Methods of geometry:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
2000
|
| Series: | A Wiley-Interscience publication
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 486 S. Ill., graph. Darst. |
| ISBN: | 0471251836 |
Staff View
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Record in the Search Index
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| adam_text | IMAGE 1
METHODS OF GEOMETRY
JAMES T. SMITH SAN FRANCISCO STATE UNIVERSITY
A WILEY-INTERSCIENCE PUBLICATION JOHN WILEY & SONS, INC.
NEW YORK * CHICHESTER * WEINHEIM * BRISBANE * SINGAPORE * TORONTO
I
IMAGE 2
CONTENTS
PREFACE XI
ABOUT THE AUTHOR XV
1 INTRODUCTION 1
1.1 EPISODES 2 1.2 ADVANCED GEOMETRY 9 1.3 THISBOOK 13 1.4 READING ABOUT
GEOMETRY 16 1.5 PROJECTS 17
2 FOUNDATIONS 19
2.1 GEOMETRY AS APPLIED MATHEMATICS 20 2.2 NEEDFOR RIGOR 23 2.3
AXIOMATIC METHOD 26 2.4 EUCLID S ELEMENTS 29 2.5 COORDINATE GEOMETRY 33
2.6 FOUNDATION PROBLEM 35 2.7 PARALLEL AXIOM 37 2.8 FIRM FOUNDATIONS 39
2.9 GEOMETRY AS PURE MATHEMATICS 42 2.10 EXERCISES AND PROJECTS 50
3 ELEMENTARY EUCLIDEAN GEOMETRY 53
3.1 INCIDENCE GEOMETRY 55 3.2 RULER AXIOM AND ITS CONSEQUENCES 57 3.3
PASCH S AXIOM AND THE SEPARATION THEOREMS 60 3.4 ANGLES AND THE
PROTRACTOR AXIOMS 64
3.5 CONGRUENCE 67 3.6 PERPENDICULARITY 71 3.7 PARALLEL AXIOM AND RELATED
THEOREMS 76 3.8 AREA AND PYTHAGORAS THEOREM 81
3.9 SIMILARITY 89 3.10 POLYHEDRAL VOLUME 92 3.11 COORDINATE GEOMETRY 100
3.12 CIRCLES AND SPHERES 106
3.13 ARES AND TRIGONOMETRIC FUNCTIONS 110 3.14 N 119
IMAGE 3
CONTENTS
4 EXERCISES ON ELEMENTARY GEOMETRY 127
4.1 EXERCISES ON THE INCIDENCE AND RULER AXIOMS 128 4.2 EXERCISES
RELATED TO PASCH S AXIOM 130 4.3 EXERCISES ON CONGRUENCE AND
PERPENDICULARITY 133 4.4 EXERCISES INVOLVING THE PARALLEL AXIOM 135
4.5 EXERCISES ON SIMILARITY AND PYTHAGORAS THEOREM 137 4.6 EXERCISES ON
CIRCLES AND SPHERES, PART 1 140 4.7 EXERCISES ON AREA 143
4.8 EXERCISES ON VOLUME 146 4.9 EXERCISES ON CIRCLES AND SPHERES, PART 2
148 4.10 EXERCISES ON COORDINATE GEOMETRY 151
5 SOME TRIANGLE AND CIRCLE GEOMETRY 157
5.1 FOUR CONCURRENCE THEOREMS 158 5.2 MENELAUS THEOREM 162 5.3
DESARGUES THEOREM 165 5.4 CEVA S THEOREM 171 5.5 TRIGONOMETRY 177
5.6 VECTOR PRODUCTS 186 5.7 CENTROID 193 5.8 ORTHOCENTER 196 5.9
INCENTER AND EXCENTERS 199 5.10 EULER LINE AND FEUERBACH CIRCLE 204
5.11 EXERCISES 211
6 PLANE ISOMETRIES AND SIMILARITIES 227
6.1 TRANSFORMATIONS 232 6.2 ISOMETRIES 240 6.3 REFLECTIONS 247 6.4
TRANSLATIONS 251
6.5 ROTATIONS 254 6.6 STRUCTURE THEOREM 258 6.7 GLIDE REFLECTIONS 261
6.8 ISOMETRIES AND ORTHOGONAL MATRICES 262
6.9 CLASSIFYING ISOMETRIES 267 6.10 SIMILARITIES 276 6.11 EXERCISES 281
IMAGE 4
CONTENTS
IX
7 THREE DIMENSIONAL ISOMETRIES AND SIMILARITIES 295
7.1 ISOMETRIES 296 7.2 REFLECTIONS 302 7.3 TRANSLATIONS AND ROTATIONS
306 7.4 GLIDE AND ROTARY REFLECTIONS 309
7.5 CLASSIFYING ISOMETRIES 312 7.6 SIMILARITIES 315 7.7 EXERCISES 317
8 SYMMETRY 327
8.1 POLYGONAL SYMMETRY 336 8.2 FRIEZES 344 8.3 WALLPAPER ORNAMENTS 355
8.4 POLYHEDRA 381
8.5 EXERCISES 407
APPENDIX A EQUIVALENCE RELATIONS 423
APPENDIX B LEAST UPPER BOUND PRINCIPLE 425
APPENDIX C VECTOR AND MATRIX AIGEBRA 429
BIBLIOGRAPHY 443
INDEX 463
|
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| 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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| id | DE-604.BV012661381 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:31:28Z |
| institution | BVB |
| isbn | 0471251836 |
| language | English |
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| physical | XV, 486 S. Ill., graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Wiley |
| record_format | marc |
| series2 | A Wiley-Interscience publication |
| spelling | Smith, James T. 1939- Verfasser (DE-588)121315444 aut Methods of geometry James T. Smith New York [u.a.] Wiley 2000 XV, 486 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier A Wiley-Interscience publication Geometrie Geometrie (DE-588)4020236-7 gnd rswk-swf Geometrie (DE-588)4020236-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008603132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Smith, James T. 1939- Methods of geometry Geometrie Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 |
| title | Methods of geometry |
| title_auth | Methods of geometry |
| title_exact_search | Methods of geometry |
| title_full | Methods of geometry James T. Smith |
| title_fullStr | Methods of geometry James T. Smith |
| title_full_unstemmed | Methods of geometry James T. Smith |
| title_short | Methods of geometry |
| title_sort | methods of geometry |
| topic | Geometrie Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008603132&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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