Atanasov K.T., Turner J.C., Shannon A.G. — New Visual Perspectives on Fibonacci Numbers :: Электронная библиотека попечительского совета мехмата МГУ

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Atanasov K.T., Turner J.C., Shannon A.G. — New Visual Perspectives on Fibonacci Numbers

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Название: New Visual Perspectives on Fibonacci Numbers

Авторы: Atanasov K.T., Turner J.C., Shannon A.G.

Аннотация:

Very little prior mathematical knowledge is assumed, other than the rudiments of algebra and geometry, so the book may be used as a source of enrichment material and project work for college students. A chapter on games using goldpoint tiles is included at the end, and it can provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2002

Количество страниц: 300

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

$(1, \sqrt{7}, \sqrt{7})$ integer triangles      132
      253
      250
$\alpha$ snowflake fractal      188
$\alpha$ -rings      205
$\alpha$ -rings, orthogonal circle      211
$\mathcal{E}$       129
$\Prod_0$       107
$\rho$ -rings      206
$\rho$ -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 $\Prod_0$       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 $4\times 4$ 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 $60^{\circ}$ 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 $\Prod_0$       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 $\Prod_0$       111
Notation for TGPs      250
Noughts and Crosses      297
Parametric solution of Diophantine equation      133
Partition of $\Prod_0$       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 $\mathcal{E}$       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 $\mathcal{E}$       130
Tribonacci sequence      42
Trigonometry in $\Prod_0$       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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