Fibonacci and Lucas numbers, and the golden section: theory and applications

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 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 S. Vajda. Includes Index. Bibliography: P. [185]-187.