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| Kasner E., Newman J. — Mathematics and the imagination |
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| Ïðåäìåòíûé óêàçàòåëü |
Principle of insufficient reason 229—230 263—264
probability 223—264
Probability, compound 248—251
Probability, equiprobability 241—242 248 251
Probability, independent events 244—247
Probability, mutually exclusive events 243—244
Probability, principle of insufficient reason 229—230 263—264
Probability, relative frequency view 230—237
Probability, statistical interpretation 230—237
Probability, subjective view 227—230
Probability, truth frequency theory 238
Problems, Brouwer’s 291—297
Problems, drawing cards from a pack 237 243—244
Problems, four-color 287—291
Problems, M bius surfaces 118 186 284—286
Problems, map-coloring 186 287—291
Problems, needle 110 246—247
Problems, number theory 186—188
Problems, of Apollonius 12—13
Problems, of coat and vest 286—287
Problems, of existence 61—62
Problems, of falling bodies 316—321 326—328 342—343
Problems, of interlocking rings 285 286 287
Problems, of seven bridges 265—268 270
Problems, pouring 161—162 190 191
Problems, relationship 183—185
Problems, ring 168—169
Problems, river-crossing 159 189—190
Problems, Russian multiplication 167—168
Problems, shunting 159—160
Problems, spider and fly 181—182
Problems, string 191—192
Problems, tower of Hanoi 169—171
Projective geometry 151
Prolate cycloid 198—199
Propositional functions 263
Pseudosphere 140 142—143 146 154—155
Ptolemy 74 117
Pure mathematics 114 116 150 152
Puzzles 156 157 158 162 168—169 177—180 189—190 191—192 300
Pythagoras 28 357 359
Pythagorean Theorem 121—122 124
Pythagoreans 268
Qu elet, Lambert Adolphe Jacques 260
Quadratic equation 17 298
Quartic equations 17
Queen of the Sciences, The 363
Quintic equations 17—18
Rcrations Mathmatiques 189
Radical 16—18
Radius of curvature 328
Railway train paradox 200
Ramsay, Frank Plumpton 221
Rate of change 111 305 316 321—323 326
Rational fractions 48
Rational numbers 49 50
Real numbers 49 50 51 53 54 55
Reason and Nature 154
Reasoning by probable inference 224 226
Reasoning by recurrence 36
Recreations, mathematical 156 192
Rectifying the parabola 331 356
Reducibility see Axioms
Relationship problems 183—185
Relative frequency view of probability 230—237
Rest, absolute 24
Richter 77
Riemann, Georg Friedrich Bernhard 139 140 142—150 181 271
Riemannian geometry 139—140 142 143 144 145 146 149 150
Ring 5 279 281
River-crossing problem 159 189—190
Rolling circles paradox 195—196
Rolling coin paradox 194—195
Rubber-sheet geometry 265—298
Ruflini, Paolo 17
Russell, Bertrand Arthur William 37 39 56 60 218 221 222 299 367
Russell’s paradox 216—217
Russian multiplication 167—168
Sanctions 294
Sand Reckoner, The 33—34
Sceptical Chymist, The 257
Scheherezade 235
Schubert, Hermann Caesar Hannibal 176
Science and Hypothesis 298
Second derivative 326—328
Self-consistency, principle of 62—63 115—116 124
Semantics 90
Series, infinite 38 64 65 66 69—70 75 76 77 78 79 80 87 109 346—347
Seven bridges’ problem 265—268 270
Seventh — Day Adventists 148
Sexagesimal notation 190
Shanks, W. 77—78
Sharp, Abraham 77
Shunting problem 159—160
Simple curves 7 276—282
Sine 355—356
Skewes 32
Skewes’ number 32 33
Slope of a tangent 324—325 330 356
Smith, David Eugene 191 367
Smith, Percey Franklyn 365
Socrates 228
| Sophie Charlotte, Queen of Prussia 39
Sophists 213
Soviet Russia 93
Space continuum 58
Space filling curve 352—353
Space, physical 28 56 65 112—113 117 119 124 131 132 133 137 149—150
Space, Time, and Gravitation 154 365
Spencer, Herbert 6
Sphere 143—145 147 181 203—204 282 283 284 290
Spider and fly problem 181—182
Square root 108 209—210
Squaring of the circle 12 65 66—69 71—79 109 331
Squaring of the parabola 330 331
Statistical interpretation of probability 230—237
Statistical view of nature 254
Statistics, in anthropology 260—261
Statistics, of air-raid casualties 262—263
Steinhaus, Hugo 367
Stereometria 332
Story, William Edward 191
Straight line 146 181—183
String problem 191—192
Subjective view of probability 227—230
Sue, Eug ne Joseph Marie 183
Sullivan, John William Navin 367
Swann, William Francis Gray 367—368
Sylvester, James Joseph 118 298
Tait, Peter Guthrie 176 191
Tangent of an angle 355—356
Tangent to a curve 324—325 356
Tarski, Alfred 205—207 219
Tartaglia, Niccol 159
Terminating decimal 64
Tesseract 109 125 126
Theologiae Christianae Principia Mathematica 261
Theorems, Banach and Tarski’s 205—207 219
Theorems, binomial 249—251 264
Theorems, Cantor’s 43—44 55
Theorems, Cavalieri’s 332
Theorems, Euler’s 266—268 290—291
Theorems, Fermat’s last 68 187—188
Theorems, geometric mean 99—100
Theorems, Goldbach’s 187
Theorems, Hausdorffs 204—205 207 219
Theorems, Jordan’s 7 276 278 279
Theorems, parhexagon 15—16
Theorems, probability of joint occurrence, of two independent events 244—245
Theorems, Pythagorean 121—122 124
Theory of cycles 12
Theory of groups 5
Theory of point sets 201—204 219 291
Theory of probability 223—264
Theory of types 63 218 221
Thirring, Hans 366
Three-dimensional geometry 120—123
Three-dimensional manifold 120—124 154 282—284
Three-dimensional space 56 115 116 130 205 206
Time continuum 58
Todhunter, Isaac 261
topology 266 271—274 276—297 300 359
Tossing coins 225 231 232 244 245
Tower of Hanoi problem 169—171
Tractrix 141 142 143
Transcendental numbers 6 49 50 53 64 78 79 84 111 117
Transfinite numbers 45 47 49 53 54 55 63 194 359
Treatise on Probability, A 238 263 366
Trigonometric functions 355—356
Trisection of an angle 12 68 72 109
Truth frequency theory of probability 238
Turbine 9—10
Twain, Mark 156 157
Two New Sciences 365
Two-dimensional manifold 278 279 282
Two-dimensional space 128
Types, theory of 63 218 221
Ultraradical 16—18
Universe Around Us, The 258
Variable quantities 5 305—306 310—312
variables, dependent 314 315 316 321
Variables, independent 314 315 316 321 326
Veblen, Oswald 151
Velocity 301 342—343 356
Veronese 118
Vieta, Francisco 74—75 80—81
Vizetelly, Frank 3
Vom Punkt zur vierten Dimension 155
Vorstudien zur Topologie 272
Wahlert, Howard E. 364
Waismann, Friedrich 219
Wallis, John 75—76 78 118
Weierstrass, Karl Theodor Wilhelm 39 43 298 332
Wessel, Caspar 100
Weyl, Hermann 221
Whitehead, Alfred North 218 368
Wolf, Abraham 356
Yoneyama 291
Young, John Wesley 151 154 368
Zeno 37—39 57 194 301 321
Zero, absolute 24
Zeuxippus 34
“Boss puzzle” see “15 Puzzle”
“Going to Jerusalem” 29—30
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