The first comprehensive survey of mathematics' most fascinating number sequences Fibonacci and Lucas numbers have intrigued amateur and professional mathematicians for centuries. This volume represents the first attempt to compile a definitive history and authoritative analysis of these famous integer sequences, complete with a wealth of exciting applications, enlightening examples, and fun exercises that offer numerous opportunities for exploration and experimentation. The author has assembled a myriad of fascinating properties of both Fibonacci and Lucas numbers-as developed by a wide range of sources-and catalogued their applications in a multitude of widely varied disciplines such as art, stock market investing, engineering, and neurophysiology. Most of the engaging and delightful material here is easily accessible to college and even high school students, though advanced material is included to challenge more sophisticated Fibonacci enthusiasts. A historical survey of the development of Fibonacci and Lucas numbers, biographical sketches of intriguing personalities involved in developing the subject, and illustrative examples round out this thorough and amusing survey. Most chapters conclude with numeric and theoretical exercises that do not rely on long and tedious proofs of theorems. Highlights include: Balanced blend of theory and real-world applications Excellent reference material for student reports and projects User-friendly, informal, and entertaining writing style Historical interjections and short biographies that add a richer perspective to the topic Reference sections providing important symbols, problem solutions, and fundamental properties from the theory of numbers and matrices Fibonacci and Lucas Numbers with Applications provides mathematicians with a wealth of reference material in one convenient volume and presents an in-depth and entertaining resource for enthusiasts at every level and from any background.
..".a 'must' for fans of Fibonacci..." (Translated from French, Bulletin AMQ, October 2005)
..".presents a look at the numerous applications of Fibonacci and Lucas numbers in a range of disciplines." (SciTech Book News, Vol. 25, No. 4, December 2001)
..".presents the history, mathematics, and applications of the Fibonacci and Lucas sequences...An important feature of the book is the many...exercises..." (Mathematical Reviews, 2002f)
..".beautiful and well worth the reading...with many exercises and a good bibliography, this book will fascinate both students and teachers." (Mathematics Teacher, Vol. 95, No. 5, May 2002)
"A delightful romp through all things Fibonacci." (American Mathematical Monthly, January 2003)
..".a delightful book which should prove of great value...the most comprehensive collection of results, theorems, and references regarding Fibonacci numbers and their applications to date..." (The Fibonacci Quarterly, February 2002)
..".a splendid compendium of everything that most of us will ever need to know about the Fibonacci and Lucas numbers...an invaluable reference for experts and non-experts alike..." (The Mathematical Gazette)
..".a definitive history and authoritative analysis ...a myriad of fascinating properties of both Fibonacci and Lucas numbers..." (Mathematical Didactics, 2003)
