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| Mumford D., Wright D., Series C. — Indra's Pearls: The Vision of Felix Klein |
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| Предметный указатель |
 see infinity
 -parameter 259 287
-value 302
3-manifold 387
3-sphere 387
Ahlfors, Lars 384 386
Aigand diagiam 41
Apollonian gasket 196—208 228 231 245 252 259 265 274 292 325 330 341 362 368
Apollonian packing see Apollonian gasket
Apollonius 194 199
Arctangent 42
Area-filling curves 329
Associative law 22
Asymptotic self-similarity 317
Automaton 356
Automorphic function 374 375
Avatamsaka Sutra xvii
Axioms 377
Beltrami, Eugenio 379
Bers, Lipman 280 291 312 313 384
BFS see breadth-first search
Bilateral symmetry 6
Binary notation 128
Bolyai, Janos xv
Boundary tracing 301—307
Breadth-first search 113—117
Butterfly effect 133
Cannon, James 331 356
Cantor set 136
Cantor, Georg 3 129 155 312 328 329
Cardano's Formula 38
Cardano, Girolamo 37
Cayley graph 105
Cayley map 89
Cayley, Arthur 105
Chaotic xvii 133 141 153
Commutative law 48
Commutator 167 169 181 185 265
Commutator, trace 193
Commuting maps 15 169
complex numbers 36—61
Complex numbers, absolute value 43
Complex numbers, argument 43
Complex numbers, imaginary part 39
Complex numbers, modulus 43
Complex numbers, polar representation 43 45
Complex numbers, programming 46—48
Complex numbers, purely imaginary 39
Complex numbers, real part 39
Complex plane 41
Complex square roots 60
composition 14—17 23 33 61
Concatenation 278 283 325
conjugate 173
Conjugate, complex 39 44
Conjugate, group 173—178 195 266
Conjugation 26—28
Conjugation of maps 27 51
Conjugation, method of 64
Continued fraction 212 294 308 316 349
Convex hull boundary 390
Core chain 271
Countable set 129 155
Cubic equation 37 38 304
Cusp 273
Cusp group see group cusp
Cyclic permutation, order 143
Decimals 125—129 154
Decimals, repeating 126 155 291
Depth-first search 113 122 141—150
Determinant 70
DFS see depth-first search
Dictionary ordering 116
DIMENSION 328 see
Diophantine equation 192
Discrete group see group discrete
Elliptic functions 374
Elliptic map see map elliptic
Epstein, D.B.A. 356 358
Erlanger Programm xvi 1 71
Euclidean algorithm 213 222 306—307
Exponential function 51—54
Exponential shrinking 103 118 170
Extended real line 86
Farey addition 212 276 316
Farey fractions 223 301 306
Farey John 212
Farey neighbours 212 223 278
Farey sequence 155 301 306
Farey tessellation 285
Fibonacci numbers 316
Figure of Eight Knot 388
Fixed point 51 78
Fixed point, attracting 51
Fixed point, equation 78 155
Fixed point, neutral 82
Fixed point, repelling 51
Ford circles 221
Fractal 138—141
Fractal dimension 140 253 254 see
Fractal dust 121
Fricke identities 189
Fricke, Robert, xvi 3 161
Fuchs, Immanuel 179 376
Fundamental region 35
Fundamental theorem of algebra 46 287
Galois, Evariste 20
Gasket see Apollonian Gasket
Gauss, Carl Friedrich 209
Gaussian integers 59
Generators see group generators
Genus of a surface 383
Geodesies 390
Geometrization conjecture 389
Golden mean 316
Grandma 85 92 227—230 264 293
Group 3 17—21 23 51
Group,  -Schottky 118
Group, automatic 356
Group, classical Schottky 102
Group, cusp 248 266 268—309
Group, degenerate 312 369
Group, discrete 239
Group, double cusp 204 248 268 275 291—301
Group, doubly-degenerate 312 339
Group, free 98 132 356
Group, Fuchsian 161 178 180
Group, Fuchsian Schottky 118 177
Group, full modular 210
Group, general Schottky 102 274
Group, generators 20 232
Group, kissing Schottky 158 170—172
Group, Kleinian 353 360
Group, Maskit 259 260 291—296
Group, maximally cusped 204
Group, modular 206—218 223 224 374
Group, more than 2 generators 365—370
Group, non-discrete 232
Group, non-free 353—364
Group, once-punctured torus 190 228
Group, parabolic commutator 228
Group, parameterized family 171
Group, quasifuchsian 161
Group, Riley 258
Group, Schottky 98—103 157
Group, single cusp 248
Group, singly-degenerate 312
