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Tietze H. — Famous Problems of Mathematics Solved and Unsolved |
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Предметный указатель |
104 148
poem 105
-dimensional non - Euclidean geometry 324
th roots of unity 222
Abel, Niels Henrik 215 ff. 218 224
Abelian integrals 224
Abel’s theorem 224
Abstract group theory 225
Abu Dschafar 278
Abu Nasr 295
Abul Wafa 295
Adams, John Couch 208
Aleph One 261 ff.
Aleph three 263
Aleph two 263
Aleph zero 261
Alephs 261
Alexandroff, Paul 120
Algebraic geometry 235 242
Algebraic number 105
Algebraic number theory 179 297 301
Algebraictopology 325
Alhogendi 278 295
Analysis 151
Analytic geometry 39
Analytic manifolds 331
Analytic number theory 151
applications 333
Applied mathematics 336
Arabic numerals 156
Archimedes 99 100 104 166 176 199 245 290 309
Aristotle 174
Arithmetic progression 144
Automorphic functions 335
Axiom of Parallels 194 314 327 328
Bachet de Mziriac 290
Beha Eddin 278 295
Berkeley, George 327
Bernoulli family 286
Bernoulli numbers 301
Bernoulli, Daniel 286
Bernoulli, Jakob 279 286 302
Bernoulli, Johann 279 286 302
Bernoulli, Nicolaus 280 302
Besicovitch, A. S. 89 104
Betti groups 325
Betti, Enrico 325
Bicontinuous correspondence 274
Birkhoff, G. D. 41 335
Bisection 50 ff.
Boltzmann, Ludwig 334
Bolyai, Johann 314
Bolzano, Bernard 247 265
Boundary 69
Brahmagupta 159 177 295
Brianchon, Charles Julien 327
Brouwer, L. E. J. 115 120
Buffon, George Louis Leclerc 174
Calculus of variations 39 40 288 332
Cantor, Georg 171 181 209 247 248 258 261 263 265
Cantor, Moritz 172 206
Cantor’s conjecture 263
Cantor’s diagonal method 274
Carathodory, Constantin 181 210 225 265 290 332 333 335
Cardano, Hieronimo 213 214 215 224
Cardano’s Formula 213 223 279
Cardinality of infinite sets 249
Cassini, Giovanni Domenico 205
Catherine the Great 289
Cauchy, Augustin 216 217 225
Cayley, Arthur 227 234 240 242
CERES 195
Christoffel, Elwin Bruno 331
Chromatic number 230
Chromatic number of a sphere with handles 241
Chromatic number of disconnected domains 242
Chromatic number of the plane 230
Chromatic number of the sphere 230
Classical non - Euclidean geometry 313 318 319 328
Classification of manifolds 336
Closed convex surface 32 41
Closed geodesic 29 31
Closed geodesics on a closed convex surface 32 33
Closed geodesics without double points 41
Closed orientable two-dimensional surfaces 86
Closed surface of genus zero 41
Clusius, Klaus 104
Cohen, Paul J. 263
Commensurable 168 ff.
Comparison of finite sets 245
Comparison of infinite sets 247 249 252
Comparison of sets 244 252
Complement 244
Completeness of the real numbers 275
complex numbers 169
Composite number 2
Cone 321
Conformal mapping 331
Congruence 306
Conic section 130 144 327
Constant negative curvature 29 30
Constructible -gons 188 ff.
Construction of the alephs 261
Construction of the regular 17-gon 189 ff.
Continued fractions 259 ff. 270
Continuity 116
Continuous function 116
Continuous variables 151
Continuum Hypothesis 263
Continuum problem 263
Contraction 320 322
Contraction in space 322
Contraction index 322
Contraction on a pseudo-sphere 321
Contraction on a sphere 320
Contraction, measure of 320
Convex bodies 31 ff. 41
Convex figures 78 ff.
Convex neighboring domains in space 80 ff. 82 89
Convex set 88
Convex surface 31 ff.
Convexity 41 78
Counting 243
Counting process 156
Courant, Richard 210
Crelle, August Leopold 216
Cube roots of unity 222
Cubic equation 211 ff. 214 223
Curvature 31 41 305 322
Curvature index 322
Curved surfaces 316 ff.
Cycloid 327
Cylinder 88
Dase, Zacharias 100 104
de Morgan, Augustus 88 226
Dead row 122 143
Decimal system 158
Dedekind, Richard 170 ff. 179 247 264 266 301 325
Degrees of infinity 243
Dense 254
Denumerable set 252
Denumerable sets, examples of 252 ff. 258
Desargues, Girard 56 83
Descartes, Ren 53 ff. 95 231 279 295
Descartes’ Rule of Signs 224
Diabolo 36 ff.
Dido 332
Dido’s problem 332 335
Differential calculus 332
Differential geometry 41 64 73
| DIMENSION 106 ff. 113 114 116 258 265 274
Dimension number 115
Dimension theory 115 247 266
Dinghas, Alexander 335
Diophantus of Alexandria 180 280 281 286 288 296
Dirac, G. A. 241
Dirichlet, Peter Gustav Lejeune 122 123 124 126 133 143 144 151 283 284 300 301 326 331
Dirichlet’s Theorem 123 124 125 144 153 193 209
Discrete variables 151
Disk test 34 ff. 42
Distribution of prime twins 9 ff.
