The Fabulous Fibonacci Numbers

In The Fabulous Fibonacci Numbers, 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.

Introduction:

Throughout these pages we will explore many manifestations, so that you may be motivated to find other instances in nature where these Fibonacci numbers surface. The book will also provide you with a gentle, yet illuminating discussion of the unusual nature of these numbers. Their interrelationships with other seemingly completely unrelated aspects of mathematics will open the door to applications in a variety of other fields and areas as remote as the stock market.

It is our desire that this book serve as your introduction to these fabulous numbers. We will provide you with the development of the Fibonacci numbers, a sort of history, one might say. Then we will investigate the many “sightings” of these numbers by subject area. For example, in geometry we will explore their relationship with the most beautiful ratio, known as the “golden ratio.,, Here the Fibonacci numbers, when taken as quotients in consecutive pairs, approach the golden ratio: 1.6180339887498948482045868343656 …

The larger the Fibonacci numbers, the closer their quotient approaches the golden ratio.

Contents:

• A 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

The Fabulous Fibonacci Numbers By Alfred S. Posamentier, Ingmar Lehmann pdf