Strange curves, counting rabbits, and other mathematical explorations
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Princeton [u.a.]
Princeton Univ. Press
2003
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| adam_text | STRANGE CURVES, COUNTING RABBITS, AND OTHER MATHEMATICAL EXPLORATIONS
KEITH BALL PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD CONTENTS
PREFACE XI ACKNOWLEDGEMENTS XIII CHAPTER ONE SHANNON S FREE LUNCH 1 1.1
THE ISBN CODE 1 1.2 BINARY CHANNELS 5 1.3 THE HUNT FOR GOOD CODES 7 1.4
PARITY-CHECK CONSTRUCTION 11 1.5 DECODING A HAMMING CODE 13 1.6 THE FREE
LUNCH MADE PRECISE 19 1.7 FURTHER READING 21 1.8 SOLUTIONS 22 CHAPTER
TWO COUNTING DOTS 25 2.1 INTRODUCTION 25 2.2 WHY IS PICK S THEOREM TRUE?
27 2.3 AN INTERPRETATION 31 2.4 PICK S THEOREM AND ARITHMETIC 32 2.5
FURTHER READING 34 2.6 SOLUTIONS 35 CHAPTER THREE FERMAT S LITTLE
THEOREM AND INFINITE DECIMALS 41 3.1 INTRODUCTION 41 3.2 THE PRIME
NUMBERS 43 3.3 DECIMAL EXPANSIONS OF RECIPROCALS OF PRIMES 46 3.4 AN
ALGEBRAIC DESCRIPTION OF THE PERIOD 48 VU CONTENTS 3.5 3.6 3.7 3.8
CHAPTER THE PERIOD IS A FACTOR OF P - 1 FERMAT S LITTLE THEOREM FURTHER
READING SOLUTIONS FOUR STRANGE CURVES 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8
4.9 CHAPTER SHARED 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 CHAPTER INTRODUCTION
A CURVE CONSTRUCTED USING TILES IS THE CURVE CONTINUOUS? DOES THE CURVE
COVER THE SQUARE? HILBERT S CONSTRUCTION AND PEANO S ORIGINAL A COMPUTER
PROGRAM A GOTHIC FRIEZE FURTHER READING SOLUTIONS FIVE [ BIRTHDAYS,
NORMAL BELLS INTRODUCTION WHAT CHANCE OF A MATCH? HOW MANY MATCHES? HOW
MANY PEOPLE SHARE? THE BELL-SHAPED CURVE THE AREA UNDER A NORMAL CURVE
FURTHER READING SOLUTIONS SIX STIRLING WORKS 6.1 6.2 6.3 6.4 6.5 6.6 6.7
INTRODUCTION A FIRST ESTIMATE FOR N A SECOND ESTIMATE FOR N! A LIMITING
RATIO STIRLING S FORMULA FURTHER READING SOLUTIONS 50 55 56 58 63 63 65
70 71 73 75 76 79 80 83 83 84 89 91 93 100 105 106 109 109 110 114 117
122 124 125 VLLL CONTENTS CHAPTER SEVEN SPARE CHANGE, POOLS OF BLOOD 127
7.1 INTRODUCTION 127 7.2 THE COIN-WEIGHING PROBLEM 128 7.3 BACK TO BLOOD
131 7.4 THE BINARY PROTOCOL FOR A RARE ABNORMALITY 134 7.5 A REFINED
BINARY PROTOCOL 139 7.6 AN EFFICIENCY ESTIMATE USING TELEPHONES 141 7.7
AN EFFICIENCY ESTIMATE FOR BLOOD POOLING 144 7.8 A PRECISE FORMULA FOR
THE BINARY PROTOCOL 147 7.9 FURTHER READING 149 7.10 SOLUTIONS 151
CHAPTER EIGHT FIBONACCI S RABBITS REVISITED 153 8.1 INTRODUCTION 153 8.2
FIBONACCI AND THE GOLDEN RATIO 154 8.3 THE CONTINUED FRACTION FOR THE
GOLDEN RATIO 158 8.4 BEST APPROXIMATIONS AND THE FIBONACCI HYPERBOLA 161
8.5 CONTINUED FRACTIONS AND MATRICES 165 8.6 SKIPPING DOWN THE FIBONACCI
NUMBERS 169 8.7 THE PRIME LUCAS NUMBERS 174 8.8 THE TRACE PROBLEM 178
8.9 FURTHER READING 181 8.10 SOLUTIONS 182 CHAPTER NINE CHASING THE
CURVE 189 9.1 INTRODUCTION 189 9.2 APPROXIMATION BY RATIONAL FUNCTIONS
193 9.3 THE TANGENT 202 9.4 AN INTEGRAL FORMULA 207 9.5 THE EXPONENTIAL
210 9.6 THE INVERSE TANGENT 213 9.7 FURTHER READING 214 9.8 SOLUTIONS
215 IX CONTENTS CHAPTER TEN RATIONAL AND IRRATIONAL 10.1 10.2 10.3 10.4
10.5 10.6 10.7 10.8 10.9 10.10 INTRODUCTION FIBONACCI REVISITED THE
SQUARE ROOT OF D THE BOX PRINCIPLE THE NUMBERS E AND TT THE
IRRATIONALITY OF E EULER S ARGUMENT THE IRRATIONALITY OF TT FURTHER
READING SOLUTIONS 219 219 220 223 225 230 233 236 238 242 243 INDEX 247
X
|
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| id | DE-604.BV019326765 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:57:44Z |
| institution | BVB |
| isbn | 0691113211 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-012793818 |
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| physical | XIII, 251 S. graph. Darst. |
| publishDate | 2003 |
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| publisher | Princeton Univ. Press |
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| spelling | Ball, Keith M. Verfasser aut Strange curves, counting rabbits, and other mathematical explorations Keith Ball Princeton [u.a.] Princeton Univ. Press 2003 XIII, 251 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Unterhaltungsmathematik Unterhaltungsmathematik (DE-588)4124357-2 gnd rswk-swf Unterhaltungsmathematik (DE-588)4124357-2 s DE-604 http://www.loc.gov/catdir/description/prin031/2003047183.html Publisher description HEBIS Datenaustausch Darmstadt application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012793818&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ball, Keith M. Strange curves, counting rabbits, and other mathematical explorations Unterhaltungsmathematik Unterhaltungsmathematik (DE-588)4124357-2 gnd |
| subject_GND | (DE-588)4124357-2 |
| title | Strange curves, counting rabbits, and other mathematical explorations |
| title_auth | Strange curves, counting rabbits, and other mathematical explorations |
| title_exact_search | Strange curves, counting rabbits, and other mathematical explorations |
| title_full | Strange curves, counting rabbits, and other mathematical explorations Keith Ball |
| title_fullStr | Strange curves, counting rabbits, and other mathematical explorations Keith Ball |
| title_full_unstemmed | Strange curves, counting rabbits, and other mathematical explorations Keith Ball |
| title_short | Strange curves, counting rabbits, and other mathematical explorations |
| title_sort | strange curves counting rabbits and other mathematical explorations |
| topic | Unterhaltungsmathematik Unterhaltungsmathematik (DE-588)4124357-2 gnd |
| topic_facet | Unterhaltungsmathematik |
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