New Visual Perspectives on Fibonacci Numbers

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World Scientific, 2002 - Mathematics - 313 pages
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This 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
Index
309

Fibonacci Vector Geometry
83

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