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Wapner L. — The Pea and the Sun: A Mathematical Paradox
Wapner L. — The Pea and the Sun: A Mathematical Paradox

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Название: The Pea and the Sun: A Mathematical Paradox

Автор: Wapner L.

Аннотация:

Wapner (mathematics, El Camino College, California) explains to general readers the Banach-Tarski Theorem, or Paradox, which shows how to disassemble a sphere and rearrange the pieces into another solid of any specified shape and volume: thus a pea could be taken apart and reassembled as the sun. He discusses its precursors and history, proof and resolution, and implications for the nature of mathematics and its relation to the physical world.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 232

Добавлена в каталог: 11.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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