New Visual Perspectives on Fibonacci Numbers

Contents: Number Theoretic Perspectives - Coupled Recurrence Relations: Introductory Remarks by the First Author The 2-Fibonacci Sequences Extensions of the Concepts of 2-Fibonacci Sequences Other Ideas for Modification of the Fibonacci Sequences Number Trees: Introduction - Turner's Number Trees Generalizations Using Tableaux On Gray Codes and Coupled Recurrence Trees Studies of Node Sums on Number Trees Connections with Pascal-T Triangles Geometric Perspectives - Finonacci Vector Geometry: Introduction and Elementary Results Vector Sequences from Linear Recurrences The Fibonacci Honeycomb Plane Fibonacci and Lucas Vector Polygons Trigonometry in the Honeycomb Plane Vector Sequences Generated in Planes Fibonacci Tracks, Groups, and Plus-Minus Sequences Goldpoint Geometry: On Goldpoints and Golden-Mean Constructions The Goldpoint Rings of a Line-Segment Some Fractals in Goldpoint Geometry Triangles and Squares Marked with Goldpoints Plane Tessellations with Goldpoint Triangles Tessellations with Goldpoint Squares Games with Goldpoint Tiles.