Fibonacci and Lucas Numbers with Applications

- Preface

- List of Symbols

- Leonardo Fibonacci

- The Rabbit Problem

- Fibonacci Numbers in Nature

- Fibonacci Numbers: Additional Occurrances

- Fibonacci and Lucas Identities

- Geometric Paradoxes

- Generalized Fibonacci Numbers

- Additional Fibonacci and Lucas Formulas

- The Euclidean Algorithm

- Solving Recurrence Relations

- Completeness Theorems

- Pascal's Triangle

- Pascal-Like Triangles

- Additional Pascal-Like Triangles

- Hosoya's Triangle

- Divisibility Properties

- Generalized Fibonacci Numbers Revisited

- Generating Functions

- Generating Functions Revisited

- The Golden Ratio

- The Golden Ratio Revisited

- Golden Triangles

- Golden Rectangles

- Fibonacci Geometry

- Regular Pentagons

- The Golden Ellipse and Hyperbola

- Continued Fractions

- Weighted Fibonacci and Lucas Sums

- Weighted Fibonacci and Lucas Sums Revisited

- The Knapsack Problem

- Fibonacci Magic Squares

- Fibonacci Matrices

- Fibonacci Determinants

- Fibonacci and Lucas Congruences

- Fibonacci and Lucas Periodicity

- Fibonacci and Lucas Series

- Fibonacci Polynomials

- Lucas Polynomials

- Jacobsthal Polynomials

- Zeros of Fibonacci and Lucas Polynomials

- Morgan-Voyce Polynomials

- Fibonometry

- Fibonacci and Lucas Subscripts

- Gaussian Fibonacci and Lucas Numbers

- Analytic Extensions

- Tribonacci 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

- References

- Solutions to Odd-Numbered Exercises

- Index

THOMAS KOSHY, Ph.D., is Professor of Mathematics at Framingham State College in Framingham, Massachusetts. He is the author of the forthcoming book Elementary Number Theory with Applications, among several other books, as well as numerous articles across a wide range of topics.

"...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)