twin primes, 34–5, 37–8
why did Beckham choose the 23 shirt?, 6–9, 16
writing, 20–9
Prisoners of the Sun (Hergé), 210, 212
probability: airplane’s wing, lift of, 22–3, 247, 249
calendars, 211–12
can you make an egg defy gravity? 225–6
casino, mathematics of, 124–7, 237–8
chaos theory, 231–5
chocolate roulette, 136–8
coin tossing and, 235–8
eclipse, 210–14
gravity of, 215–17, 225–6
lottery, 114–20, 123–4
magic squares, 139–44
making choices random, 112–14, 188–19
Monopoly, how can mathematics help you win at, 133–4
nim, 138–9, 179
number 19, 211–12
Number Mysteries game show, 134–6
perfect shuffle, 121–2
pendulums, 227–8, 231–2
planetary, 209
poker (see poker); quadratic equations, 217–21
rock-paper-scissors, how to become world champion, 110–12
soccer ball, movement of, 209
spotting patterns, 11–12
weather, 209, 250
weight of falling object, 215–16
why does a boomerang come back?, 221–5
will the solar system fly apart?, 228–33
why numbers like to clump, 120–1
Pythagoras’s theorem, 23
quadratic equations, 23
algebra and, 220–1
first use of, 218–19
soccer ball and, 217–18
squaring and, 218–19
Wayne Rooney and, 217–21
quantum physics, 250
Quatuor pour la fin du temps (Quartet for the End of Time, The ), 14–16
rabbits and sunflowers used to find prime numbers, 40–2
random processes, 34
randomizing choices, 112–13, 119
Real Madrid, 6–10
record-breaking primes, 46–8, 50
rice and chessboard to find primes, using, 44–6, 48–9
Riemann hypothesis, 52–3, 123
rings, unlinking the, 100, 108
Robinson, Raphael, 47
rock-paper-scissors: how to become world champion, 110–3
making choices random, 110–3, 119
origin of game, 110
Rooney, Wayne, 217–8, 221
Royal Game of Ur, 128–9
Russell, Ed, 145
Sacks, Oliver, 35–6
Sagrada Familia, 142
Schroeppel, Richard, 143
Schwarz, Hermann, 59
science fiction writers, prime numbers and, 18–19
Scott, David, 215
Scrabble, 161
scytale, 159
Second World War and, 165–70
semaphore, 173–6
shape of the universe: Asteroids and, 97–100
how can we tell we’re not living on a bagel-shaped planet? 100–4
infinity of, 106
what shape is our?, 55, 104–7
shapes, 55–108
Archimedean solids, 63–5, 67, 70, 74, 78, 131–2
bubbles, 55, 56–9, 70–7
Catalan solids, 78
crystals of garnet, 78
cube, 60–1
diamond, radial symmetry of, 55
dimensions greater than 1 but smaller than 2, 86–91
DNA and, 55, 69
dodecahedron, 61 65, 76–8, 106–7, 129, 132
equilateral triangles, 60
Euclid and, 62
ferns, 86
foam and, 70–7
fractal, 79–91
great rhombicosidodecahedron, 64
hexagonal honeycomb as most efficient structure, 74
human lung, 55, 86, 89
icosahedron, 61–2, 68–9, 129–32
imagining shapes, 70
Johnson solids, 78
leaf, shape of, 55
molecular structure of water, 78
octahedron, 52, 61, 64, 74, 129, 132
pentagons, 62 75–6
Platonic solids, 61, 63–4, 68–9, 77, 79, 129–30, 132
Poinsot solids, 78
pomegranate, 77–8
rhombic dodecahedron, 78
shaky polyhedra, 78
six-pointed snowflake, 55, 77–9
snub dodecahedron, 65
soccer ball, how to make the world’s roundest, 59–60, 61, 64
sphere, 56–62
teabags, 65–8
tetrahedron, 60–1, 63–4, 67–8, 73, 77, 79, 128–9
tetrakaidecahedron, 76
truncated tetrahedron, 63–4
universe, what shape is it?, 55, 104–7
viruses, shape of, 68–9
Water Cube (Beijing Olympic swimming center), is it unstable?, 70–6
zonohedra, 78
shell evolution, prime numbers and, 42
shuffle, perfect, 121–3, 197
side-blotched lizard (Uta stansburiana ), 110–11
Sieve of Eratosthenes, 30–2, 34
smart cards, 207
Smith, Edson, 47–8
smoke signals, 170
soccer ball: how to make the world’s roundest, 59–60, 61, 64
science of moving, 246–51
shaped dice, 131–2
solar system, future of, 228–33
solutions, 107, 156, 207–8
South Africa, fractal dimension of coastline, 89
space travel, 216
Sparta, 159
sphere, 56–9
calculating volume of, 57–9
making a, 59–62
as most efficient shape in nature, 57, 59
Spreckelsen, Otto von, 94–5
squaring, 202, 218
St. Augustine, 27–8, 210
steganography, 159
substitution cipher, 159–77
sudoku, 143–5, 154
Sullivan, Thomas, 66
Tarry, Gaston, 143
Taylor, Jean, 74
Taylor, Richard, 90–1
telephone number, what odds it is a prime number?, 50–1
Tesseract, The (Garland), 97
Tetley, 66
tetrahedron, 60–1, 63–4, 67–8, 73, 77, 79, 128–9
tetrakaidecahedron, 76
three-color map problem, 152–3
Timaeus (Plato), 60
Tintin, 210, 212
topology: birth of, 150
classification, 98
maps, 98
torus, 98–9, 102, 108
towers, use of to communicate, 170–2
Trafalgar, Battle of (1805), 173
travelling salesman problem, 150–1, 156
triangle: equilateral, 61, 64, 70, 79, 132
isosceles, 132
right-angled, 23
turbulence, 209–10, 248–50
twin primes, 34–5, 37–8
UCLA, 47
universe, what shape is it?, 55, 97–107
Asteroids (computer game) and, 97–106
future of, 228–33
how can we tell we’re not living on a bagel-shaped planet?, 100–4
infinity of, 106
what shape is our? 104–7
Upsilon Andromedae, 233
Venus, 233
Victory, HMS, 173
Vigenére, Blaise de, 165–6
Virahanka, 43
viruses, shape of, 68–9
visual codes, 170–6
Voyager 2, 190
Wackher, Matthäus, 78
Water Cube (Beijing Olympic swimming center), 70–6
Watson, James, 69
Watts, William, 56–7
Weaire, Denis, 75–6
weather forecasting, 209, 234–5, 238, 250
Weber, Wilhelm, 176–7
websites: a note on, vii
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nbsp; Number Mysteries, vii, 9, 14, 32, 37, 62, 112, 129, 140, 144, 160, 170, 225, 243
White Wilderness (film), 238–9
winning streak, secret of, 109–56
casino, mathematics of, 124–7
chocolate roulette, 136–8
dice, 128–33
Eulerian path, 147–52
how good are you at randomness?, 113–14
lottery, 114–20
magic, 120–4
magic squares, 139–45
Monopoly, 133–6
“needle in a haystack” problems, 151–2, 155–6
NP, 152–6
Number Mysteries game show, 134–6
perfect shuffle, 121–2
poker and prime numbers, 121–4
rock-paper scissors, 110–12
travelling salesman problem, 150–1
Woolley, Sir Leonard, 128
writing primes, 20–9
X-ray crystallography, 78
Yong, Shao, 180
zeta function, 52