Fibonacci and Lucas Numbers with Applications [Hardcover]

Thomas Koshy (Author)

Book Description

ISBN-10: 0471399698 | ISBN-13: 978-0471399698 | Publication Date: August 10, 2001 | Edition: 1

The first comprehensive survey of mathematics' most fascinating number sequences
Fibonacci 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 integer sequences, complete with a wealth of exciting applications, enlightening examples, and fun exercises that offer numerous opportunities for exploration and experimentation.
The author has assembled a myriad of fascinating properties of both Fibonacci and Lucas numbers-as developed by a wide range of sources-and catalogued their applications in a multitude of widely varied disciplines such as art, stock market investing, engineering, and neurophysiology. Most of the engaging and delightful material here is easily accessible to college and even high school students, though advanced material is included to challenge more sophisticated Fibonacci enthusiasts. A historical survey of the development of Fibonacci and Lucas numbers, biographical sketches of intriguing personalities involved in developing the subject, and illustrative examples round out this thorough and amusing survey. Most chapters conclude with numeric and theoretical exercises that do not rely on long and tedious proofs of theorems. Highlights include:
* Balanced blend of theory and real-world applications
* Excellent reference material for student reports and projects
* User-friendly, informal, and entertaining writing style
* Historical interjections and short biographies that add a richer perspective to the topic
* Reference sections providing important symbols, problem solutions, and fundamental properties from the theory of numbers and matrices
Fibonacci and Lucas Numbers with Applications provides mathematicians with a wealth of reference material in one convenient volume and presents an in-depth and entertaining resource for enthusiasts at every level and from any background.

Editorial Reviews

Review

"…a 'must' for fans of Fibonacci…" (Translated from French, Bulletin AMQ, October 2005)

"...presents a look at the numerous applications of Fibonacci and Lucas numbers in a range of disciplines." (SciTech Book News, Vol. 25, No. 4, December 2001)

"...presents the history, mathematics, and applications of the Fibonacci and Lucas sequences...An important feature of the book is the many...exercises..." (Mathematical Reviews, 2002f)

"...beautiful and well worth the reading...with many exercises and a good bibliography, this book will fascinate both students and teachers." (Mathematics Teacher, Vol. 95, No. 5, May 2002)

"A delightful romp through all things Fibonacci." (American Mathematical Monthly, January 2003)

"...a delightful book which should prove of great value...the most comprehensive collection of results, theorems, and references regarding Fibonacci numbers and their applications to date..." (The Fibonacci Quarterly, February 2002)

"...a splendid compendium of everything that most of us will ever need to know about the Fibonacci and Lucas numbers...an invaluable reference for experts and non-experts alike..." (The Mathematical Gazette)

"...a definitive history and authoritative analysis ...a myriad of fascinating properties of both Fibonacci and Lucas numbers..." (Mathematical Didactics, 2003)

Review

[Koshy's] book is without doubt the most comprehensive and scholarly work on Fibonacci numbers to date and I am sure that it will quickly signal its presence and impose itself as an authoritative reference manual on Fibonacci numbers.
—Napoleon Gauthier, Royal Military College of Canada, Kingston, ON

What a gem this is! [...] My only regrest about the book is that it wasn't around years ago. It fills such a void.
—Monte Zerger, Adams State College, Alamosa, CO

See all Editorial Reviews

Product Details

• Hardcover: 648 pages
• Publisher: Wiley-Interscience; 1 edition (August 10, 2001)
• Language: English
• ISBN-10: 0471399698
• ISBN-13: 978-0471399698
• Product Dimensions: 9.1 x 6.6 x 1.4 inches
• Shipping Weight: 2.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #2,073,603 in Books (See Top 100 in Books)

More About the Author

Thomas Koshy, Ph. D., is Professor of Mathematics at Framingham State College, Framingham, Massachusetts. He received Faculty of the Year Award in 2007. He is the author of seven books and numerous articles on a wide spectrum of topics. His "Fibonacci and Lucas Numbers with Applications," published by Wiley, won the Association of American Publishers' new book award in 2001. The second edition of his popular "Elementary Number Theory with Applications," published by Academic Press appeared in 2007.

Customer Reviews

Most Helpful Customer Reviews

19 of 19 people found the following review helpful:

5.0 out of 5 stars As complete a coverage as is currently possible, January 12, 2002

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
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This review is from: Fibonacci and Lucas Numbers with Applications (Hardcover)

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.

6 of 6 people found the following review helpful:

4.0 out of 5 stars wide range of results and many typos, May 17, 2008

By 

Jean-philippe Poton (Hino, Tokyo, Japan) - See all my reviews
(REAL NAME)   

This review is from: Fibonacci and Lucas Numbers with Applications (Hardcover)

Overall, this is a good book, covering many aspects of the fibonacci numbers, however, at about a 100USD, the potential buyer should be warned that there is a lot a typographical errors in the book.

While it is frequent to find a few notation's mistakes in every mathematics book, this one is way over average, most of them fortunately are quite obvious and easy to correct, but, in some cases, it simply makes the demonstration unreadable and the reader is better off working out the proof by himself; luckily, most of the proofs are quite elementary.
For the reader patient enough to go through this book simultaneously reading and correcting it, it definitely is a worthy repository of results involving Fibonacci and Lucas numbers.

3 of 3 people found the following review helpful:

3.0 out of 5 stars In the land of the blind. . ., December 19, 2009

By 

Stuart Thiel (Chicago) - See all my reviews
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Amazon Verified Purchase

This review is from: Fibonacci and Lucas Numbers with Applications (Hardcover)

There's nothing wrong with this book, exactly, but it suffers from being too technical to be a popular book on Fibonacci and too breezy and gimmicky to be a mathematics text. It flits and floats and flies from sub-topic to sub-topic, sometimes visiting the same sub-topic more than once, without discernable pattern. While I have no doubt that that Koshy knows his stuff and his discussion in each sub-chapter is more or less correct, I wish I had a better sense of what's left out.

Fibonacci has always been a dilettante's heaven, and dilettantes need books, like Koshy's could have been, that give them a sense of what's known and what's not. If you're staring into the fire some winter night and suddenly go, Hark!, you need an easy way to decide if your Hark! is worth pursuing, and if so what's already been done. You don't need mathematical rigor, at least not beyond some bare minimum. You need to know if anyone ever bothered to work out a general formula, for general k, for the coefficients of a(0)F(i)^k + a(1)F(i+1)^k + a(2)F(i+2)^k + . . . + a(m)F(i+m)^k = 0. (someone did: see Lewis, More Power to Fibonacci, Mathematics Gazette July 2003.)

A one-volume (affordable) Fibonacci encyclopedia reliably answering the breadth question would be nearly priceless. Koshy's book is not it. You have to buy this book; there's nothing else out there, that I know about, anyway, matching its breadth or depth. And, I suppose Koshy deserves his royalties simply for stepping into the market niche where I was waiting. But there's something missing.

PS. People who know their stuff have warned us about the many typos in this book. I have found a few myself. So, test those Fibonacci identities before you use them, the same way you would test thin ice.