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Kasner E., Newman J. — Mathematics and the Imagination
Kasner E., Newman J. — Mathematics and the Imagination



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Íàçâàíèå: Mathematics and the Imagination

Àâòîðû: Kasner E., Newman J.

Àííîòàöèÿ:

Explores some of the lesser known and more imaginative aspects of mathematics, such as the googolplex, four-dimensional geometry, puzzles, paradoxes, the laws of chance, rubber-sheet geometry, and the historical development of calculus. Originally published by Simon and Schuster in 1940.


ßçûê: en

Ðóáðèêà: Ìàòåìàòèêà/

Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö

ed2k: ed2k stats

Ãîä èçäàíèÿ: 2001

Êîëè÷åñòâî ñòðàíèö: 400

Äîáàâëåíà â êàòàëîã: 21.04.2008

Îïåðàöèè: Ïîëîæèòü íà ïîëêó | Ñêîïèðîâàòü ññûëêó äëÿ ôîðóìà | Ñêîïèðîâàòü ID
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Ïðåäìåòíûé óêàçàòåëü
$\pi$      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 $\pi$)      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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