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| Wapner L. — The Pea and the Sun: A Mathematical Paradox |
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| Предметный указатель |
3D printers 174
Absorbed 100
Achilles 6
Adams, Ansel 2
Aleph 12
Anagram 176
Antinomy 50 55
Appel, Kenneth 200
Aquinas, Saint Thomas 7
Aristotle 6
Associativity 86
Attractor 181
Augenstein, Bruno 2 176 185 190
Axiom of Choice xiii 13 21 23 28 32 34 36 37 38 41 45 46 79 95 110 111 132 134 151 165 170 175 192 196
BabyBT 107
Babylonians 192
Bach, Johann Sebastian 44
Bair, Rene 17
Banach — Schroeder-Bernstein Theoem 157 158
Banach — Tarski paradox xii
Banach — Tarski theorem xii 143 169 203
Banach — Tarski Theorem, proof of 144
Banach, Stefan 18
Barber paradox 56 78
Beltrami, Eugenio 41
Bernstein, Felix 17
Bers, Lipman 2
Big bang theory 178 179
Bijection 108 119 120 121 123 124
Birch and Swinnerton — Dyer conjecture 195
Bolyai, Johann 40
Bolzano, Bernhard 109 117
Borel, Emile 17
Braess's paradox 50
Burali — Forti paradox 78 176
Butterfly effect 183
Cantor dust See Cantor set
Cantor set 127 183
Cantor's Continuum Hypothesis 13 36
Cantor's paradox 78
Cantor's theorem 76
Cantor, Ceorg 2 5 37 108 109 110 122 123
cardinal number 78
Cardinality 8 71 114
Carnap, Rudolf 25 29
Casimir effect 177
Casimir, Hendrick 177
Chaos 180
Choice set 16 151
Circle squaring problem 94
Classification of the finite simple groups 200
Clay Mathematics Institute of Cambridge, Massachusetts (CMI) 193
Clipping 61
Closure 86
Cohen, Joel 50
Cohen, Paul 17 34 77
Complement of a set 73
complex numbers 141
Complex plane 141
Congruence by dissection 87
Congruent 79
Constructivist 3
Continuum 118
Continuum Hypothesis 14 32 37 38 77 192
Copernicus, Nicolas 166
Cosmology 179
Countable 9
Cubic close packing 201
Curry Triangle 63
Curry, Paul 63
Dchn invariant 98
Dedekind definition 110
Dedekind, Richard 110 122 123
Dehn, Max 97
Dense 10 196
Denumerable 9
Dewdney, A.K. 174
Dichotomy Paradox 6
Difference of sets 74
Digital fabricators 174
Disappearing Rabbit Paradox 63
DNA 199
DNA computers 199
Dougherty, Randal 196
Dudeney, Henry E. 88 93 94
Duplication version 23 143 156
Dyer, Wayne, Dr. 189
Egyptians, ancient 192
Eigen, Manfred 171
Einstein, Albert 33 167 171 188
El Naschie, M.S. 179 183 190
Electron-muon puzzle 185
Empty set 71
Equidecomposable 98 99 143 154
Equivalence classes 132 134
Escher, Maurits C. 43 47
Euclid's Fifth Postulate 40
Experimental mathematics 203
Face-centered packing 201
Febbers 174
Feferman, A.B. 26
Fermat's last theorem 195 200
Feynman, Richard 169
Finitist 3
Fitzgerald — Lorentz equations 167
Flyspeck Project 202
Forcing 38
Foreman, Matthew 196
Formal proof 202
Formalism 3
Four-Color-Map Problem 200
Fraenkel, Abraham 15
French, Robert 148 153
Fundamenta Mathematicae 20 22 139
Galilei, Galileo 109 166
Gamow, George 179
Gardner, Martin 55 63 96 190
Gauss, Carl Friedrich 7 40 193
Get Off the Earth puzzle 57 60
Givant, Steven 27
Glide reflection 85
Go-Go philosophy 190
Go-Go Principle 178 188
Godcl, Kurt 2 25 28 37 38 39 77
Godel number 30
Godel's Incompleteness Theorem 36
Graham, Ronald 3 203
Greece, ancient 192
Gribbin, John 189 190
Group 86
Hadamard, Jacques 17
Hadrons 184 185 186
Hahn, Hans 29
Haken, Wolfgang 200
Hales, Thomas 201
Halmos, Paul 197
Hardy, G.H. 171
Hausdorff Paradox 21 45 46 144 150 153 156 169
Hausdorff, Felix 13 21 77
Hawking, Stephen 179
Hein, Paul 96
Heliocentric theory 166
Hexagonal close packing 201
Hilbert curve 125
Hilbert's Hotel 100
Hilbert's problems, first 13
Hilbert's problems, third 98 106
Hilbert, David 13 15 43 98 100 125 192
