List of Symbols.
The Rabbit Problem.
Fibonacci Numbers in Nature.
Fibonacci Numbers: Additional Occurrances.
Fibonacci and Lucas Identities.
Generalized Fibonacci Numbers.
Additional Fibonacci and Lucas Formulas.
The Euclidean Algorithm.
Solving Recurrence Relations.
Additional Pascal-Like Triangles.
Generalized Fibonacci Numbers Revisited.
Generating Functions Revisited.
The Golden Ratio.
The Golden Ratio Revisited.
The Golden Ellipse and Hyperbola.
Weighted Fibonacci and Lucas Sums.
Weighted Fibonacci and Lucas Sums Revisited.
The Knapsack Problem.
Fibonacci Magic Squares.
Fibonacci and Lucas Congruences.
Fibonacci and Lucas Periodicity.
Fibonacci and Lucas Series.
Zeros of Fibonacci and Lucas Polynomials.
Fibonacci and Lucas Subscripts.
Gaussian Fibonacci and Lucas Numbers.
Tribonacci Polynomials. Appendix 1: Fundamentals.
Appendix 2: The First 100 Fibonacci and Lucas Numbers.
Appendix 3: The First 100 Fibonacci Numbers and Their Prime Factorizations.
Appendix 4: The First 100 Lucas Numbers and Their Prime Factorizations.
Solutions to Odd-Numbered Exercises.
"...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)