## New Visual Perspectives on Fibonacci NumbersThis book covers new ground on Fibonacci sequences and the well-known Fibonacci numbers. It will appeal to research mathematicians wishing to advance the new ideas themselves, and to recreational mathematicians, who will enjoy the various visual approaches and the problems inherent in them. There is a continuing emphasis on diagrams, both geometric and combinatorial, which helps to tie disparate topics together, weaving around the unifying themes of the golden mean and various generalizations of the Fibonacci recurrence relation. 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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### Contents

PART A NUMBER THEORETIC PERSPECTIVES | 1 |

The 2Fibonacci sequences | 7 |

Extensions of the concepts of 2Fibonacci sequences | 29 |

Other ideas for modification of the Fibonacci sequence | 39 |

Number Trees | 51 |

Generali2ations using tableaux | 57 |

On Gray codes and coupled recurrence trees | 63 |

Studies of node sums on number trees | 71 |

Goldpoint Geometry | 181 |

The goldpoint rings of a linesegment | 205 |

Some fractals in goldpoint geometry | 215 |

Triangles and squares marked with goldpoints | 229 |

Plane tessellations with goldpoint triangles | 245 |

Tessellations with goldpoint squares | 269 |

Games with goldpoint tiles | 293 |

309 | |

### Other editions - View all

New Visual Perspectives on Fibonacci Numbers K T Atanassov,V Atanassova,A G Shannon,J C Turner Limited preview - 2002 |

### Common terms and phrases

3-chain 4-tiles algebras an+2 ATANASSOV B-point B-ring basic Fibonacci Burnside's theorem Chapter chimney colour construction coordinates count cross-ratio cube cyclic groups defined diagram dust-set elements equilateral triangles example Fi9ure Fibonacci numbers Fibonacci Quarterly Fibonacci sequence Fibonacci Star Fibonacci vector polygons Fibonacci vector sequence fixed points formulae four fractal generali2ations geometric given golden ratio golden tiles goldpoint Goldpoint Geometry Hence honeycomb plane hori2ontal side identity inequivalent initial vectors inner hexagons integer point integer triangle jigging jigging matrix jigsaw jigsaw rules labelled limit ray line-segment linear form Lucas vector mathematical modulo node Number Theory number trees obtain pairs pentagon permutation plane TTQ player plus-minus Proof properties real numbers recurrence equation recurrence relation respectively rhombus rotational symmetry s-string schemes segment SGPs shortest vector shown solution square T-transform TGPs tile figures tile the plane track tracksets Turner vector recurrence xn+i