Geometry by discovery:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1998
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 410 S. Ill., graph. Darst. |
| ISBN: | 0471041777 |
Internformat
MARC
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| 100 | 1 | |a Gay, David |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Geometry by discovery |c David Gay |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1998 | |
| 300 | |a XIV, 410 S. |b Ill., graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804126526677975040 |
|---|---|
| adam_text | IMAGE 1
GEOMETRY
BY
DISCOVERY DAVID GAY UNIVERSITY OF ARIZONA
JOHN WILEY & SONS, INC. NEW YORK # CHICHESTER # WEINHEIM BRISBANE #
TORONTO # SINGAPORE
IMAGE 2
CONTENTS
1 GETTING STARTED: STRATEGIES FOR SOMNG PROBLEMS 1 THE PROBLEM OF FIVE
PLANES IN SPACE 2 STRATEGIES FOR SOLVING PROBLEMS 15 BABY GAUSS AND A
FORMULA 18 A COLLECTION OF PROBLEMS 20 A TRICK YIELDS ANOTHER FORMULA 28
PROOFS WITHOUT WORDS 29 MINI-PROJECTS 32 REFERENCES 40 2 EPISODES IN THE
MEASUREMENT OFLENGTH, AREA, AND VOLUME 41 THE ODOMETER PROBLEM 42 MAKING
SENSE OF THE FORMULA FOR THE CIRCUMFERENCE OF A CIRCLE 43 THE GARDEN
PLOT PROBLEM 58 AREA PRINCIPLES AND STRATEGIES 60 THE CIRCULAR GARDEN
PLOT PROBLEM 65 VOLUME MEASUREMENT 69 THE SPHERE VOLUME PROBLEM 72 THE
TRIANGULAER PYRAMID PROBLEM 74 ARCHIMEDES SOLUTION TO THE SPHERE VOLUME
PROBLEM 91 NOTES 98 REFERENCES 99 3 POLYHEDRA 101 WHAT IS A
THREE-DIMENSIONAL COUNTERPART TO A POLYGON IN THE PLANE? 101 REGULAER
POLYHEDRA 108 CLASSIFICATION OF REGULAER POLYHEDRA 110 VI
IMAGE 3
XII * CONTENTS
POSSIBLE REGULAER POLYHEDRA 112 NUMERICAL DATA ASSOCIATED WITH A
POLYHEDRON 112 EULER S FORMULA 114 AN APPLICATION OF EULER S FORMULA 117
PREDICTING WITH EULER S FORMULA 120 THE SOCCER BALL 128 NOTES 132
REFERENCES 138
4 SHORTEST PATH PROBLEMS 139 THE SPEAKER WIRING PROBLEM 139 THE PROBLEM
OF THE MILKMAID, THE RIVER, AND THE COW 144 PATHS OF LIGHT; MIRRORS 148
THE COWBOY PROBLEM 151
ELLIPSES 153 PARABOLAS 157 THE THREE CITIES OPTICAL NETWORK PROBLEM 163
HOW TO CONSTRUCT THE SPECIAL POINT FOR THE THREE CITIES PROBLEM? 167
INSCRIBED ANGLES IN A CIRCLE: A PAUSE FOR REVIEW 168 THE THREE CITIES
PROBLEM, CONCLUDED 171 NOTES 175
REFERENCES 177
5 KALEIDOSCOPES 179 TWO-MIRROR KALEIDOSCOPES 180 GOOD KALEIDOSCOPE
ANGLES 192 BAD KALEIDOSCOPE ANGLES: AN ANALYSIS 196
THREE-MIRROR KALEIDOSCOPES I: ALL MIRRORS PERPENDICULAR TO A FOURTH
PLANE 207 GOOD TRIANGULAER KALEIDOSCOPES 209 MAKING A KALEIDOSCOPE 211
THREE-MIRROR KALEIDOSCOPES II: THREE MIRRORS MEETING IN A POINT 216
NOTES 225 REFERENCES 226
IMAGE 4
CONTENTS # XIII
6 SYMMETRY 227 MIRROR SYMMETRY AND TRANSFORMATIONAL GEOMETRY 229 MIRROR
SYMMETRY AS A FUNCTION 230 ROTATIONAL SYMMETRY 237 KALEIDOSCOPES 241
SUCCESSIVE MIRROR REFLECTIONS IN TWO PARALLEL LINES 241 TRANSLATIONAL
SYMMETRY 245 PRODUCTS OF MIRROR REFLECTIONS 248 WHERE ARE WE? HOW DID WE
GET HERE? WHERE ARE WE GOING? 255
PRODUCTS OF THREE REFLECTIONS 256 SYMMETRIES OF FRIEZE PATTERNS AND
WALLPAPER DESIGNS 260 SYMMETRIES IN SPACE 266 MIRROR REFLECTIONS IN
SPACE 266 ROTATIONS IN SPACE 267 SYMMETRIES OF A REGULAER TETRAHEDRON,
