Table of Contents

Preface xiii

1 The Art of Mathematics 1

2 How Many Guards Does an Art Gallery Need? 4

3 Aspects of Aspect Ratios 8

4 Vickrey Auctions 11

5 How to Sing in Tune 13

6 The Grand Jeté 15

7 Impossible Beliefs 17

8 Xerography - Déjà Vu All Over Again 19

9 Making Pages Look Nice 22

10 The Sound of Silence 25

11 A Most Unusual Cake Recipe 28

12 Designing Roller Coasters 31

13 The Beginning of the Universe Live on TV 35

14 Coping with Stress 38

15 Art Is Critical 40

16 Culinary Arts 42

17 Curved Triangles 45

18 The Days of the Week 49

19 The Case for Procrastination 52

20 Diamonds Are Forever 54

21 How Do You Doodle? 57

22 Why Are Eggs Egg-Shaped? 59

23 The EI Greco Effect 62

24 Eureka 64

25 What the Eye Tells the Brain 67

26 Why the Flag of Nepal Is Unique 70

27 The Indian Rope Trick 73

28 An Image That Defeats the Eye 76

29 It's Friday the Thirteenth Again 79

30 Strip Friezes 82

31 The Gherkin 86

32 Hedging Your Bets 89

33 Infinity at the Theater 91

34 Shedding Light on (and with) the Golden Ratio 92

35 Magic Squares 94

36 Mondrian's Golden Rectangles 97

37 Monkey Business with Tiles 100

38 Pleasing Sounds 103

39 New Tiles from Old 106

40 The Nine-Degree Solution 108

41 Paper Sizes and a Book in the Hand 111

42 Penny Blacks and Penny Reds 114

43 Prime Time Cycles 119

44 If You Can't Measure It, Why Not? 122

45 The Art of Nebulae 124

46 Reverse Auctions: Going Backward for Christmas 127

47 Ritual Geometry for the Gods 130

48 Prize Rosettes 133

49 Getting a Handle on Water Music: Singing in the Shower 135

50 Sizing Up Pictures 137

51 Triquetra 140

52 Let It Snow, Let It Snow, Let It Snow 143

53 Some Perils of Pictures 146

54 Drinking with Socrates 149

55 Strange Formulae 151

56 Stylometry: Mathematics Rules the Waves 155

57 Getting It Together 158

58 When Time Has to Reckon with Space 160

59 How to Watch TV 163

60 Curvaceous Vase Profiles 165

61 All the Wallpapers in the Universe 168

62 The Art of War 171

63 Shattering Wineglasses 174

64 Let the Light Shine In 176

65 Special Triangles 178

66 Gnomons Are Golden 180

67 The Upside-down World of Scott Kim 182

68 How Many Words Did Shakespeare Know? 184

69 The Strange and Wonderful Law of First Digits 188

70 Organ Donor Preferences 192

71 Elliptical Whispering Galleries 194

72 The Tunnel of Eupalinos 196

73 A Time-and-Motion Study of the Great Pyramid 200

74 Picking Out Tigers in the Bushes 203

75 The Art of the Second Law 205

76 On a Clear Day … 207

77 Salvador Dali and the Fourth Dimension 209

78 The Sound of Music 212

79 Chernoff's Faces 214

80 The Man from Underground 216

81 Möbius and His Band 219

82 The Bells, the Bells 222

83 Following the Herd 225

84 Finger Counting 229

85 The Other Newton's Hymn to the Infinite 231

86 Charles Dickens Was No Average Man; Florence Nightingale No Average Woman 234

87 Markov's Literary Chains 236

88 From Free Will to the Russian Elections 239

89 Playing with Supreme Beings 242

90 The Drawbacks of Being a Know-all 244

91 Watching Paint Crack 245

92 Pop Music's Magic Equation 248

93 Random Art 251

94 Jack the Dripper 255

95 The Bridge of Strings 260

96 Lacing Problems 264

97 Where to Stand to Look at Statues 267

98 The Hotel Infinity 270

99 The Color of Music 273

100 Shakespeare's Monkeys: The New Generation 276

Notes 281