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Авторизация |
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Atanasov K.T., Turner J.C., Shannon A.G. — New Visual Perspectives on Fibonacci Numbers |
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Предметный указатель |
integer triangles 132
253
250
snowflake fractal 188
-rings 205
-rings, orthogonal circle 211
129
107
-rings 206
-rings, complementary 207
14 inner hexagons 266
2-chains 252
2-F-sequences 7
2-Fibonacci sequences 7
2-jigsaws 238
3-tile counting 254
3-tiles of SGPs, linear form 276
4-tile counting 255
4-tile linear forms 255
5-tile counting 258
6-tile counting 259
6-tile hexagons 259
6-tile shapes 258
6-tile studies 258
A-progression 41
Adjacency matrix 245
Aesthetic qualities of T 174
Aspects, two, of TGPs 249
Autogeneration 45
Axes in 113
B-points 114
Base 215
Basic theorem, first 20
Basic theorem, second 24
Burnside’s Theorem 245 250 254 257 259 272
Capturing 4-squares 301
Centroid of equilateral triangle 126
Challenges for square 300
Christmas puzzle 183
Codes for tetrahedra of TGPs 281
Condition for a B-point 115
Constructing (90, 60, 30) triangles 127
Constructing a rhombus 127
Constructing a tetrahedron 280
Constructions 188
Constructions, length a 188
Constructions, powers of a 189
Constructions, SGP square and star 196
Constructions, the switch 188
Convergence limit lines 119
Convergence properties of vector polygons 119
Counting (2n)-tiles 257
Counting 2-SGP jigsaws 273
Counting 2-tiles 276
Counting 3-tiles 276
Counting 4-tiles of SGPs 277
Counting linear forms, general 276
Counting the TGP tetrahedra 280
Cross-ratios in AB 185
Cyclic group tracksets 157
Deficiency 138
Determining subgroups from tracksets 165
Diophantine equation 132
Dust-sets 215
Equivalence of n-jigsaws 236
Equivalence of schemes 31
ET-transform 124
ET-transform of (90, 60, 30) triangles 130
ET-transforms of triangles 123
ET-transforms of vector polygons 134
F-triangles 90
Fibonacci chimney 149 157
Fibonacci golden star, two sub-stars 198
Fibonacci golden stars 197
Fibonacci honeycomb plane 107
Fibonacci mathematics 187
Fibonacci sequence generalization multiplicative form 39
Fibonacci sequence via arithmetic progression 41
Fibonacci track recurrence 153
Fibonacci vector geometry 86
Fibonacci vector identities 92
Fibonacci vector plane 139
Fibonacci vector polygons 119 137
Fibonacci vector sequences 108
Fibonacci vectors 85 108
filling cubes with SGP cubes 285
Filling the Squares 298
Fixed points 250
Formulae for ST-transforms 124
Four-squares equation 88
Fractal of pentagons 225
Fractals in gp geometry 215
Fractional dimension 217
Game, Goldpoint Chess 302
Games with SGPs 297
Games with TGPs 295
Games, TGP equipment 294
General Fibonacci sequence 85
General Fibonacci vector sequence 95 96 108
Generalized Fibonacci sequence 9 42
Geometric properties of G 96
Golden mean triangles 193
Golden motif triangle 224
Golden snowflake 216
Golden tile equivalence 232
Golden tiles 232
Golden triangles, flat and sharp 193
Goldpoint Chess 302
Goldpoint comb 220
Goldpoint counting 197
Goldpoint definition 230
Goldpoint density, simple 197
Goldpoint dust-set 219 220
Goldpoint fractals 215
Goldpoint fractals, interior/exterior 227
Goldpoint geometry 87
Goldpoint geometry, objectives 187
Goldpoint Hex Combat 296
Goldpoint Hex Solitaire 295
Goldpoint motif triangle 223 224
Goldpoint rings 205
Goldpoint rings, definition of 205
Goldpoint Rubik’s Cube 304
Goldpoint shield 216 217
Goldpoint Square Dominoes 298
Goldpoint star jewel 222
Goldpoint triangle dominoes 295
Goldpoints 183
Goldpoints, count in 202
Goldpoints, count in the Fibonacci Star 202
Goldpoints, definition 184
Goldpoints, snowflake fractal 191
Group of B-points 115
Group of rotations 263
H-points 114
Harmonic range 185
Herta Freitag 216 220
Herta’s shield 216
Hexagon 6-tiles, set of 261
Hexagon symmetries 263
Hexagon tiling 245
Hexagons in 114
Hexagons, inner 14 266
Higher order goldpoints 184
Honeycomb plane 87 114 140
Identity-spectra 157
Identity-spectrum 159
