Overview

A study of Fibonacci sequences and the well-known Fibonacci numbers. It should be of interest to research mathematicians wishing to advance the ideas themselves, and to recreational mathematicians, who should 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 text 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 seeks to provide much material for stimulating mathematical activities involving geometric puzzles of a combinatoric nature.

Full Product Details

Author:   Krassimir T Atanassov (Bulgarian Academy Of Sciences, Bulgaria) ,  Vassia K Atanassova (Univ Of Sofia, Bulgaria) ,  Anthony G Shannon (The Univ Of New South Wales, Australia) ,  John C Turner (Univ Of Waikato, New Zealand)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Edition:   2nd ed.
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.00cm
Weight:   0.594kg
ISBN:  

9789812381149

ISBN 10:   9812381147
Pages:   332
Publication Date:   10 October 2002
Audience:   College/higher education ,  Professional and scholarly ,  General/trade ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

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.

Reviews

.,. reflects new development especially the role of Fibonacci numbers in Matiyasevich's negative solution of Hilbert's tenth problem.?

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