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1. The Golden Ratio and Fibonacci
2. The Fabulous Fibonacci Numbers
3. Fibonacci Numbers
4. 1001 Fibonacci Numbers: The Miracle
5. Geometry of Design: Studies in
6. Recursion: Function, Parent, Ancestor,

1. The Golden Ratio and Fibonacci Numbers
by R. A. Dunlap
Hardcover: 162 Pages (1998-03)
list price: US$49.00 -- used & new: US$37.28
(price subject to change: see help)
Asin: 9810232640
Average Customer Review: 4.5 out of 5 stars
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In this text, the basic mathematical properties of the golden ratio and its occurrence in the dimensions of two- and three-dimensional figures with fivefold symmetry are discussed. In addition, the generation of the Fibonacci series and generalized Finobacci series and their relationship to the golden ratio are presented. These concepts are applied to algorithms for searching and function minimization. The Fibonacci sequence is viewed as a one-dimensional aperiodic, latice and these ideas are extended to two- and three-dimensional Penrose tilings and the concept of incommensurate projections. The structural properties of aperiodic crystals and the growth of certain biological organisms are described in terms of Fibonacci sequences. ... Read more

Customer Reviews (2)

5-0 out of 5 stars The definitive book on the subject
This book is not absolutely perfect, but it is so much better than any other one on the subject that it deserves a 5-star rating. The majority of books on Fibonacci numbers and the golden ratio fall into three categories: (1) Books for children, (2) Mystical mumbo-jumbo, and (3) Books claiming you can use Fibonacci numbers to win in the stock market (!). Even Mario Livio's book, which is better than most, uses so much of its space to _debunk_ some of the mystical mumbo-jumbo that it de-emphasizes the wonderful patterns that can be found in the Fibonacci sequence, which is beautiful enough in its mathematical properties that one doesn't need to make such digressions. Dunlap's book, by contrast, _does_ emphasize those patterns. And when it's not directly addressing the Fibonacci sequence's properties, it's discussing things like the golden ratio and Penrose tilings, which are completely within the category of mathematics related to the topic.

I really enjoyed the book, even though it has some typographical errors and minor omissions. The formulas collected in the third appendix alone justify buying the book. I could wish that there were more given, but this is the best collection I have seen.

4-0 out of 5 stars It's the Beauty of Mathematics
Well, I have studied these numbers and other fascinating phenomena in mathematics, and I never found it enough. So, every book I read about this stuff I found a new set of new things, or at least a new view/review of the old things I knew. After my short study (7 years now) in the field of Number theory and Related topics, I dare say, that this book was another addition to my knowledge that -thanks GOD- I didn't waste. ... Read more

2. The Fabulous Fibonacci Numbers
by Alfred S. Posamentier, Ingmar Lehmann
Hardcover: 364 Pages (2007-06-21)
list price: US$28.98 -- used & new: US$15.19
(price subject to change: see help)
Asin: 1591024757
Average Customer Review: 4.0 out of 5 stars
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The most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature—from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world.

With admirable clarity, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. The authors begin with a brief history of their distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal’s triangle, to name a few. Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings. ... Read more

Customer Reviews (8)

4-0 out of 5 stars Good in some ways, bad in others
It was very hard to assign a star rating to this book. There are thingss I like very much, and others I definitely do not.

On the good side, it is a very attractive presentation of the beautiful patterns appearing in the mathematics of the Fibonacci sequence. It is not quite as heavy on the mathematics as Dunlap's or Vajda's books (which may make it an easier read for those whose math isn't as strong as mine!) but what it does, it does very nicely, using tables and pictures to make the patterns very clear.

On the bad side, I wish the authors would not accept so credulously such myths as the one of Greek architect Phidias' using the golden section in his design (this has already been debunked by Livio) or the numerological nonsense promulgated by people who try to spread the idea that the Fibonacci sequence can be used to predict the stock market. People following such misguided ideas are likely to lose their shirts, so this sort of credulous myth-spreading is dangerous, not just bad judgment.