PART I 268 PRODUCT OF A MIRROR REFLECTION WITH A ROTATION 269
SYMMETRIES OF A REGULAER TETRAHEDRON, PART II 272 SYMMETRIES OF THE CUBE,
PART I 274 SYMMETRIES OF THE REGULAER TETRAHEDRON AND THE CUBE, CONCLUDED
276 A THREE-DIMENSIONAL KALEIDOSCOPE 277
NOTES 279 REFERENCES 282
7 WHAT SHAPES ARE BEST? 283 THE GARDEN PROBLEM 284 THE STORAGE PROBLEM
290 MORE GARDEN, STORAGE, AND BUILDING PROBLEMS TO SOLVE 291
RELATED PROBLEMS AND NEXT STEPS 294 THE POST OFFICE PROBLEM 297 THE
CEREAL BOX PROBLEM 298 THE ISOPERIMETRIC PROBLEM 304
DIDO S PROBLEM 310 PICKING THE RAISINS OFF THE CAKE 314
THREE-DIMENSIONAL ANALOGUE TO THE ISOPERIMETRIC PROBLEM 321 NOTES 323
REFERENCES 325
IMAGE 5
XIV # CONTENTS
O BEEHIVES AND OTHER PACKING PROBLEMS 327 THE IRRIGATION PROBLEM 327 THE
SOUP CAN PACKING PROBLEM 329 THE CITY ELEMENTARY SCHOOL PARTITIONING
PROBLEM 331
JENSEN S INEQUALITY 334 A PROOF THAT THE HEXAGONAL ARRANGEMENT IS BEST
337 MODELING NATURAL PHENOMENA WITH ARRANGEMENTS OF CIRCLES 341 THE WINE
BOTTLE PACKING PROBLEM 347
THE BALL BEARING SHIPPING PROBLEM 350 SPHERE PACKING EXPERIMENTS 351 A
RETURN TO THE BALL BEARING PROBLEM 359 CAPS FOR THE BEEHIVE CELLS 362
BODY CENTERED CUBIC PACKING 363 BEEHIVES AND THE ISOPERIMETRIC PROBLEM
FOR SPACE-FILLING POLYHEDRA 368 THE CUBIC CLOSE PACKING SPACE GRID 370
THE CUBIC CLOSE PACKING SPACE GRID FROM THE CANNONBALL PERSPECTIVE 373
NOTES 377
REFERENCES 380
9 WHERE TO GO FROM HERE? PROJECT IDEAS 383 PROJECT IDEAS 383 RESOURCES
399 COMMUNICATING PROJECT RESULTS 402 NITTY-GRITTY ON PUTTING TOGETHER
AN EFFECTIVE DISPLAY 404
PROJECT EVALUATION 405 THE BOTTOM LINE 406
CREDITS 407
INDEX 409
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.2/076 |
| dewey-search | 516.2/076 |
| dewey-sort | 3516.2 276 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:18:52Z |
| institution | BVB |
| isbn | 0471041777 |
| language | English |
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| physical | XIV, 410 S. Ill., graph. Darst. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Wiley |
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| spelling | Gay, David Verfasser aut Geometry by discovery David Gay New York [u.a.] Wiley 1998 XIV, 410 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Geometria larpcal Géométrie ram Geometry 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=008071049&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gay, David Geometry by discovery Geometria larpcal Géométrie ram Geometry Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 |
| title | Geometry by discovery |
| title_auth | Geometry by discovery |
| title_exact_search | Geometry by discovery |
| title_full | Geometry by discovery David Gay |
| title_fullStr | Geometry by discovery David Gay |
| title_full_unstemmed | Geometry by discovery David Gay |
| title_short | Geometry by discovery |
| title_sort | geometry by discovery |
| topic | Geometria larpcal Géométrie ram Geometry Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Geometria Géométrie Geometry Geometrie |
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