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Tietze H. — Famous Problems of Mathematics Solved and Unsolved
Tietze H. — Famous Problems of Mathematics Solved and Unsolved

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Название: Famous Problems of Mathematics Solved and Unsolved

Автор: Tietze H.

Аннотация:

This book seeks to resemble such a convenient аlpine railway up into the world of mathematics. It can give nothing to the man in whom no chord vibrates rcsponsively to the peculiar harmonies of this realm of thought, who accepts with inward indifference the technological and scientific acquisitions which he uses cvciy day of his life, and which were made possible only by the fruitful contributions of mathematics. But we venture to hope that there will also be readers who will not remain entirely untouched by the aura which breathes in this realm that affects most people as being so unapproachable. It is possible, if fate so wills it, that there may even be some young man with unspent energies and with the necessary ability, who will feel the urge to pursue the subject more seriously, spurred by the distant vision offered to him here. For I confess that what is offered here will not be able to satisfy him, nor should it. From the railway route along which we here guide the reader are excluded, because of their difficulty of access, many of the most important mountain heights and lines of advance.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1965

Количество страниц: 399

Добавлена в каталог: 15.04.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$e$      104 148
$e$ poem      105
$n$-dimensional non - Euclidean geometry      324
$n$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 M$\acute{e}$ziriac      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
Carath$\acute{e}$odory, 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 $p$ 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 $n$-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$\acute{e}$      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 K$\ddot{o}$nigsberg 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
Fr$\acute{e}$chet, Maurice      120
Fr$\acute{e}$nicle 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, $\acute{E}$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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