Impossibilty of integer squares 124
Incidence and reflection angles 151
Inherent 137
| Inherent sequence 170
Inherent transformation matrix 139
Inherent Type I solution 143
Inherent vector sequence 135
Inner hexagons 259 296
Inner hexagons, diagrams 267
Integer (60, 60, 60) triangles 124
Integer (90, 45, 45) triangles 123
Integer equilateral triangles 123 124
Integer line-segments 116
Integer point cover 112
Integer triangles 123
Integer vector 137
Integer vector sequences 85
Integer-vectors 95
Inter-linked recurrence equations 7
Invariant mappings 250
Jig-chains 245
Jigging matrix 251
Jigging matrix, SGPs 269
Jigging SGP-cubes 285
Jigsaw combination rules 232
Jigsaw formation 236
Jigsaw hexagons 267
Jigsaw pattern 232
Jigsaw-distinct SGPs 269
Knot from a trackset 172
Latin Square tracksets 157
Limit rays of G 100
Limit vector 101
Limit vectors, properties 104
Limiting ray of vector sequences 109
Linear TGP form 238
Location of B-points 114
ls-string 245
LTGP 238
Lucas vector polygon 151
Lucas vector polygons 119
m-squares equation 90
Mathematical mission 174
Maximal applicability 174
Minimal completeness 174
Motif 215
Multiplicative schemes 39
n-jigsaw 236
n-tiles of SGPs 276
Nearest neighbours of a point in 111
Notation for TGPs 250
Noughts and Crosses 297
Parametric solution of Diophantine equation 133
Partition of 110
Partition of integer lattice 107
Pell vector plane 139 144
Pentagom fractal, interior unicursals 228
Pentagon, exterior goldpoint fractal 227
Pentagons and S-triangles 224
Pentagram star 216
Period spectra 157
Period-spectrum of C4 159
Period-spectrum of V4 159
Periodic tracks 155
Permutation group 250
Plus-minus algebras 168
Plus-minus operation 169
Plus-minus recurrence form 169
Plus-minus recurrence tree 170
Plus-minus sequences modulo p 169
Points in the honeycomb plane 111
Projection of AB onto axes 117
Proof of 700 hexagon tiles 263
Properties of B-points 114
Pseudo-inverses 140
Ptolemaic dust-set 227
Purely periodic track 155
Quadrilateral on vector polygon 121
Redundancy 138
Regular pentagon, properties 225
Rhombus counting 253
Rhombus counts 239
Rhombus theorem 230
Rhombuses 252
Rotation group 250
Rotation of TGPs 234
Rotational symmetry 257
Second order recurrence equations inter-linked 7
Segment of length a 187
Sequence of goldpoint rings 210
SGP tessellations 269
SGP types 242
SGPs 233 241
SGPs, jigging matrix 269
SGPs, symmetry rotations 272
Simple goldpoint count 197
Six SGPs, set of representatives 273
Six types of SGP, diagrams 270
Six types of SGP, proof 270
Snowflake fractal 191
Snowflake fractal dimension 192
Spectra of cyclic groups 166
Spiral vector-product track 156
Square with goldpoints 194
Squares combat 300
Squares with goldpoints 241
Substitution, 3-F-sequences 30
Sums of squares equation 134
Tessellations with goldpoint squares 269
Tetrahedron sequence 91
TGP 3-chains, tetrahedra 281
TGP labelling 236
TGP n-chains 251
TGP orientation 236
TGP tetrahedra, 2 examples 281
TGP types 233
TGP, linear jigsaw 238
TGPs 233
TGPs, 4 types of proof 249
The ET-transform set 129
The Fibonacci star 183
Tiled cube, two SGP types 284
Tiled cubes 283
Tiled cubes, three SGP types 285
Tiling cubes with SGPs 282
Tiling of polyhedra 279
Tiling with TGPs 243
Tilings with TGPs 239
Track 153
Track in S 154
Tracks in groups 154
Trackset equivalent to group 163
Trackset from an operation table 158
Transform of Fibonacci vector polygons 135
Transmission matrix 152
Triangle on Fibonacci vectors 122
Triangles on vector polygons 121
Triangles with collinear inner, transform points 131
Triangles with collinear triples in 130
Tribonacci sequence 42
Trigonometry in 123
Triple-set 155
Type I inherent transformation 148
Type I vector recurrence equation 137
Type II vector recurrence equation 137
Type II vector recurrence relation 144
Type-I hexagons 264
Type-II hexagons 264
Type-III hexagons 264
Type-IV hexagons 265
Types of TGP 233
Upward and downward Fibonacci chimneys 150
Uses of ET-transforms 126
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