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| Kasner E., Newman J. — Mathematics and the Imagination |
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| Ïðåäìåòíûé óêàçàòåëü |
 41—42 49 50 61 66—67 71 72 74 75—79 89 109 110 111 246 247
Abbott, Edwin Abbott 128 363
Abel, Niels Henrik 17
Absolute rest 24
Absolute zero 24
Acceleration 301 326 342—343
Achilles and the tortoise paradox 37 38 57—58 62
Advanced Calculus 298
Ahrens, Wilhelm Ernst Martin Georg 189 191 363
Air-raid casualties, statistics of 262—263
Alcuin 159
Aleph-null 45 54
Alephs 45 46—47 62 63
Alexander of Macedon 343
Algebraic equations with integer coefficients 6 49 64 71 79 84 109 111
Algebraic invariant 298
Algebraic numbers 49 50 110
Alte Probleme — Neue Loesungen 219
American Journal of Mathematics, The 178 191
American Mathematical Monthly 363 364
Amusements in Mathematics 189
Analysis situs 266 271—274 287
Analytic Theory of Probability 240
Analytical geometry 95—99 103 120—123 305 306 314
Analytical Theory of Heat, The 254
Annals of Mathematics 191
Anthropology, statistics in 260—261
Anti-snowflake curve 348—351
Apollo 71
Apollonius 12 13
Applied mathematics 114 116 150 151
Approximation, methods of 318 333—334 336—337
Arabs 17 185
Arago, Dominique Francois Jean 190
Archimedean number (see ) 75
Archimedes 33—34 69 74 310 331
Architecture of the Universe, The 367
Area under a curve 335—339
Argand, Jean Robert 100
Aristotle 62 117 213 230—231
Arithmetic 28 43 46 68 81 92 300 341
Arithmetic fallacies 208—211
Arithmetic tricks 163—164
Arithmetical progression 82
Arrow in flight paradox 37 38—39 58—60 62 301 321
Aspects of Science 367
Augustine, Saint 112 150
Axiom, reducibility 63 218 221
Babylonians 190
Bachet, Claude-Gaspard, Sieur de Meziriac 157
Ball, Walter William Rouse 189 190 191 219 221 363
Banach and Tarski’s theorem 205—207 219
Banach, Stephen 205—207 219
Barrow, Isaac 323
Beethoven, Ludwig van 362
Bell, Eric Temple 142 363
Beltrami, Eugenio 142
Bergson, Henri 65 108
Berkeley, George, Bishop 40
Bernoulli, James 240
Binary notation 165—173
Binomial theorem 249—251 264
Bismarck, Otto Edward Leopold, Prince von 177
Black, Max 363
Bliss, Gilbert Ames 363—364
Bolsheviks 8
Boltzmann, Ludwig 95 258
Bolyai, Johann 118 135
Bolzano, Bernhard 39 40—42
Bom belli, Raphael 91
Booth, John Wilkes 236
Bouton 191
Boyle, Robert 257—258
Bridgman, Percy Williams 84 364
Briggs, Henry 81 84
Brouncker, William, Viscount 78
Brouwer, Luitzen Egbertus Jan 37 221 291 292 298
Brouwer’s problem 287—291
Brownian movement 24—25
Budget of Paradoxes 79 261 365
Buergi, Jobst 110
Buffon, George Louis Leclerc, Count de 110 246—247
Cabalists 269
Cajori, Florian 81 298 355 364
Calculus 299—343
Calculus of probability 228 229 230 238—251 252 253
Calculus, differential 14 75 299 310 322—329 330 341
Calculus, integral 75 299 310 329—342
Camera, Primo 23
Cantor, Georg 39 41 42—57 62 63 194 364
Cantor’s diagonal array 52—53
Cantor’s paradox 43 44
Cantor’s theorem 43—44 55
card tricks 163
Cardan, Girolamo 91 168
Cardinal numbers 64
Cardinal of the continuum 53 55
Cardinality 44 45 46 48 49 54 55
