The Fabulous Fibonacci Numbers
Publication Date: May 30, 2007
Categories: Number Theory
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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, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a 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 is dean of the School of Education and professor of mathematics education at Mercy College in Dobbs Ferry, New York. Previously, he had the same positions at the City College of the City University of New York for forty years. He has published over fifty-five books in the area of mathematics and mathematics education, including Pi: A Biography of the World's Most Mysterious Number (with Ingmar Lehmann).
Ingmar Lehmann is retired from the mathematics faculty at Humboldt University in Berlin. For many years he led the Berlin Mathematics Student Society for gifted secondary-school students, with which he is still closely engaged today. He is the coauthor with Alfred S. Posamentier of The Secrets of Triangles, The Glorious Golden Ratio, and three other books.
"This is a wonderful introduction...You may end up amazed and incredulous."
- Leon M. Lederman, Nobel Laureate
“The mathematics in this book is a delight: surprising, insightful, and comprehensive… the result is by turns rigorous, entertaining, and eye-poppingly speculative.”
“…a work that, although aimed at a general audience and presupposing no knowledge of mathematics beyond the high school precalculus level, succeeds in entertaining all audiences…Educators, as well as the mathematically curious, are encouraged to pick up this volume. The discussions of Fibonacci numbers in nature, art, architecture, and music are very thorough…highly recommended.”
“The authors have breathed life into what could be considered a fairly dry subject by demonstrating how commonplace items make use of the Fibonacci numbers…there is a great deal of math involved but taken step at a time, it is not that difficult to understand and this understanding leads to a an even greater appreciation of everything from a flower garden to classical music. Overall, this is an interesting if challenging read for the layperson and a gold mine for the mathematically inclined.”
-Monsters and Critics
“…the authors have presented a compelling and well-developed book, and one that might well make converts out of some hard-core math phobics…an elegant book that enhances their argument that mathematics is ‘the queen of sciences’.”
“…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.”