The Fabulous Fibonacci Numbers [Hardcover]

Alfred S. Posamentier (Author), Ingmar Lehmann (Author)

Book Description

Publication Date: June 21, 2007

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, mathematics 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 popularising 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.

Editorial Reviews

Review

"...delightful...accessible to anyone who enjoys or enjoyed high school mathematics. Mathematics teachers from middle school through college will find this book fun to read and useful in the classroom. The authors consider more properties, relationships, and applications of the Fibonacci numbers than most other sources do...I enjoyed reading this book...a valuable addition to the mathematical literature." -- Mathematics Teacher, Vol. 102, No. 1, August 2008

About the Author

Alfred S. Posamentier (New York, NY) is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published over 40 books in the area of mathematics and mathematics education, including Pi: A Biography of the World’s Most Mysterious Number and Math Charmers: Tantalizing Tidbits for the Mind. Ingmar Lehmann (Berlin, Germany) is on the mathematics faculty at Humboldt University in Berlin and the coauthor of Pi: A Biography of the World’s Most Mysterious Number.

Product Details

• Hardcover: 385 pages
• Publisher: Prometheus Books; First Edition edition (June 21, 2007)
• Language: English
• ISBN-10: 1591024757
• ISBN-13: 978-1591024750
• Product Dimensions: 9.2 x 6.3 x 1 inches
• Shipping Weight: 1.3 pounds (View shipping rates and policies)
• Average Customer Review: 3.6 out of 5 stars  See all reviews (9 customer reviews)
• Amazon Best Sellers Rank: #58,297 in Books (See Top 100 in Books)

More About the Author

Alfred S. Posamentier (River Vale, NJ) is the dean of the School of Education and professor of mathematics education at Mercy College in Dobbs Ferry, NY. He was formerly the dean of the School of Education and professor of mathematics education at the City College of New York. He has published over forty-five books in the area of mathematics and mathematics education, including The Pythagorean Theorem: The Story of Its Power and Beauty; Math Charmers: Tantalizing Tidbits for the Mind; and (with Ingmar Lehmann) Mathematical Amazements and Surprises; The Fabulous Fibonacci Numbers; and Pi: A Biography of the World's Most Mysterious Number.

Customer Reviews

Most Helpful Customer Reviews

121 of 125 people found the following review helpful:

2.0 out of 5 stars Not so Fabulous, October 26, 2007

By 

R. Snell (South Australia.) - See all my reviews
(REAL NAME)   

This review is from: The Fabulous Fibonacci Numbers (Hardcover)

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.

24 of 25 people found the following review helpful:

1.0 out of 5 stars The good, and the bad, November 10, 2008

By 

John Sharp (England) - See all my reviews

This review is from: The Fabulous Fibonacci Numbers (Hardcover)

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.

23 of 31 people found the following review helpful:

5.0 out of 5 stars A complicated subject presented in a very uncomplicated manner., August 30, 2007

By 

Claudia Etheridge (Tucson, Arizona USA) - See all my reviews
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Amazon Verified Purchase

This review is from: The Fabulous Fibonacci Numbers (Hardcover)

The book provides much of the available information on the 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. It describes the actual sequence, then demonstrates the connection that the numbers have to the natural, as well as to the world 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 the subject. Whether you are a mathematician or simply have an inquisitive mind, you will always 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.