Distribution of the primes 3 ff.
Divergent series 302
Divison of an angle 58
Dodecahedral subdivision 236
dodecahedron 236
Double torus 72 233
Dtirer, Albrecht 45
Du Bois - Reymond, Paul 181 265
Dual of a subdivision 83
Duodecimal system 159 ff.
Dupin indicatrix 42
Dyadic system 176
Edge of a map 239
Einstein, Albert 330
Elementary domain 237
Elements of a set 244
ellipse 40
Ellipsoid of rotation 27
Ellipsoid, oblate 27
Ellipsoid, triaxial 28
Elliptic functions 208 209 224 331
Elliptic geometry 328
Empty set 244
Encke, Johann Franz 133
Equality of sets 244
Equations of degree greater than four 211 215
Equivalence of sets 249
Equivalent sets 245 249 252
Ergodic theory 332
EROS 29
Essential properties 72
Euclid 7 8 9 19 20 154 168 187 194 216 294 307 327
Euclidean algorithm 154
Euclidean geometry 308 ff. 328
Euclid’s Elements 8 19 168
Euclid’s theorem 8
Euler characteristic 87 241
Euler, Leonhard 18 19 99 148 202 215 216 234 282 284 286 296 297 301 302
Euler’s Knigsberg bridge problem 87
Euler’s polyhedral theorem 87 231 239 240 241
Extension of the number system 166 ff.
Faulhaber, Johann 56
Fermat exponent 283
Fermat primes 188
Fermat, Pierre de 126 202 279 284 286 288 295 296 297
Fermat’s last problem 281 ff.
Fermat’s Little Theorem 281
Ferrari, Luigi 213 214 215
Ferro, Scipione del 214
Fibonacci, Leonardo 176
finite 243
Fixed direction 21 23 24 25
Foundations of mathematics 264
Foundations of set theory 264
Four color problem 230 ff.
Four-dimensional chess 113
Four-dimensional chess domain 113
Four-dimensional chess space-time world 113 324
Fourier, Jean Baptiste 126 225
Fourth roots of unity 222
Frchet, Maurice 120
Frnicle de Bessy, Bernard 282 284 295 296
Frederick the Great 286 288 289 302
French school 302
Fricke, Robert 180
Function theory 224
Functions of several complex variables 336
Fundamental theorem of algebra 208 225
Fuss, Nicolaus von 289
Galilei, Galileo 205
Galle, Johann Gottfried 208
Galois theory 216 219 220
Galois, variste 217 ff. 225
Gauss primes 188 204
Gauss, Carl Friedrich 64 87 125 126 133 170 171 182 187 193 204 208 209 215 217 218 225 234 283 285 286 287 290 296 305 310 312 314 315 324 325 326
Gauss’ theorem on regular polygons 188 189
Genus of a surface 87 88
Geodesics 27 40 64
Geodesics on an ellipsoid 28
Geodesics on closed convex surfaces 32
Geometric perceptions, formation of 305
Germain, Sophie 283
Goldbach conjecture 335
Graph theory 235
Grassmann, Hermann 83
Great circles 24 25 26 40
Gregory, James 105
Group theory 220 225
Guthrie, Francis 88 226
Guthrie, Frederick 77 88 226
Hadamard, Jacques 127 133 134 332
Hamilton, William Rowan 333
Hamilton’s dodecahedron game 87
Handles 86
Hardy, Godfrey Harold 335
Harnack, Axel 265
Heawood, Percy John 86 87 231 240 241 242
Heawood’s five color theorem 231 232 237 240 241
Heawood’s number 86 241
Heine, Eduard 181 247 248 265
Helmholtz, Hermann 111
Henry, Charles 296
Heredity, theory of 312
Herglotz, Gustav 29 41 331
Hermite, Charles 225
Herschel, Friedrich Wilhelm 206
Hilbert, David 117 119 266 301 332 335
Homogeneity of space 323
Humboldt, Alexander von 125 126 197 198 209
Hurewicz, Witold 120
Huyghens, Christian 205
Hypatia 180
Hyperbola 145
Hyperbolic geometry 328
Hyperboloid of one sheet 29
Ideals 170
imaginary numbers 166 177 195
Imbedding properties of surfaces 87 88
Imbedding property 317
Incommensurable 168 169
Independence of the continuum hypothesis 263
Infinite 243
Infinite descent, method of 282 296
Infinite numbers 243
Infinite set 246
Infinitude of prime twins 10
Infinitude of the primes 7 8
infinity 243
Inner (intrinsic) properties 318
Integral calculus 332
Integral logarithm 16 133 150 152
Integral logarithm curve 151
Integraph 98
Intermediate Value Theorem 265
Intrinsic (inner) properties of a surface 87 88
Invariance of dimension number 120
Irrational numbers 166 168 170 171 177 247 292
Isoperimetric problem 335
Jordan separation theorem 85
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