfield></datafield></record></collection>
id	DE-604.BV035102132
illustrated	Not Illustrated
indexdate	2024-12-20T13:20:13Z
institution	BVB
isbn	9780821839003 0821839004
language	English
lccn	2007060795
oai_aleph_id	oai:aleph.bib-bvb.de:BVB01-016770100
oclc_num	150256520
open_access_boolean
owner	DE-19 DE-BY-UBM DE-634 DE-824 DE-11 DE-384
owner_facet	DE-19 DE-BY-UBM DE-634 DE-824 DE-11 DE-384
physical	xxi, 546 Seiten Diagramme
publishDate	2007
publishDateSearch	2007
publishDateSort	2007
publisher	American Mathematical Society
record_format	marc
spellingShingle	Barker, William H. 1946- Howe, Roger 1945- Continuous symmetry from Euclid to Klein Geometry, Plane Group theory Symmetry groups Euklidische Geometrie (DE-588)4137555-5 gnd
subject_GND	(DE-588)4137555-5
title	Continuous symmetry from Euclid to Klein
title_auth	Continuous symmetry from Euclid to Klein
title_exact_search	Continuous symmetry from Euclid to Klein
title_full	Continuous symmetry from Euclid to Klein William Barker, Roger Howe
title_fullStr	Continuous symmetry from Euclid to Klein William Barker, Roger Howe
title_full_unstemmed	Continuous symmetry from Euclid to Klein William Barker, Roger Howe
title_short	Continuous symmetry
title_sort	continuous symmetry from euclid to klein
title_sub	from Euclid to Klein
topic	Geometry, Plane Group theory Symmetry groups Euklidische Geometrie (DE-588)4137555-5 gnd
topic_facet	Geometry, Plane Group theory Symmetry groups Euklidische Geometrie
url	http://www.loc.gov/catdir/toc/fy0803/2007060795.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016770100&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT barkerwilliamh continuoussymmetryfromeuclidtoklein AT howeroger continuoussymmetryfromeuclidtoklein

Verfügbarkeit

‌

Inhaltsverzeichnis