So how do you rate a book with so much good and so much bad in it? I've given it 4 stars because the good parts are so good. If the authors had spared us the myths, I would have given it 5.

4-0 out of 5 stars Interesting book, but needs refinements.
The book is very interesting both for a technical reader and just a lover. It is easy to read, but has also some rigorous proofs in the appendix. The only limitation is that the book would have needed another revision before publication.

1-0 out of 5 stars The good, and the bad
There is a lot of good information here, where the maths is standard.
Unfortunately the book is very sloppily written and badly edited.
Some ideas are well referenced, but others are not attributed, like the Odom construction from the equilateral triangle in a circle.
It contains lots of errors and the usual extrapolations that are not valid.
For example, the nautilus shell is said to be golden section without any proof (it has nothing to do with the GS) and the cover perpetuates that myth.
The Art section is very bad with the usual chosing of data and stretching it to fit the hypothesis. Better to read Mario Levi's book to see why this is rubbish.This is in line with many poorly presented diagrams showing an editorial and author lack of visual sense. For example figure 2-22 is squashed horizontally.
There are lots of lists of what people say on the internet with no critical views as if they are trying to sell the book because of this popular view. This perpetuation of mis-information clouds one's ability to believe the rest of the book.
It's very sad that what is mostly a good collection is so shoddily presented and mixed up with great deal of wrong information.

5-0 out of 5 stars Fibonnacci comes alive
A great book.Has everything i would need for a research project plus so much more.The author did a great job.

5-0 out of 5 stars A fascinating review of the history of the Fibonacci numbers
The most intriguing number pattern in math is the Fibonacci sequence, a pattern which begins with two ones, each succeeding number of which is the sum of the two numbers immediately preceding it. And it's not just a mathematical incongruity, but occurs throughout nature itself, building the case for the mathematical basis of nature itself. Any college-level collection strong in science and nature - and many a public lending library- will find this a fascinating review of the history of the Fibonacci numbers and their applications to everything from nature to art and the stock market.
... Read more

3. Fibonacci Numbers
by Nicolai N. Vorobiev
Paperback: 176 Pages (2003-01-31)
list price: US$49.95 -- used & new: US$31.48
(price subject to change: see help)
Asin: 3764361352
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Since their discovery hundreds of years ago, people have been fascinated by the wondrous properties of Fibonacci numbers. Being of mathematical significance in their own right, Fibonacci numbers have had an impact on areas like art and architecture, and their traces can be found in nature and even the behavior of the stock market.

Starting with the basic properties of Fibonacci numbers, the present book explores their relevance in number theory, the theory of continued fractions, geometry and approximation theory. Rather than giving a complete account of the subject, a few chosen examples are treated exhaustively. They not only reveal the bearing of Fibonacci numbers on mathematics, but also provide very readable marvels of mathematical reasoning. This book is the translation of the 6th Russian edition (the first edition appeared in the early fifties and became a standard source of information on the subject).

The prerequisites for reading this book are minimal. A certain acquaintance with elementary operations and a readyness for mathematical thought are enough to follow the presentation to remarkable mathematical depths. Apart from anybody interested in the Fibonacci numbers as such, the book can be used for under-graduate courses on this subject, touching on several mathematical areas on the way. Fibonacci numbers create a fascinating and beautiful world of original problems which many amateurs and professionals find exciting to explore. The books is an invitation and a comprehensive guidebook to this world. ... Read more

4. 1001 Fibonacci Numbers: The Miracle Begins with Unity and Order Follows
by Mr. Effectiveness
 Kindle Edition: Pages (2010-01-13)
list price: US$5.99
Asin: B00347AE0M
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Product Description
This provides an interesting perspective on the numbers of the Fibonacci sequence and Unity, Value, Order, and Restoration. It provokes thought into the deeper considerations, such as the relationships to Sacred Geometry, Golden Mean, PHI, Golden Proportion, Magic Reciprocals, Stellated Dodecahedron, Golden Rectangle, Numerical Investigations, Pascal's Triangle, Probabilities, Prime Numbers and does Expose One of the patterns in the sequence. There are others... ... Read more

