New Visual Perspectives on Fibonacci Numbers

Includes index.

Includes bibliography and references.

Section 1. Coupled recurrence relations.
1. Introductory remarks by the first author
2. The 2-Fibonacci sequences
3. Extensions of the concepts of 2-Fibonacci sequences
4. Other ideas for modification of the Fibonacci sequence
Section 2. Number trees.
1. Introduction
Turner's number trees
2. Generalizations using tableaux
3. On Gray codes and coupled recurrence trees
4. Studies of node sums on number trees
5. Connections with Pascal-T triangles
Part. B. Geometric perspectives.
Section 1. Fibonacci vector geometry.
1. Introduction and elementary results
2. Vector sequences from linear recurrences
3. The Fibonacci honeycomb plane
4. Fibonacci and Lucas vector polygons
5. Trigonometry in the honeycomb plane
6. Vector sequences generated in planes
7. Fibonacci tracks, groups, and plus-minus sequences
Section 2. Goldpoint geometry.
1. On goldpoints and golden-mean constructions
2. The goldpoint rings of a line-segment
3. Some fractals in goldpoint geometry
4. Triangles and squares marked with goldpoints
5. Plane tessellations with goldpoint triangles
6. Tessellations with goldpoint squares
7. Games with goldpoint tiles

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.