Hodge conjecture 195
Hofstadter, Douglas R. 45
| Horgan.John 200
Hoyle, Fred 179
Hyperbolic geometry 41
Hyperbolic plane 45 203
Hyperwebster dictionary 135 141
Identity 86
Image 79
Infinite set 107
infinity 5
Initial singularity 179
Injection 108 120
Injection definition 110
Inner product 83
Inside Out Torus Paradox 66
International Congress of Mathematics 43
Intuitionist 3
Inverse 86
Isometries 79
Jigsaw congruence 87
Jigsaw fallacies 57
Jones, Roger 185 189 190
Kepler's Sphere Packing Conjecture 201
Kepler, Johannes 167 202
Kronecker, Leopold 8 14 37
Laczkovich, Miklos 95
Laplace, Pierre-Simon 42
Lebesgue measure 126 168
Lebesgue, Henri 17
Length of a rotation 146
Leptons 184
limerick 176
Limit cycle attractors 182
Lindemann, Ferdinand 95
Linear chaos 184
Lobachevskian geometry 40
Lobachevsky, Nicolai 40
Logical positivism 29
Lorenz, Edward N. 182
Loyd Vanishes 57
Loyd, Sam 57 88 89 93 94
Lvov 19 24 25
Magnification version 23 144 156
Mass Gap Hypothesis 194
Mathematica 203
Mathematical realism 2
Matrix 82
Mazurkiewicz, Stefan 138
McKenzie, Ralph 27
Measure 126 168
Menger, Karl 29
Mesons 184
Metalanguages 56
Metamathematics 192
Millennium Prize Problems 193
Mills, Robert 194
Moore's law 198
Moore, E.H. 125
Morganstern, Oskar 32 33
Mycielski, Jan xiii 45 186 187 203
Navier — Stokes equations 194
Neutrons 184
Newton, Isaac, Sir 167
Non-Cantorian set theories 192
Non-Euclidean geometry 40 45
Nonlinear dynamics 180
Nonmeasurable set xiii 132 133 168
Null set 71 176
One-to-one correspondence 10
Onto 108
open 196
Optical computers 199
Orbit 151 180
Ordinal number 78
P versus NP problem 194
Paradox 49
Paradox, Type 1, Type 2, or Type 3 See Type 1 paradox Type or
Paradoxien des Unendlichen (Paradoxes of the Infinite) 109
Particle Physics 184
Pea and the sun paradox xii 144
Peano, Giuseppe 124
Phase space 180
Pickering, Andrew 189 190
Piecewise congruent 99 143
Platonism 2
Platonist 11
Poincare conjecture 195
Poincare disc 45 47
Poincare, Henri 13 193 195
Point set 70
Poles 150
Porkert, Adele 32
Power set 75
Preimage 79
Prescient power of mathematics 189
Probabilistic proof 101
Product matrix 83
Proof of Banach — Tarski Theorem See Banach — Tarski Theorem proof
Property of Baire 196
Protons 184
Ptolemy, Claudius 166
Pythagorean Iheorem 91
Quadrature of the circle 95
Quantum computer 199
quantum mechanics 42
Quarks 184 185 186
Qubit 199
Rational numbers 10
Reeds 61
Reflection 85
Relativity. See special theory of relativity
Replicators 174
Resolution 165
Riemann hypothesis 193 195 203
Riemann zeta function 193
Riemann, Bernhard 40 193
Riemannian geometries 40
Robinson, R.M. 185 187
Rotation 82 145
Rucker, Rudy 30
Russell's antinomy 56
Russell's paradox 56 79
Russell, Bertrand 15 16 29 56 190
Schroeder — Bernstein technique 123
Schroeder — Bernstein theorem 76 120 162
Scientific determinism 42
Scissors congruence 87 105
Scottish Cafe See Szkocka Cafe
Second International Congress of Mathematicians 13
Self-reference 42
Set 70
Set, intersection 72
Set, theory 5
Set, union 72
Shifting from infinity 100 154 155 156
Shifting to infinity 100 101 112
Shor, Peter 199
Sierpiriski Carpet 130 131
Sierpiriski — Mazurkiewicz Paradox 138 141
Sierpiriski — Menger Sponge 130
Sierpiriski, Waclaw 138 139 141
Silicon chip 199
Simply connected 195
Simpson's paradox 52 65
Single point attractors 182
Soma Cube 96
Space filling curve 124
Special theory of relativity 167
Spherical (Riemannian) geometry 41
Squaring of the circle 95
Standard Model of particle physics 184
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