New Visual Perspectives on Fibonacci Numbers

New Visual Perspectives on Fibonacci Numbers

by K. T. Atanasov
     
 

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… See more details below

Overview

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.

Product Details

ISBN-13:
9789812381149
Publisher:
World Scientific Publishing Company, Incorporated
Publication date:
10/28/2002
Pages:
332
Product dimensions:
6.10(w) x 9.48(h) x 0.89(d)

Related Subjects

Table of Contents

Introduction
Foreword
Preface
Pt. ANumber Theoretic Perspectives
Sect. 1Coupled Recurrence Relations
1Introductory remarks by the first author3
2The 2-Fibonacci sequences7
3Extensions of the concepts of 2-Fibonacci sequences29
4Other ideas for modification of the Fibonacci sequence39
Sect. 2Number Trees
1Introduction - Turner's Number Trees53
2Generalizations using tableaux57
3On Gray codes and coupled recurrence trees63
4Studies of node sums on number trees71
5Connections with Pascal-T triangles75
Pt. BGeometric Perspectives
Sect. 1Fibonacci Vector Geometry
1Introduction and elementary results85
2Vector sequences from linear recurrences95
3The Fibonacci honeycomb plane107
4Fibonacci and Lucas vector polygons119
5Trigonometry in the honeycomb plane123
6Vector sequences generated in planes137
7Fibonacci tracks, groups, and plus-minus sequences153
Sect. 2Goldpoint Geometry
1On goldpoints and golden-mean constructions183
2The goldpoint rings of a line-segment205
3Some fractals in goldpoint geometry215
4Triangles and squares marked with goldpoints229
5Plane tessellations with goldpoint triangles245
6Tessellations with goldpoint squares269
7Games with goldpoint tiles293
Index309

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