Carlyle, Thomas 39
Carroll, Lewis 61
Carslaw, Horatio Scott 364
Casting out nines 164—165
Catenary 107
Catherine II of Russia 265
Catherine of Aragon 236
Cauchy, Augustin Louis, Baron 14
Cavalieri, Bonaventura 332
Cavalieri’s theorem 332
Cayley, Arthur 118 156 186 298
Centroid 340
Ceulen, van, Ludolph 75
Chaldeans 28
Chance 223—264
Chance, calculus of 239—251
Chance, Love, and Logic 264 367
Change 300 301 302 304 321
Charlemagne 157 159
Chaucer, Geoffrey 3
Chess 32—33 68 115 173 222
Chinese 90
Chinese ring puzzle 169
circle 10—14 17 41—42 66—67 73 78 80 277 278 279 280 282 310—312 337 343—344
Circle, squaring of the 12 65 66—69 71—79 109 331
Class of all classes not members of themselves 216—217
Classes 28—31 42—58 61 62 63 120 132 151—152 154 216—217
Clausius, Rudolf Julius Emmanuel 258
Clebsch, Rudolf Friedrich Alfred 298
clock 14
Co-ordinates 96—99 102 120 121 122 123 314
Coat and vest problem 286—287
Coefficients of an equation 109—110
Cohen, Morris Raphael 137 150—154 224 264 364
Colerus, Egmont 155
Collected Scientific Papers (of P.G. Tait) 191
Combinations 242—244
Combinatorial analysis 242 243
complex numbers 95 101—102 103 210
Complex plane 101—102
Compound interest 86—87 111
Compound probability 248—251
Comte, Auguste 67
Condorcet, Marie Jean Antoine Nicolas, Marquis de 253—254
Confessions (of St. Augustine) 150
Congruence 126 202 204 205 206 219
Conic sections 17 107
Connectivity, nonsimple 279—283 284
Connectivity, simple 276—277 281 282 283 290
Continued fractions 75 78 85—86
Continuum 53 55 56 58
Continuum, cardinal of the 53 55
| Contributions to the Founding of the Theory of Transfinite Numbers 364
Convergence of a series 64 69 70 109
Cooley, Hollis Raymond 364
Cosine 355—356
Countable classes 45 47 49
Counting 27 28—30 34
Courant, Richard 364
Course of Pure Mathematics, A 365
Craig, John 261
Creative Evolution 108
Cretans 62—63 221
Crime of Sylvester Bonnard, The 189
Crisscross curve 353—355
Cryptograms 233—235
Cubic equation 17
Cubit 173 191
Curtate cycloid 200
Curvature 28 147—148 328
Curves of error 257—260
Curves, anti-snowflake 348—351
Curves, catenary 107
Curves, circle 10—14 17 41—42 66—67 73 78 80 277 278 279 280 282 310—312 337 343—344
Curves, clock 14
Curves, crisscross 353—355
Curves, curtate cycloid 200
Curves, cycle 11—13
Curves, cycloid 196—200
Curves, ellipse 17
Curves, hyperbola 17
Curves, nonsimply-connected 7 281
Curves, parabola 17 106—107 308 330 331
Curves, patho-circle 13
Curves, pathological 343—355
Curves, prolate cycloid 198—199
Curves, simply-connected 7 276—282
Curves, snowflake 344—350
Curves, space-filling 352—353
Curves, tractrix 141 142 143
Curves, turbine 9—10
CYCLE 11—13
Cycloid 196—200
da Vinci, Leonardo 362
Dampier, William, Sir 259 260
Dantzig, Tobias 111 264 364—365
Darwin, Charles Galton 264
Dase, Johann Martin Zacharias 77
Davis, Watson 25
De Moivre, Abraham 103
de Morgan, Augustus 79 228 261 365
Decimal notation 164 165 166 167
Decimal, nonterminating 51—53 64 167
Dedekind, Richard 41
Deductive method 232
Definite integral 339—341
Delphic oracle 71 157
Denumerable classes 45 49 50