5. Geometry of Design: Studies in Proportion and Composition
by Kimberly Elam
Paperback: 96 Pages (2001-08-01)
list price: US$21.95 -- used & new: US$11.27
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Asin: 1568982496
Average Customer Review: 4.0 out of 5 stars
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At last, a mathematical explanation of how art works presented in a manner we can all understand. Kimberly Elam takes the reader on a geometrical journey, lending insight and coherence to the design process by exploring the visual relationships that have foundations in mathematics as well as the essential qualities of life.

Geometry of Design-the first book in our new Design Briefs Series-takes a close look at a broad range of twentieth-century examples of design, architecture, and illustration (from the Barcelona chair to the Musica Viva poster, from the Braun handblender to the Conico kettle), revealing underlying geometric structures in their compositions. Explanations and techniques of visual analysis make the inherent mathematical relationships evident and a must-have for anyone involved in graphic arts. The book focuses not only on the classic systems of proportioning, such as the golden section and root rectangles, but also on less well known proportioning systems such as the Fibonacci Series. Through detailed diagrams these geometric systems are brought to life giving an effective insight into the design process. ... Read more

Customer Reviews (24)

5-0 out of 5 stars Love this kind of stuff
I am always on the look out for info on the Golden Section and this little book has some great info and diagrams on the golden section. There are some interesting analysis of art and graphics from the past. I take some of the comments with a grain of salt but this is a good one for any aspiring artist and graphic designer.

5-0 out of 5 stars Highy Recomended
I thinkthis book graphical display it point wonderfully. I bought two copies of this book one for me and another for a proffesor of architecture who is a friend of mine. I would highly recomend this book.

4-0 out of 5 stars Good book for design students
This is a good book for the graphic design student. It offers information that you probably WILL NOT encounter in a classroom. It has alot of great information for those of us who aren't mathematically savvy, but can understand visual proportions and the book offers alot of examples with nice semi-transparent grids and overlays so that you can view the images within the context of the authors talking points.

This book WILL NOT however teach you how to use the information as a strict method of design. In other words, it gives the reader the power to understand and use the information as a compositional aid, not a strict guideline for layouts like a grid system.

Overall, I would say that if you feel that you already have a thorough knowledge of grids and/or an understanding of the golden ratio, than this book may be slightly redundant for you, but if you are new to art/design, than this book will offer alot of useful information in a quick, easy to understand read.

I would suggest reading this book in conjunction to one of the many great books about grids so that you can gain further understanding of the information.

4-0 out of 5 stars Good book for designers
This coffee table book is one of my favorites.It doesn't go in depth into the subject matter but rather grazes over real-world examples with diagrams and simple explanations.Fun book to read, but not for the serious of study.

3-0 out of 5 stars From Architect Perpsective
I bought this book primarily to see the studies of proportions in architecture.There are very few examples (really only 4 pages dedicated to that subject and 3 buildings analyzed) shown here.It does, however, give a myriad of ways to lay out different proportions using rectangles, circles, triangles, pentagons, etc.These, along with the examples of proportion in nature and on the human body were enough to spark my imagination as to how proportion can be used in design of buildings, but if you are looking for broad analysis of architectural proportions, look elsewhere.The examples that are given are mainly of poster design in the 1900s and Modern furniture design. ... Read more

6. Recursion: Function, Parent, Ancestor, Fibonacci Number, Fractal, Fractal-Generating Software, Shape, Differential Geometry, Integral
Paperback: 132 Pages (2010-01-12)
list price: US$65.00
Isbn: 6130345666
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High Quality Content by WIKIPEDIA articles! Recursion, in mathematics and computer science, is a method of defining functions in which the function being defined is applied within its own definition. The term is also used more generally to describe a process of repeating objects in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. ... Read more

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