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
