
Strange Curves, Counting Rabbits, and Other Mathematical Explorations (Paperback)
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Dispatched in 4 business days When will my order arrive?  DescriptionHow does mathematics enable us to send pictures from space back to Earth? Where does the bellshaped curve come from? Why do you need only 23 people in a room for a 50/50 chance of two of them sharing the same birthday? In "Strange Curves, Counting Rabbits, and Other Mathematical Explorations", Keith Ball highlights how ideas, mostly from pure math, can answer these questions and many more. Drawing on areas of mathematics from probability theory, number theory, and geometry, he explores a wide range of concepts, some more lighthearted, others central to the development of the field and used daily by mathematicians, physicists, and engineers. Each of the book's ten chapters begins by outlining key concepts and goes on to discuss, with the minimum of technical detail, the principles that underlie them. Each includes puzzles and problems of varying difficulty. While the chapters are selfcontained, they also reveal the links between seemingly unrelated topics. For example, the problem of how to design codes for satellite communication gives rise to the same idea of uncertainty as the problem of screening blood samples for disease. Accessible to anyone familiar with basic calculus, this book is a treasure trove of ideas that will entertain, amuse, and bemuse students, teachers, and math lovers of all ages.
 Publisher: Princeton University Press
 Published: 05 November 2006
 Format: Paperback 272 pages
 See: Full bibliographic data
 Categories: Probability & Statistics  Applied Mathematics  Popular Science
 ISBN 13: 9780691127972 ISBN 10: 0691127972
 Sales rank: 614,188
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Full bibliographic data for Strange Curves, Counting Rabbits, and Other Mathematical Explorations
 Title
 Strange Curves, Counting Rabbits, and Other Mathematical Explorations
 Authors and contributors
 Physical properties
 Format: Paperback
Number of pages: 272
Width: 152 mm
Height: 229 mm
Thickness: 18 mm
Weight: 399 g  Language
 English
 ISBN
 ISBN 13: 9780691127972
ISBN 10: 0691127972  Classifications
Nielsen BookScan Product Class 3: T8.0
B&T Book Type: NF
BIC E4L: SCP
DC22: 510
LC subject heading:
BIC subject category V2: PBT
B&T General Subject: 710
Abridged Dewey: 510
LC classification: QA
Ingram Subject Code: MA
Libri: IMA
WarengruppenSystematik des deutschen Buchhandels: 26280
B&T Merchandise Category: UP
BISAC V2.8: MAT025000, MAT003000
BIC subject category V2: PDZM
Thema V1.0: PBT, PDZ Illustrations note
 89 line illus. 7 tables.
 Publisher
 Princeton University Press
 Imprint name
 Princeton University Press
 Publication date
 05 November 2006
 Publication City/Country
 New Jersey
 Table of 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 ParityCheck 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 3.5 The Period Is a Factor of p 150 3.6 Fermat's Little Theorem 55 3.7 Further Reading 56 3.8 Solutions 58 Chapter Four Strange Curves 63 4.1 Introduction 63 4.2 A Curve Constructed Using Tiles 65 4.3 Is the Curve Continuous? 70 4.4 Does the Curve Cover the Square? 71 4.5 Hilbert's Construction and Peano's Original 73 4.6 A Computer Program 75 4.7 A Gothic Frieze 76 4.8 Further Reading 79 4.9 Solutions 80 Chapter Five Shared Birthdays, Normal Bells 83 5.1 Introduction 83 5.2 What Chance of a Match? 84 5.3 How Many Matches? 89 5.4 How Many People Share? 91 5.5 The BellShaped Curve 93 5.6 The Area under a Normal Curve 100 5.7 Further Reading 105 5.8 Solutions 106 Chapter Six Stirling Works 109 6.1 Introduction 109 6.2 A First Estimate for n 110 6.3 A Second Estimate for n 114 6.4 A Limiting Ratio 117 6.5 Stirling's Formula 122 6.6 Further Reading 124 6.7 Solutions 125 Chapter Seven Spare Change, Pools of Blood 127 7.1 Introduction 127 7.2 The CoinWeighing 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 Eficiency Estimate Using Telephones 141 7.7 An Eficiency 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 Chapter Ten Rational and Irrational 219 10.1 Introduction 219 10.2 Fibonacci Revisited 220 10.3 The Square Root of d 223 10.4 The Box Principle 225 10.5 The Numbers e and p 230 10.6 The Irrationality of e 233 10.7 Euler's Argument 236 10.8 The Irrationality of p 238 10.9 Further Reading 242 10.10 Solutions 243 Index 247