Introduction | |
Foreword | |
Preface | |
Number Theoretic Perspectives | |
Coupled Recurrence Relations | |
Introductory remarks by the first author | p. 3 |
The 2-Fibonacci sequences | p. 7 |
Extensions of the concepts of 2-Fibonacci sequences | p. 29 |
Other ideas for modification of the Fibonacci sequence | p. 39 |
Number Trees | |
Introduction - Turner's Number Trees | p. 53 |
Generalizations using tableaux | p. 57 |
On Gray codes and coupled recurrence trees | p. 63 |
Studies of node sums on number trees | p. 71 |
Connections with Pascal-T triangles | p. 75 |
Geometric Perspectives | |
Fibonacci Vector Geometry | |
Introduction and elementary results | p. 85 |
Vector sequences from linear recurrences | p. 95 |
The Fibonacci honeycomb plane | p. 107 |
Fibonacci and Lucas vector polygons | p. 119 |
Trigonometry in the honeycomb plane | p. 123 |
Vector sequences generated in planes | p. 137 |
Fibonacci tracks, groups, and plus-minus sequences | p. 153 |
Goldpoint Geometry | |
On goldpoints and golden-mean constructions | p. 183 |
The goldpoint rings of a line-segment | p. 205 |
Some fractals in goldpoint geometry | p. 215 |
Triangles and squares marked with goldpoints | p. 229 |
Plane tessellations with goldpoint triangles | p. 245 |
Tessellations with goldpoint squares | p. 269 |
Games with goldpoint tiles | p. 293 |
Index | p. 309 |
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