Fibonacci and Lucas numbers with applications

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

The First 100 Fibonacci and Lucas Numbers

The First 100 Fibonacci Numbers and Their Prime Factorizations

The First 100 Lucas Numbers and Their Prime Factorizations.