New Visual Perspectives on Fibonacci Numbers
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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PART A NUMBER THEORETIC PERSPECTIVES
The 2Fibonacci sequences
Extensions of the concepts of 2Fibonacci sequences
Other ideas for modification of the Fibonacci sequence
Generali2ations using tableaux
On Gray codes and coupled recurrence trees
Studies of node sums on number trees
The goldpoint rings of a linesegment
Some fractals in goldpoint geometry
Triangles and squares marked with goldpoints
Plane tessellations with goldpoint triangles
Tessellations with goldpoint squares
Games with goldpoint tiles
Fibonacci Vector Geometry