how to use to send secret messages over the internet, 200–3
what is?, 194–6, 198–9
clump, why numbers like to, 120
coastline of Britain, how long is?, 80–1, 84–5, 88–9
codes, 157–208
Battle of Trafalgar, use at, 173
binary, 138–9, 179–81
Bletchley Park, 169–70
Caesar shifts, 160–1
chaos theory and, 228
computer, 190–207
cryptanalysis, 161–89
DNA, 158
early methods of sending, 158–9
elliptical curve cryptography (ECC), 204–7
Enigma machine, 166–70
error-correcting, 145, 188–90
flags used as, 170, 172–3
frequency analysis, 165–77
Help! (Beatles) and, 174–5
how to toss a coin fairly across the internet, 190–2
how to use to read minds, 185–90
internet, 190–208
ISBN, 184–5
Kama Sutra, 159–61, 165
Mary Queen of Scots use of, 164, 190
Morse code, 177–9, 181
one-time pad, 165
predictability of, 235–8
Second World War and, 165–70
semaphore, 173–6
smoke signals, 170
steganography, 159
substitution cipher, 159–77, 207–8
telescope and, 170
towers and, 170–2
visual, 170–6
what is?, 157
why cracking numbers equals cracking codes, 192–4
coin tossing: how to toss a coin fairly across the internet, 190–2
predictability of, 235–7
Coldplay, 179, 182–3, 188
Columbus, Christopher, 212–13
Columbus, Ferdinand, 212
computer codes, 190–207
Contact (Sagan), 18
Cooper, Bob “The Rock,” 112
Crick, Francis, 69
Crucifixion (Corpus Hypercubus) (Dali), 96
cryptanalysis, 161–89; see also codes
cube: four-dimensional, 93–7
hypercube, 94–6
as soccer ball shape, 60–1
Water Cube (Beijing Olympic swimming center), 70–7
Cube (film), 17
Curious Incident of the Dog in the Night-time (Haddon), 17
Da Vinci Code (Brown), 41
Dalí, Salvador, 96
denticles, 249
Descartes, René, 45, 91–3, 95
deterministic systems, 230–1, 235
Diaconis, Persi, 235–6
dice: classic soccer ball shape and, 131–2
cube-shaped, 129
discovering all the possible, 129–32
Dungeons and Dragons, 129–32
first, 128–9
prime numbers and, 51–2
tetrahedral, 128–9; 20-faced, 130–1
“difference engine,” 166
diplomatic party problem, 152–3
Dirichlet, Gustav Lejeune, 191
Discordianists, 7
DNA, 19, 55, 69, 98, 158
code, 158
shape of, 98
dodecahedron, 61, 65, 76–8, 106–7, 129, 132
doubling, 44, 48–50
duality, 131
Dungeons and Dragons, 129–30
Dürer, Albrecht, 142
easy challenge, an, 192, 208
eclipse, 210–14
eggs: can you make an egg defy gravity?, 225–6
sending codes with, 158–9
Egypt, ancient, 10, 20–1, 25, 29, 110, 128, 220
Electronic Frontier Foundation, 47
Elements, The (Euclid), 62
Elizabeth I, Queen, 46, 164
elliptical curve cryptography (ECC), 204–7
Elvenich, Hans-Michael, 47
Enigma machine, 166–70
equilateral triangle, 60, 61, 64–5, 70, 79, 132
Eratosthenes, 31–4
Erdös, Paul, 34
error-correcting codes, 145, 188–90
Euclid, 32–3, 35, 62
Euler, Leonhard, 46, 143–50
Fermat’s little theorem, version of, 197–9
Graeco-Latin squares and, 144–6
path, 147–8, 150
soldiers puzzle, 143–5
European Football Championship (1968), 235
extraterrestrials, using prime numbers to communicate with, 6, 18–19
falling cat theorem, 236
falling object, weight and speed of, 216
fantasy football game, prime number, 9–10
Fermat, Pierre de: “last” theorem, 196
little theorem, 196, 197–9, 203
prime numbers, work on, 36–7, 45, 123, 191, 196–200, 208
ferns, 86
Fibonacci numbers, 40–3, 113–14
Fifth Symphony (Beethoven), 176–7
Finer, Jem, 16
Finkel, Irving, 129
fishy formula game, 243–6
flags, communicating with, 170, 172–3
foam, 70–7
four dimensional geometry: four-dimensional cube, 93–7
how to see in
four dimensions, 91–4
invention of, 91–4, 105
fractals: brains drawn to, 90
chaos theory and, 232–3
coastline of Britain and, 80–4, 88–9
dimensions greater than 1
but smaller than 2, 86–9
ferns and, 86
fractal dimensions, 86–91
generated by simple mathematical rules, 86
human lung, 86, 89
Jackson Pollock and, 89–91
natural evolution of, 86
snowflake and, 79
Freeman, Robert, 175
frequency analysis, 165–77
future, quest to predict, 209–51
airplane’s wing, lift of, 222–3, 247, 249
