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.
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Book Description
Editorial Reviews
Review
...Gains a good deal of interest if the reader has some knowledge of these traditional results and techniques. -- New Zealand Mathematical Society Newsletter
Altogether this is a very stimulating book. -- Mathematics Abstracts
I recommend this book to anyone interested in iteratice processes on integers. -- MAA Online Book Review
Reflects new developments especially the role of Fibonacci numbers in Matiyasevich's negative solution of hilbert's tenth problem. -- Choice
Altogether this is a very stimulating book. -- Mathematics Abstracts
I recommend this book to anyone interested in iteratice processes on integers. -- MAA Online Book Review
Reflects new developments especially the role of Fibonacci numbers in Matiyasevich's negative solution of hilbert's tenth problem. -- Choice
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Inside This Book
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The germ of the idea which has been unfolded with my colleagues came to me quite unexpectedly. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
goldpoint geometry, goldpoint rings, convolution trees, plane iro, honeycomb plane, null knot, jigsaw rules, ordinary arithmetic progression, integer triangle, track recurrence, inner hexagons, motif triangle, golden tiles, limit rays, snowflake fractal, vector polygons, shortest vector, vector geometry, vector sequence, geometric observations, tile figures, jigsaw patterns, direction ratios, star jewel, recurrence equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Coupled Recurrence Relations New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The germ of the idea which has been unfolded with my colleagues came to me quite unexpectedly. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
goldpoint geometry, goldpoint rings, convolution trees, plane iro, honeycomb plane, null knot, jigsaw rules, ordinary arithmetic progression, integer triangle, track recurrence, inner hexagons, motif triangle, golden tiles, limit rays, snowflake fractal, vector polygons, shortest vector, vector geometry, vector sequence, geometric observations, tile figures, jigsaw patterns, direction ratios, star jewel, recurrence equation Key Phrases - Capitalized Phrases (CAPs): (learn more)
Coupled Recurrence Relations New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 9
books:
See all 9 books this book cites
- The Divine Proportion by H. E. Huntley on page 244, and page 307
- Fibonacci and Lucas Numbers by Verner E. Jr. Hoggatt on page 48
- Polyhedron Models by Magnus J. Wenninger on page 287
- Combinatory Analysis (Dover Books on Mathematics) by Percy A. MacMahon on page 81
- Mathematical Chemistry: International Conference Proceedings by D.J. Klein on page 48
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