Impossible? Surprising Solutions to Counterintuitive Conundrums

By Julian Havil | Go to book overview

Index
aleph null, 73
algebraic integers, 44
Arecibo Message, 89
Ars Conjectandi, 120
Ashes, the, 11
Ask Marilyn, 12, 59
axiom of choice, 212
base independent law, 192
Basel Problem, 122
Bayes, Thomas, 61
Benford, Frank, 192
Berkeley sex bias case, 20
Berlekamp, Elwyn, 52
Bernoulli, Daniel, 127
Bernoulli, Jacob, 119
Bernoulli, Johann, 40
Besicovitch set, 153
Besicovitch, Abram, 147
Bible code, 132
binary
data, 88
repetition codes, 55
Birkoff, George, 146
Boas Jr, Ralph P., 118, 216
Bohr, Harold, 149
Borovik, Alexandre, 117
Braess, Dietrich, 32
Buffon's Needle, 146
Cantor's
diagonal array, 73
normal form, 208
Cardiste, The, 140
Cayley, Arthur, 166
ceiling functions, 227
CETI, see Communication with Extra Terrestrial Intelligence
combination formula, 104
common knowledge, 6, 7
definition, 5
red and blue hats, 6
Communication with Extra Terrestrial Intelligence, 88
complete base 2 representation, 203
complex logarithm, 40
conditional probability, 62, 135, 199
consecutive integers, 9
continued fractions, 172
convergents, 172
conversion between common and mutual knowledge, 6
cost functions, 33
cross-leaved Reed–Solomon codes, 59
Crum's problem, 163
cumulative density function, 196
Curious Incident of the Dog in the Night-time, The, 66
De Moivre, Abraham, 91
De Morgan, 40
deltoid, 151
Doctrine of Chances, The, 93
Duck, John Russell, 140
Ebert, Todd, 52
Educational Times, 166
Encounter 2001 Message, 90
epsilon zero, 207
equal distribution, 185
error
correcting, 55
detecting, 55
Euclid's Elements, 43
Euler's constant, 101, 170

-233-

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Impossible? Surprising Solutions to Counterintuitive Conundrums
Table of contents

Table of contents

  • Title Page iii
  • Contents ix
  • Acknowledgments xi
  • Introduction 1
  • Chapter 1 - It's Common Knowledge 3
  • Chapter 2 - Simpson's Paradox 11
  • Chapter 3 - The Impossible Problem 21
  • Chapter 4 - Braess's Paradox 31
  • Chapter 5 - The Power of Complex Numbers 39
  • Chapter 6 - Bucking the Odds 50
  • Chapter 7 - Cantor's Paradise 68
  • Chapter 8 - Gamow–stern Elevators 82
  • Chapter 9 - The Toss of a Coin 88
  • Chapter 10 - Wild-Card Poker 103
  • Chapter 11 - Two Series 113
  • Chapter 12 - Two Card Tricks 131
  • Chapter 13 - The Spin of a Needle 146
  • Chapter 14 - The Best Choice 165
  • Chapter 15 - The Power of Powers 176
  • Chapter 16 - Benford's Law 190
  • Chapter 17 - Goodstein Sequences 201
  • Chapter 18 - The Banach–tarski Paradox 210
  • Appendix 221
  • Index 233
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