calendars, 211–12
casinos and, 237–8
chaos theory, 230–33
coin tossing and, 235–7
eclipse, 210–14
eggs, 225–6
gravity and, 215–16, 226–8
lemmings, death of, 238–42
number 19 and 211–12
pendulums, 226–8, 231–3
quadratic equations, 218–21
soccer balls, science of moving, 246–51
weather forecasting, 209, 234–5, 238, 250
weight of falling object, 216
why does a boomerang come back?, 221–5
will the solar system fly apart?, 228–33
Galilei, Galileo, 55, 215–17, 226–8, 247
gambling: casino, mathematics of, 124–7, 237–8
how to cheat at poker and do magic using the million-dollar prime number, 121–4
lottery, 114–20, 124
perfect shuffle, 121–3
Gaudí, Antonio, 142
Gauss, Carl Friedrich: coded communication, work on, 176–7
prime numbers, work on, 51–2, 123
Gematria, 26
geometry, 56, 91–4, 97–8, 105,. 206–7, 221–2
Archimedean solids, 63–5, 67, 70, 74, 78, 131–2
bubbles, 55, 56–9, 70–7
Catalan solids, 78
crystals of garnet, 78
cube60–1
diamond, radial symmetry of, 55
dimensions greater than 1
but smaller than 2, 86–9
DNA and, 55, 69
dodecahedron, 61, 65, 76–8, 106–7, 129, 132
equilateral triangles, 61
Euclid, 61–2
ferns, 86
foam and, 70–7
fractal, 79–91
great rhombicosidodecahedron, 164
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 octahedron, 64, 74–5
truncated tetrahedron, 63–4
universe, what shape is it? 55
viruses, shape of, 68–9
Water Cube (Beijing Olympic swimming center) 70–6
zonohedra, 78
golf balls, 247
Google, 150
Graeco-Latin squares, 144, 146
gravity: can you make an egg defy? 225–6
weight and speed of falling object, 216
Great Internet Mersenne Prime Search (GIMPS), 46–7
Greece, ancient, 29–32, 44–5, 48, 56–7, 62–3, 98, 104, 190, 205
Gregorian calendar, 211–12
gyroscopic effect, 222–3
Hardy, G. H., 18, 164
Heisenberg, Werner, 250
Help! (Beatles), 174–5
hexagonal honeycomb as most efficient structure, 74
hexakis icosahedron, 132
Histiaeus, 158
Holmes, Susan, 236
honeybees, 74
Hooke, Robert, 170–1
hopscotch, prime number, 37–40
human lung, 55, 86, 89
Hun-Yu, Chang, 49–50
Hurwitz, Alex, 47
hypercube, 94–6
I Ching—Book of Changes, 179
icosahedron, 61–2, 68–9, 129–32
imaginary numbers, 52–3
India, 23, 43–5, 129, 141–2, 220
induction, 148
infinity, idea of, 58
Inspector Morse (television series), 178–9
internet: Great Internet Mersenne Prime Search (GIMPS), 46–7
how to toss a coin fairly across the, 190–2
how to use a clock to send secret messages over the, 200–3
security and codes, 190–207
ISBN (International Standard Book Number), 184–5
Islam, 141, 211, 220
isosceles triangle, 132
Italian lottery, 114–15
iTunes, 182
Jarvis, Frazer, 145
Jewish/Hebrew outlook on prime numbers, 26–7
Jordan, Michael, 6–7
JPEGs, 182
Kabbalah, 26
Kama Sutra, 159–61, 165
Kelvin, Lord, 74–6
Kepler conjecture, 77
Kepler, Johannes, 77–9
al-Khwarizmi, Muhammad ibn-Musa, 220
al-Kindi, Ya’qub, 161–2
Klug, Aaron, 69
Koch snowflake, 83, 87
Koch, Helge von, 83, 87
Königsberg, 145–50
Koran, 220
LA Galaxy, 8
La Grande Arche, Paris, 94–5
laminar flow, 248–9
lateral thinking, 139–40, 199
latitude and longitude, 92
laws of nature, 228
leaf, shape of, 55
Leibniz, Gottfried, 58, 179–81
lemmings, death of, 238–42, 245
Life: A User’s Manual (Perec), 144
London Ritz casino, 237
London Underground, 98, 146
Longplayer, 16
lottery: calculating the odds, 115–20, 124
how can I win?, 114–20
Italian, 114–15
Number Mysteries, 115–20, 156
UK (National Lottery), 5, 116, 119
magic: perfect shuffle, 121–3, 197
using the million-dollar prime number problem in, 52–3, 121–3
magic squares, 139–44; 3 x 3, 142; 4 x 4, 142; 6 x 6, 142; 9 x 9, 141, 142; 15 x 15, 142
Dürer and, 142
first, 141
Graeco-Latin squares, 144, 146
sudoku and, 143–5, 154
Magnus effect, 247, 249
Magnus, Heinrich, 247
Man Who Mistook His Wife for a Hat, The (Sacks), 35
Mandelbrot, Benoit, 84–5
maps, topological, 98–9
Mary Queen of Scots, 164, 190
A Mathematician’s Apology (Hardy), 164
Maya, 24–5, 29
Melancholia (Dürer), 142
Mercury (planet), 233
