Description
Book SynopsisThe 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.
Trade 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
Table of ContentsA History and Introduction to the Fibonacci Numbers; The Fibonacci Numbers in Nature; The Fibonacci Numbers and the Pascal Triangle; The Fibonacci Numbers and the Golden Ratio; The Fibonacci Numbers and Continued Fractions; A Potpourri of Fibonacci Number Applications; The Fibonacci Numbers Found in Art and Architecture; The Fibonacci Numbers and Musical Form; The Famous Binet Formula for Finding a Particular Fibonacci Number; The Fibonacci Numbers and Fractals; Epilogue; Index.
