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Other titles in the Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts series:
Fibonacci and Lucas Numbers with Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)by Thomas Koshy
Synopses & Reviews
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.
Book News Annotation:
Gathering materials from a wide range of sources, Koshy (mathematics, Framingham State College) presents a look at the numerous applications of Fibonacci and Lucas numbers in a range of disciplines. The intent of the work is to comprehensively show how these sequences are not only useful, but also how they have a tendency to show up in both the natural and manmade world. Koshy has kept long proofs to a minimum and includes the answers to odd-numbered exercises in the text.
Annotation c. Book News, Inc., Portland, OR (booknews.com)
Faszinierende Anwendungen, Beispiele und Übungen zum Thema der Fibonacci- und Lucas-Zahlen, für die sich Fachleute und Amateure gleichermaßen interessieren werden! Besprochen werden die Eigenschaften der Zahlen und zum Teil verblüffende Umsetzungen, u.a. in der Mustererkennung, der Beweistheorie, der Graphentheorie, der Matrizenrechnung und der Trigonometrie. Der Text macht neugierig und setzt nur mittlere mathematische Vorkenntnisse voraus. Willkommene Zugaben sind mathematikhistorische Einschübe und Kurzbiographien wichtiger Persönlichkeiten.
Includes bibliographical references (p. 562-576) and index.
About the Author
THOMAS KOSHY, Ph.D., is Professor of Mathematics at Framingham State College in Framingham, Massachusetts. He is the author of the forthcoming book Elementary Number Theory with Applications, among several other books, as well as numerous articles across a wide range of topics.
Table of Contents
List of Symbols.
The Rabbit Problem.
Fibonacci Numbers in Nature.
Fibonacci Numbers: Additional Occurrances.
Fibonacci and Lucas Identities.
Generalized Fibonacci Numbers.
Additional Fibonacci and Lucas Formulas.
The Euclidean Algorithm.
Solving Recurrence Relations.
Additional Pascal-Like Triangles.
Generalized Fibonacci Numbers Revisited.
Generating Functions Revisited.
The Golden Ratio.
The Golden Ratio Revisited.
The Golden Ellipse and Hyperbola.
Weighted Fibonacci and Lucas Sums.
Weighted Fibonacci and Lucas Sums Revisited.
The Knapsack Problem.
Fibonacci Magic Squares.
Fibonacci and Lucas Congruences.
Fibonacci and Lucas Periodicity.
Fibonacci and Lucas Series.
Zeros of Fibonacci and Lucas Polynomials.
Fibonacci and Lucas Subscripts.
Gaussian Fibonacci and Lucas Numbers.
Tribonacci Polynomials. Appendix 1: Fundamentals.
Appendix 2: The First 100 Fibonacci and Lucas Numbers.
Appendix 3: The First 100 Fibonacci Numbers and Their Prime Factorizations.
Appendix 4: The First 100 Lucas Numbers and Their Prime Factorizations.
Solutions to Odd-Numbered Exercises.
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