Continuous symmetry: from Euclid to Klein
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2007]
|
| Subjects: | |
| Online Access: | Table of contents Inhaltsverzeichnis |
| Physical Description: | xxi, 546 Seiten Diagramme |
| ISBN: | 9780821839003 0821839004 |
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Record in the Search Index
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| 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
|
| adam_txt |
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 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
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| index_date | 2024-07-02T22:14:34Z |
| indexdate | 2024-07-09T21:22:15Z |
| institution | BVB |
| isbn | 9780821839003 0821839004 |
| language | English |
| lccn | 2007060795 |
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| physical | xxi, 546 Seiten Diagramme |
| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | American Mathematical Society |
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| spelling | Barker, William H. 1946- Verfasser (DE-588)141066091 aut Continuous symmetry from Euclid to Klein William Barker, Roger Howe Providence, Rhode Island American Mathematical Society [2007] © 2007 xxi, 546 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Geometry, Plane Group theory Symmetry groups Euklidische Geometrie (DE-588)4137555-5 gnd rswk-swf Euklidische Geometrie (DE-588)4137555-5 s DE-604 Howe, Roger 1945- Verfasser (DE-588)171158407 aut Erscheint auch als Online-Ausgabe 978-1-4704-1197-8 http://www.loc.gov/catdir/toc/fy0803/2007060795.html Table of contents GBV Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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_exact_search_txtP | 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 |
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