Fibonacci and Lucas Numbers with Applications

Rating:
Summary: As complete a coverage as is currently possible
Review: As a longtime subscriber to The Fibonaci Quarterly and a regular contributor to the problem column, I thought I was well-versed in the many applications of the Fibonacci and Lucas numbers. The contents of this book quickly led to an attitude adjustment on my part. It is astonishing and almost mystifying at times to see these numbers appearing in situations where "intuition" would tell us that they have no reason to be involved.
Subjects such as Fibonometry, where Fibonacci and Lucas numbers are related using trigonometric functions, demonstrates that the mathematics world is one where there are some topics that just seem to be attractors for many others. You start at one point and follow a logical path and suddenly, unexpectedly you arrive at the Fibonacci and/or Lucas numbers. The number of identities betwixt and between these two sets of numbers is so large, that one wonders if some of them may forever remain undiscovered.
There is a great deal of material in this book that could be selected for use in mathematics courses at almost all levels, starting at the position of precalculus. The inductive proofs of some of the identities are excellent demonstrations of how induction is used in mathematics. An extensive problem set is given at the end of each chapter, and solutions to the odd-numbered exercises are included in an appendix.
This is one of those books that all mathematicians should own. The problems and demonstrations in this book can be used as fodder for students hungry for interesting problems with solutions that teach them something. It demonstrates how mathematics is interrelated and how even simple definitions can lead to very complex and universal results.

Published in Journal of Recreational Mathematics, reprinted with permission.