The Fabulous Fibonacci Numbers
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.
27 pages matching proof in this book
Results 1-3 of 27
What people are saying - Write a review
LibraryThing ReviewUser 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
The Fibonacci Numbers in Nature
The Fibonacci Numbers and
11 other sections not shown