Mersenne prime, 28, 45–7, 49
Messiaen, Olivier, 14–16
million-dollar prizes, 2, 6
minesweeper, 153–4
Mitterrand perspective, 94
Mitterrand, François, 94
mobile phones, 207, 237
modular or clock arithmetic, 36, 195
Monopoly, how can mathematics help you win at?, 133–4
Montgomery, Richard, 236
Morse code, 177–9, 181
Morse, Samuel, 177
M13 globular star cluster, 19
musicians exploit prime numbers, 6, 14, 17
Mussolini, Benito, 115
name, calculating the value of, 26
NASA, 19, 190, 215
National Lottery (UK), 5, 116, 119
Navier-Stokes equations, 250
negative number, concept of, 29
“needle in a haystack” problem, 151–2, 155
Nelson, Horatio, 173, 190
Newton, Isaac, 58, 105, 229–30, 237
nim, 138–9, 179
Norway, fractal dimension of coastline, 89–90
NP-complete problems, 151–4
NP v P, 151–2
Number Mysteries: app, vii;
lottery, 115–20, 156
game show, 134–6
website, vii, 9, 14, 32, 37, 62, 112, 129, 140, 144, 160, 170, 225, 243
octahedron, 52, 61, 64, 74, 129, 132
one-time pad, 165
orbits, stability of, 229–31, 233
Oscar II of Sweden and Norway, King, 229
Ozanam, Jacques, 143
packing problem, 155–6
Pappus of Alexandria, 63
Paris, 94–6
Pasco, Lieutenant John, 173
pattern recognition, 166
pendulums, 226–8, 231–3
chaos theory and, 235
double, 227–8
magnets and, 231–2
predictability of, 226–8
pentagons, 61, 62, 64, 65, 67, 69, 76–7, 130–1
Pentakis dodecahedron, 132
Perelman, Grigori, 107
perfect numbers, 27–8
perfect shuffle, 121–2
PG Tips, 66–8
Phelan, Robert, 75–6
Phelippes, Thomas, 164
Planck constant, 82
Plateau, Joseph, 72–4, 76
Plato, 32, 56, 60–4, 67, 69, 78, 106
Platonic solids, 61, 63–4, 68–9, 77, 79, 129–30, 132
Plutarch, 63
Poincaré conjecture, 107
Poincaré, Henri, 98–9, 107, 229–31, 233, 237
poker: how to cheat at using the million-dollar prime number, 121–4
perfect shuffle, 121–3
probability of, 123–4
Texas Hold’em, 123–4
tips, 123–4
Pollock, Jackson, 89–91
pomegranate, 77–8
Popham, Sir Home, 173
population dynamics: lemmings, 238–42
rabbits, 40–3
Porta, Giovanni, 158
P-proble
m, 152
predictability: airplane’s wing, lift of, 222–3, 247, 249
calendars, 211–12
can you make an egg defy gravity? 225–6
casino, mathematics of, 124–7, 237–8
chaos theory, 230–5
chocolate roulette, 136–8
coin tossing and, 235–7
eclipse, 210–14
gravity of, 215–16, 225–6
lottery, 114–20, 123–4
magic squares, 139–45
making choices random, 112–14, 118–19
Monopoly, how can mathematics help you win at, 133–4
nim, 138–9, 179–80
number 19, 211–12
perfect shuffle, 121–3
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
Pregel, river, 145–6, 149
prime numbers: 1 as a, 10
American cicada and, 10–14, 15–17
as building blocks of all numbers, 6, 8, 10, 18
autism and, 35–6
Babylonian, 21, 23–5, 29
China and, 28–9
cicada game, 14
codes and, 190–207
communicating with extraterrestrials and, 6, 18–19
crossing universe with a dragon noodle and, 49–50
curious incident of the never-ending, 5–53
in ancient Egypt, 20–1, 25, 31
dice and, 51–2
doubling and, 44–5, 48–9
fantasy football game, 9–10
Fibonacci numbers, 40–3
finding, 5–53
get rarer and rarer in a regular way, 51–3
Great Internet Mersenne Prime Search (GIMPS), 46–7
in ancient Greece, 30–4, 45, 48
Guinness book of, 46–9
hopscotch, 37–40
how long would it take to write a list of all the primes?, 32–3
importance of, 5–8
internet security and, 6, 190–207
in literature, 17
in movies, 17
Jewish, 26–7
Mayan, 24–5, 29
Mersenne prime, 28, 45–7, 49
musicians exploit, 6, 14, 17
perfect numbers and, 27–8
poker, magic, and Riemann hypothesis, 123
“The Quartet for the End of Time,” 14–16
rabbits and sunflowers used to find, 40–2
record breaking, 46–8, 50
rewards for finding, 6
rice and chessboard to find, using, 44–5
Riemann hypothesis, 123
science fiction writers love of, 18–19
shell evolution and, 42
Sieve of Eratosthenes, 30–2, 34
telephone number, what odds it is a prime number, 50–1
The Number Mysteries: A Mathematical Odyssey through Everyday Life Page 24
