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Fibonacci and Lucas numbers with applications /

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The first comprehensive survey of mathematics' most fascinating number sequencesFibonacci 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 i...

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Bibliographic Details
Main Author: Koshy, Thomas
Format: eBook
Language:English
Language Notes:English.
Published: New York : Wiley, ©2001.
Series:Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts.
Subjects:
Fibonacci numbers.
Lucas numbers.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Front Matter
  • 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
  • Fundamentals
  • 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
  • References
  • Solutions to Odd-Numbered Exercises
  • Index
  • Pure and Applied Mathematics.
  • 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.