Book Description
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 (5)

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.

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.

Not so Fabulous
This is a beautifully produced book. The front jacket is amongst the most attractive I have seen and the back cover is dense with quotations from reviews singing its praises, including one from a Nobel Laureate. Oh dear, how we can be deceived by outside appearances! The text contains so many errors, misleading statements and moments of such stupidity that to discuss them all would require a volume about equal in size to the original.
Let me take you through a few examples: -
Page 21. 41/12 is neither a square number nor an integer as claimed in the text.
Page 22.There is no contradiction in Fibonacci stating that the problem under discussion is indeterminate and for him then to give a (correct) solution to it.
Page 33. The proof of Property 2 given in appendix B is a proof by contradiction, not a proof by induction as stated.
Page 34. Many of the factors listed in Figure 1-9 are wrong. See, for example, the factors given for the sixth Fibonacci number.
Page 40. Figure 1-11 is confusing. What is the rectangle on the RHS supposed to indicate?
Page 48, Figures 1-14 and 1-15. Contrary to their captions, both would seem to contain an odd number of rectangles.
Page 49. Line 7 and line 18 are identical, lines 8 and 19, to which each is supposed to be equal, are not equal.
Page 49. Line 20. 1156 does not equal 342, and 342 is not the 29th Fibonacci number.
Page 51, last line but one. 520 is not the product of 18 and 29.
Page 56. The written summary of property 13 is wrong.
Page 80. Footnote should read `fourth difference', not `third difference'.
Page 82. Why express amazement that, in a table of differences for the Fibonacci sequence, each new line of differences repeats the original sequence. Give the way in which the sequence is generated, how could it possibly be otherwise.
Pages 91, 93 and 102. The term `left justified' has a different meaning on each page.
Pages 111 and 112. Having defined Phi such that 1/Phi = Phi - 1, the authors express amazement that their fractional parts are equal. They then expand each to 1000 DECIMAL PLACES to demonstrate this.
Chapter 3. The suggestion that the Fibonacci sequence is in some way connected to the powers of 2 and to the sequence of numbers generated by the partitioning of a circle, simply on the basis that all three sequences can be located in Pascal's Triangle, is nonsense.
Page 120. The claim that by replacing the `1' in the exact value of Phi with e^(i x Pi) establishes a deep and meaningful connection between Phi, Pi, e and i either the height of stupidity or a confidence trick.
These are not the worst examples, just a random selection from the first 120 pages.They keep on coming thick and fast throughout the rest of the book.
Any `general reader' who tries to follow the mathematical developments set out here will only have confirmed a belief that mathematics does not make sense. The authors and their publishers have done mathematics a grave disservice in having produced such a carelessly written and shoddily edited volume. This is terribly sad; if more care had been taken over researching, writing and editing, it could have been the best popular mathematics book in years.

A complicated subject presented in a very uncomplicated manner.
The book provides much of the available information onthe Fibonacci numbers.It starts with the life of Leonardo da Pisa,the man who first introduced the numbers to the world almost a thousand years ago. Itdescribes the actual sequence, then demonstrates the connection that thenumbers have to the natural, as well as to theworld of the visual arts and of music.Even the stock market is not immune of the influence of the Fibonacci sequence.
What particularly impressed me about this book is the clarity with which the authors present thesubject.Whether you are a mathematician or simply have an inquisitive mind,you willalways know the exact meaning of the subject under discussion.In fact, you can skip the (sometimes) long mathematical formulae and still never lose track of the narrative.
A wonderful book that makes one ponder on the origin and significance of the created world.A must for mathematicians, scientists and generally educated individuals.A must also for those who believe that our universe and all its contents are only the product of a series of coincidences.These people may change their minds after becoming familiar with the Fibonacci numbers.

Encompassing and Interesting
The book contains many interesting and unpredictable properties of the Fibonacci numbers. I learned a lot of new things about them. ... Read more

Book Description

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).

Book Description
Informative text provides a general introduction to the golden ratio andFibonacci numbers for those researchers and graduate students who areworking in fields where these numbers have found applications. DLC: Golden section. ... Read more

Customer Reviews (2)

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.

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

Book Description
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 (20)

Inspiring Book
Want to be better or the best at what you do?This is the kind of book you use to fuel inspiration at a foundational level.

A Must Have
Kim Elam's book is not only a fascinating read, but beautifully designed as well, making it a perfect example of its subject. A must for all artists and designers.

A very good seller!
It was very fast to get the product and I experience a very good seller!

Good Intro with examples
As a design student i have found this book to be very informative, yet it doesn't really get into too much detail which for me is good. This book is good for understanding the golden seccion and how it has been applied in some of the most memorable designs of all times as well as in architecture and other forms. If you want a full, no-details-left-out kind of book this is not it. The most important thing about this book is the examples. for begginers it really helps to see that proportion and composition is not just a matter of intuition or chance.

pretty good read
Good for students of design, it lay outs the basic geometric principles of composition.
I would expect a more in depth analysis of geometry and how it has been used in art and design (geodesics, tensegrity etc).
a good start! ... Read more