Math Goes to the Movies

301 Pages·2012·5.8 MB·English

by  Burkard Polster

Math Goes to the Movies
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MATH GOES TO THE MOVIES
Burkard Polster
Marty Ross
The Johns Hopkins University Press
Baltimore
(cid:2)c 2012TheJohnsHopkinsUniversityPress
Allrightsreserved.Published2012
PrintedintheUnitedStatesofAmericaonacid-freepaper
987654321
TheJohnsHopkinsUniversityPress
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LibraryofCongressControlNumber:2011943465
ISBN13:978-1-4214-0483-7(hc)
ISBN10:1-4214-0483-4(hc)
ISBN13:978-1-4214-0484-4(pbk)
ISBN10:1-4214-0484-2(pbk)
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Contents
Preface xi
Part I Movies
1 Good Math Hunting 3
1.1 How to Become a Math Consultant 3
1.2 Actors Versus Blackboards 4
1.3 Lambeau, the Fields Medalist 5
1.4 A Professor Turns Actor 6
1.5 Mathematics: “Perceval” 7
1.6 Students in Action 8
1.7 Mathematics: Graph Theory 1 9
1.8 Mathematics: Eigenvalues 12
1.9 Mathematics: Graph Theory 2 13
1.10 Mathematics: Graph Theory 3 16
1.11 Mathematics: The Salieri Scene 17
1.12 Further References and Remarks 18
1.13 Parodies 18
2 The Clever Hand Behind A Beautiful Mind 21
2.1 Real Math Beats Fake Math 23
2.2 Signature Scene 23
2.3 The Riemann Hypothesis 27
2.4 The Blonde and the Nobel Prize 33
2.5 Hand Double 36
2.6 Bits and Pieces 37
3 Escalante Stands and Delivers 41
3.1 Welcome to the Finger Man 42
3.2 Filling the Hole 42
3.3 Let X Be the Number of Girlfriends 45
v
vi Contents
3.4 Newton Was an Idiot 46
3.5 The Students Stand and Deliver, Again 50
3.6 Will the Real Jaime Escalante Please Stand Up? 51
4 The Annotated Pi Files 53
4.1 Max the Mathematician 53
4.2 Mathematics Is the Language of Nature 54
4.3 Pattern in Pi 54
4.4 Numerology: Father + Mother = Child 57
4.5 The Fibonacci Numbers and the Golden Ratio 58
4.6 Archimedes the Goldfish 63
4.7 Coincidence, or Is It? 64
4.8 Back to the Golden Ratio 66
4.9 Staring into the Sun 67
4.10 The Name of God 69
4.11 Living Happily Ever After 69
5 Nitpicking in Mathmagic Land 71
5.1 Tiny Nitpick: What Is Pi? 71
5.2 Historical Nitpick: Pythagoras and the Pythagoreans 72
5.3 Small Nitpick: Pythagorean Music 73
5.4 Medium Nitpick: The Golden Section 74
5.5 Large Nitpick: Three-Cushion Billiards 77
5.6 NOTpick 82
5.7 Notes 83
6 Escape from the Cube 85
6.1 The Cube in Cube 85
6.2 First Insight: The Power of Primes 86
6.3 How to Avoid Prime Numbers 87
6.4 Second Insight: The Cube in Coordinates 89
6.5 Third Insight: Permutations 90
6.6 Final Insight: Prime Powers 95
6.7 Other Cubes 96
7 The Incredible Shrinking Room 97
7.1 How Good a Puzzler Are You? 98
7.2 Answers to the Puzzles 99
7.3 Notes 102
8 Murder in the Hot House 103
8.1 The Story 103
8.2 Let’s Kill Some Mathematicians 104
8.3 The Writing on the Wall 106
8.4 Let’s Run Away and Join the Circus 107
Contents vii
9 A Word Problem for Die Hards 109
9.1 Playing Billiards with the Die Hard Problem 110
9.2 A Recipe 111
9.3 Thwarting a Different Simon 112
9.4 The Least Common Multiple 112
9.5 References 113
10 7×13 = 28 115
10.1 First Proof: Bogus Division 115
