Math Goes to the Movies Book

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

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

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

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

16.10 A Golden Argument 189

16.11 Poetic 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

18.10 A Tough Competition 205

18.11 Scary 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

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

21.10 Chaos, Fractals, and Dynamical Systems 266

21.11 Communicating with Aliens 266

21.12 Code Breaking 267

21.13 Calculus 268

21.14 Infinity 272

21.15 Paradoxes 273

21.16 Probability, Gambling, and Percentages 275

21.17 Famous Formulas, Identities, and Magic Squares 276

21.18 Mathematical Games 279

Movie Index 281