Gathering materials from a wide range of sources, Fibonacci and Lucas Number with Applications presents a look at the numerous applications of Fibonacci and Lucas numbers in a range of disciplines.
The intent of Fibonacci and Lucas Number with Applications is to comprehensively show how these sequences are not only useful, but also how they have a tendency to show up in both the natural and manmade world.
Fibonacci and Lucas Number with Applications has kept long proofs to a minimum and includes the answers to odd-numbered exercises in the text.
Contents:
- Leonardo Fibonacci
- The Rabbit Problem
- Fibonacci Numbers in Nature
- Fibonacci Numbers: Additional Occurrences
- 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
- 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
Index
to see books • videos • cd-roms of related interest