Group, totally degenerate 312
Group, two-generator, Grandma's 265
Group, unit circle 89
| Group, upper half plane 86
Hausdorff dimension 136 139 155 256—259 309 313
Hokusai, Great Wave 371
Holt, Derek 356 358 360 381
Hyperbolic 3-space 386 388
Hyperbolic functions 47
Hyperbolic geometry 314 333 373 376
Hyperbolic map see map hyperbolic
Hyperbolic plane 379 381
Hyperbolic space 164
Hyperbolization theorem 389
Ideal triangle 196 199 221
Identity transformation 19 93 98 354
IFS see random search
Image 10
Imaginary axis 41
incircle 197 199
Independence of starting point 133 155
Indra's net ii xvii
infinity 55—57
Invariant 15 98 101 164 373 374
Inverse, in group 23
inversion 54—56
Iowa 4
Irrational number 34 50 53 214 310 314 333 350
Iteration 5 51 153 303
Jergensen's doubly-degenenerate group 331
Jergensen's point 319
Jergensen's singly-degenerate group 314
Jergensen, Troels 256 312 333 388
Jordan curve 226
Jordan, Camille 20
Julia set 291
KBMAG 358 360 381
Kissing chain of circles 157
Klein, Felix vii xvi 1 2 20 38 62 71 100 105 161 190 373 374 377 380
Kleinian group see group Kleinian
Knot complements 388
Kra, Irwin 367 372
Lie, Sophus 20
Limit, algebraic 343
Limit, geometric 343
Limit, point 121—125
Limit, set 100 121
Lindenmaier or L-system 329
Loxodrome 64
Loxodromic map see map loxodromic
Mandelbrot set viii 215 291
Mandelbrot, Benoit viii 121 139 152 253 329
MAP 10 12
Map, affine 51 60
Map, angle preserving 77
Map, classification 81
Map, conformal 383 384
Map, conjugating 27 64
Map, elliptic 79
Map, extremal quasiconformal 384
Map, hyperbolic 79 87
Map, inverse 12 61
Map, linear 33
Map, loxodromic 79
Map, Markov 338
Map, Moebius 62—95
Map, nearly parabolic 243 252
Map, non-linear 66
Map, orientation preserving 77
Map, pairing 91 96 97
Map, parabolic 79
Map, quasiconformal 384
Map, stretch 89
Map, trace 84
Mapping 10
Markov chain 154
Markov conjecture 191 283 352
Markov identity 189
Maskit's slice 287—292
Matrix algebra 72—74
Matrix inverse 73
McMullen, Curt x xi 139 140 156 197 256 291 317 321 324 333 345 349
Minsky, Yair 291 324 391
Modular function 374
Modular group see group modular
Modular necklace 214
Modular, arithmetic 144
Moduli 383
Moebius map see map Moebius
Moebius, August xvi 71
Motions 4
Multiplier 79
Necklace conditions 168 361
Necks, problem of 184 248—252
Neighbour fractions see Farey neighbours
Newton solver 302—307 309
Newton's method 287 302
nodes 103
Non-discrete group see group non-discrete
Non-Euclidean geometry 373 377 see geometry
Non-Euclidean space 164 see space
Normalization 227
Orbit 18 21 50 51
Ordinary set 109 161
Orientation, of generators 297
Parabolic map see map parabolic
Parallel postulate 378
Parameters 111 171 227
Peano curves 329
Period 126
Plotting limit points 132—135
Poincare conjecture 389
Poincare disk 380
Poincare, Henri 100 376
Point at infinity see infinity
Polar coordinates 42—45
Polynomial equation of degree n 46
Prefix 126
Preserves angles and circles 58
Programming 28—33
Programming, automatic groups 358—360
Programming, boundary tracing 304—307
Programming, depth-first search 145—150
Programming, drawing curves 182—187
Programming, Euclid's algorithm 307
Programming, Moebius maps 76 91
Programming, Newton's method 302—307
Programming, Schottky groups 111—117
Programming, sealing gaps 215—221
Programming, special words algorithm 217—221 260—264
Pseudo-code 30
Puncture 189
Quadratic equation 37
Quadratic form 209
Quasicircle 161
Quasifuchsian see group quasifuchsian
RADIANS 43
Random search 113 152—154
Real axis 41
Real trace ray 296 390
Recipes, Grandma's 227—233
Recipes, Grandma's Special Four-Alarm 260—261 362
Recipes, Jergensen's 256—257
Recipes, Maskit's 259—260
Recipes, Moebius maps 85—92
Recipes, Riley's 258—259
Recipes, Schottky groups 117—119
Recursion 150
Reflection 6
Regular set see ordinary set
Renormalization 322
Repetend 126
Richardson, Lewis Fry 253
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