The Fabulous Fibonacci Numbers

Front Cover
Prometheus Books - Mathematics
0 Reviews
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.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.
 

What people are saying - Write a review

LibraryThing Review

User Review  - fpagan - LibraryThing

Could double as a rival to Livio's book on the golden ratio [phi, (sqrt(5)+1)/2, 1.618...], so intimately is the latter entwined with the Fibonacci sequence. E.g., there's a proof that (1/sqrt(5)) (phi^n - (- 1/phi)^n) is a direct formula for the nth Fibonacci number. Thorough and enjoyable. Read full review

Contents

Acknowledgments
9
The Fibonacci Numbers in Nature
59
The Fibonacci Numbers and
77
The Fibonacci Numbers and
107
The Fibonacci Numbers
161
A Potpourri of Fibonacci Number
177
The Fibonacci Numbers Found in
231
The Fibonacci Numbers
271
The Famous Binet Formula for Finding
293
The Fibonacci Numbers
307
Epilogue
327
List of the First 500 Fibonacci Numbers
343
Proofs of Fibonacci Relationships
349
References
371
Copyright

Other editions - View all

Common terms and phrases

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.

Bibliographic information