Denumerably infinite classes 45 49
Dependent variable 314 315 316 321
Derivative 14 111 322—329 341—342 356
Descartes, Rene 65 95 96 290 306 359
Diagonal proof, Cantor’s 52—53
Dice 237 239 244 245
Dichotomy Paradox 37—38
Die Paradoxien des Unendlichen 40
Differential and integral calculus 364
Differential calculus 14 75 299 310 322—329 330 341
Differentiation 5 322—323 325—326 341 342
DIMENSION 119—121
Diophantus 187
Discriminant 298
Divergence of a series 109
Doughnut 281 282 287
Doyle, Arthur Conan, Sir 263
Drawing cards from a pack 237 243—244
Dresden, Arnold 191 365
Dtirer, Albrecht 185
Dudeney, Henry Ernest 189
Duodecimal notation 190
Duplication of the cube 12 66 68 71—72 109
Dyadic notation 165—173
d’Alembert, Jean le Rond 246
e 49 50 66 80 84—86 87—88 89 110 111
Eddington, Arthur Stanley, Sir 23 32 131 154 365
Egyptians 8 17 66 74 167
Einfuhrung in das mathematische Denken 219
Einstein, Albert 22 23 29
Elementary Mathematics from a Higher Standpoint 366
Elements 9—10 151—152 154
Elements (of Euclid) 4 108 113
Elements of Non-Euclidean Plane Geometry and Trigonometry 364
Elements of the Differential and Integral Calculus 365
ellipse 17
Ellipsoid 147
Encyclopedie 246
Enriques, Federigo 365
Epimenides paradox 62—63 221
Equations, algebraic 6 298
Equations, cubic 17
Equations, quadratic 17
Equations, quartic 17
Equations, quintic 17—18
Equations, with integer coefficients 6 49 64 71 79 84 109 111
Equiprobability 241—242 248 251
Error, probability curve of 257—260
Essai philosophique sur la probabilite 264
Euclid 4 62 69 108 113—114 115 134 135 137—140 143 147—150 187 192 271 304
Euclidean geometry 116 134 137 138 139 140 143 149 150
Euclidean manifold 123—124
Euler, Leonhard 85—86 92 93 103 156 185 265—268 269 290—291
Euler’s theorem 266—268 290—291
Evolution 6 93
Existence 61—62 63
Exponential function 88—89 111 300 342
Exponents 82 110
Factorial 111
Fallacies, arithmetic 208—211
Fallacies, geometric 211—213
Fallacies, mathematical 207—213
Falling bodies 316—321 326—328 342—343
Fermat, Pierre de 68 156 187 188 239—240 306
Fermat’s Last Theorem 68 187—188
Finite classes 43
Finite numbers 19 22 23 32—33 47 63
Flatland — A Romance of Many Dimensions 128 363
Flaubert, Carolyn 158
Flaubert, Gustave 158
Formalists 62 222
Forsyth, Andrew Russell 154
Foundation of Physics 154
Foundations of Science, The 367
Four-color problem 287—291
Four-dimensional geometry 93 113 115 116 118 119 124 300 359
Four-dimensional manifold 123—124 154
Fourier, Jean Baptiste Joseph 254—255
Fourth dimension 116 117 118 119 124 125 127—128 130 131
Fourth Dimension Simply Explained, The 366
Fractions, continued 75 78 85—86
Fractions, rational 48
France, Anatole 189
Franklin, Benjamin 186
Frege, Gottlob 218
Function 5 14 304 309 312—316 318—327 332
Function, exponential 88—89 111 300 342
Function, monogenic 14
Function, one-valued 64
Function, polygenic 14
Function, trigonometric 355—356
Functions of a real variable, theory of 201
Fundamental Concepts of Algebra and Geometry 154 368
Galileo 41 198 252 365
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