The Golden Ratio and Fibonacci Numbers (Hardcover)

~ (Author) "The golden ratio is an irrational number defined to be..." (more)
Key Phrases: baby rabbit pairs, golden rhombus, adult rabbit pairs, Geometric Problems, Basic Properties of the Golden Ratio, World Scientific Publishing (more...)

Editorial Reviews

Product Description

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.

Product Details

• Hardcover: 162 pages
• Publisher: World Scientific Publishing Company (March 1998)
• Language: English
• ISBN-10: 9810232640
• ISBN-13: 978-9810232641
• Product Dimensions: 8.5 x 6 x 0.7 inches
• Shipping Weight: 14.4 ounces (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon.com Sales Rank: #541,179 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

25 of 25 people found the following review helpful:

5.0 out of 5 stars The definitive book on the subject, February 2, 2006

By	Bruce R. Gilson (Wheaton, MD United States) - See all my reviews (REAL NAME)

Amazon Verified Purchase

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.

20 of 60 people found the following review helpful:

4.0 out of 5 stars It's the Beauty of Mathematics, September 23, 2000

By A Customer

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.