Fibonacci and Lucas Numbers, and the Golden Section

✍ Scribed by Steven Vajda

• Publisher: Ellis Horwood Limited
• Year: 1989
• Tongue: English
• Leaves: 200
• Edition: 1
• Category: Library

✦ Synopsis

This text for advanced undergraduates and graduate students surveys the use of Fibonacci and Lucas numbers in areas relevant to operational research, statistics, and computational mathematics. It also covers geometric topics related to the ancient principle known as the Golden Section, plus Meta-Fibonacci numbers and Platonic solids. 1989 edition.

✦ Table of Contents

Table of contents
Preface
I Introduction
II Background
III Relationships
IV Fibonacci numbers and the Golden Section
V Fibonacci series
VI Divisibility properties
VII Congruences and uniformity
VIII Continued fractions and convergents
IX Fibonacci representation
X Search and games
XI Hyperbolic functions and Fibonacci numbers
XII Meta-Fibonacci sequences (a letter from B. W. Conolly)
XIII The Golden Section in the plane
XIV The Golden Section in three-dimensional space
Appendix
1. Congruences
2. The Euclidean Algorithm. Continued fractions
3. Quadratic residues. Quadratic reciprocity
4. Binomial coefficients
5. Difference equations
6. Linear equations and determinants
List of formulae
References
Fibonacci and Lucas numbers and their prime factors
Index