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Full Product Details

Author:   Thomas Koshy
Publisher:   John Wiley and Sons Ltd
Imprint:   John Wiley & Sons Inc
Dimensions:   Width: 15.90cm , Height: 4.10cm , Length: 23.90cm
Weight:   1.150kg
ISBN:  

9780471399698

ISBN 10:   0471399698
Pages:   672
Publication Date:   03 October 2001
Audience:   General/trade ,  College/higher education ,  Professional and scholarly ,  General ,  Undergraduate
Format:   Hardback
Publisher's Status:   Unknown
Availability:   In Print  
Limited stock is available. It will be ordered for you and shipped pending supplier's limited stock.

Table of Contents

Preface. List of Symbols. Leonardo Fibonacci. The Rabbit Problem. Fibonacci Numbers in Nature. Fibonacci Numbers: Additional Occurrances. Fibonacci and Lucas Identities. Geometric Paradoxes. Generalized Fibonacci Numbers. Additional Fibonacci and Lucas Formulas. The Euclidean Algorithm. Solving Recurrence Relations. Completeness Theorems. Pascal's Triangle. Pascal-Like Triangles. Additional Pascal-Like Triangles. Hosoya's Triangle. Divisibility Properties. Generalized Fibonacci Numbers Revisited. Generating Functions. Generating Functions Revisited. The Golden Ratio. The Golden Ratio Revisited. Golden Triangles. Golden Rectangles. Fibonacci Geometry. Regular Pentagons. The Golden Ellipse and Hyperbola. Continued Fractions. Weighted Fibonacci and Lucas Sums. Weighted Fibonacci and Lucas Sums Revisited. The Knapsack Problem. Fibonacci Magic Squares. Fibonacci Matrices. Fibonacci Determinants. Fibonacci and Lucas Congruences. Fibonacci and Lucas Periodicity. Fibonacci and Lucas Series. Fibonacci Polynomials. Lucas Polynomials. Jacobsthal Polynomials. Zeros of Fibonacci and Lucas Polynomials. Morgan-Voyce Polynomials. Fibonometry. Fibonacci and Lucas Subscripts. Gaussian Fibonacci and Lucas Numbers. Analytic Extensions. Tribonacci 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. References. Solutions to Odd-Numbered Exercises. Index.

Reviews

...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)

Author Information

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.

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