10.2 Second Proof: Bogus Multiplication 117
10.3 Third Proof: Bogus Addition 118
10.4 Play it Again, Abbott 119
10.5 General Bogus Math 120
11 One Mirror Has Two Faces, Two Mirrors Have ... 121
11.1 Real Life 121
11.2 Prime Numbers 122
11.3 Calculus 123
11.4 Mathematical Miscellany 127
11.5 The Other Mirror 130
11.6 Notes 131
12 It’s My Turn for Some Serious Mathematics 133
12.1 The Snake Rears Its Lovely Head 133
12.2 The Classification of Finite Simple Groups 136
12.3 Questions and Answers 139
12.4 Notes 139
Part II Mathematics
13 Beautiful Math, or Better Off Dead 143
13.1 The Direct Approach 143
13.2 The Poetic Approach 146
13.3 The All-Singing, All-Dancing Approach 148
13.4 Any Place, Any Time 149
14 Pythagoras and Fermat at the Movies 151
14.1 Pythagoras’s Theorem 151
14.2 Fermat’s Last Theorem 154
14.3 Fermat’s Last Tango 157
15 Survival in the Fourth Dimension 161
15.1 Time, Space, Both, or What? 162
15.2 The Hypercube Via Analogy 163
viii Contents
15.3 Picturing the Hypercube 165
15.4 Dimension Drive 171
15.5 Intersections 173
15.6 The Hypersphere 175
16 To Infinity, and Beyond! 177
16.1 Mystical Musings 178
16.2 Toward Infinity, but Getting Lost 178
16.3 Toward Infinity, and Almost Getting There 179
16.4 Toward the Infinitely Small: Romantic Zeno 180
16.5 To Infinity: Are We There Yet? 181
16.6 Fishing with a Really Big Net 182
16.7 Infinity Pays Its Way 184
16.8 Pretty Patterns, Pretty Pi 186
16.9 Golden Infinity 188
16.10A Golden Argument 189
16.11Poetic Summation 190
17 Problem Corner 191
17.1 Problems for Wizkids, and a Wizdog 191
17.2 Math Quiz for Mortals 195
17.3 Devilish Problems 197
17.4 Crazy Problems for Extra Credit 198
18 Money-Back Bloopers 199
18.1 Boosting the Computer 199
18.2 Playing the Percentages 199
18.3 The Curse of Pi 201
18.4 Prime Problems 202
18.5 Slips of the Tongue 204
18.6 Less Is More 204
18.7 Simple Arithmetic? 204
18.8 A Very Tough Quadratic 205
18.9 The Algebra Problem 205
18.10A Tough Competition 205
18.11Scary Geometry 206
19 The Funny Files 209
19.1 Sex 209
19.2 Geometry 210
19.3 Arithmetic 212
19.4 Algebra and Word Problems 218
19.5 Mathematicians in Action 221
19.6 Doing the Impossible 223
Contents ix
19.7 What Are the Odds? 226
19.8 Odds And Ends 227
Part III Lists
20 People Lists 231
20.1 Real Mathematicians 231
20.2 Female Mathematicians 235
20.3 Interesting Math Teachers and Classroom Scenes 237
20.4 Wizkids 239
20.5 Mathematicians and Murder 240
20.6 Famous Actors Being Mathematical 244
20.7 Math Consultants 250
21 Topics Lists 251
21.1 Counting to 101 251
21.2 Math Titles but No Math 252
21.3 Pythagoras’s Theorem and Fermat’s Last Theorem 252
21.4 Geometry 254
21.5 Higher Dimensions 258
21.6 Topology 260
21.7 Golden Ratio and Fibonacci Numbers 261
21.8 Pi 262
21.9 Prime Numbers and Number Theory 263
21.10Chaos, Fractals, and Dynamical Systems 266
21.11Communicating with Aliens 266
21.12Code Breaking 267
21.13Calculus 268
21.14Infinity 272
21.15Paradoxes 273
21.16Probability, Gambling, and Percentages 275
21.17Famous Formulas, Identities, and Magic Squares 276
21.18Mathematical Games 279
Movie Index 281