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Fibonacci and Lucas Numbers with Applications, 2nd Edition, Volume Two

Fibonacci and Lucas Numbers with Applications, 2nd Edition, Volume Two

Thomas Koshy

ISBN: 978-1-118-74229-7

Jun 2018

736 pages

Description

Fibonacci and Lucas numbers have intrigued amateurs and professionals for centuries, and for the first time under one cover, this book unifies advanced properties, applications, and occurrences of the extended Fibonacci-related family.  In addition, the book offers analysis of these famous integers, complete with a wealth of exciting applications, enlightening examples, and fun exercises that provide numerous opportunities for exploration and experimentation.  Fibonacci and Lucas numbers, Pell and Pell-Lucas numbers, Jacobsthal and Jacobsthal-Lucas numbers, and the corresponding univariate and bivariate polynomials are discussed. The author also details the close link between univariate Fibonacci and Lucas polynomials using differential and integral calculus and between Pell and Pell-Lucas polynomials and numbers.  Extensive combinatorial interpretations of the bivariate polynomials using linear and circular tilings are provided as well as the inclusion of Fibonacci-Pell and Lucas-Pell-Lucas hybridities.  Most of the chapters end with exercise sets, and brief solutions/proofs of odd-numbered exercises appear at the end of the book.  Solutions to the even-numbered problems can be obtained via written request to the Publisher.  The Appendix contains three tables covering the first 100 Fibonacci and Lucas numbers; the first 100 Pell and Pell-Lucas numbers; and the first 100 Jacobsthal and Jacobsthal-Lucas numbers.  Topical coverage includes: Fibonacci trees; Fibonacci quadratics; Fibonacci and Lucas identities; advanced applications; Fibonacci and Lucas determinants; univariate Fibonacci and Lucas polynomials; bivariate Fibonacci and Lucas families; bivariate Pell and Jacobsthal families; combinatorial interpretations of bivariate Fibonacci and Lucas polynomials; links with Pascal's Triangle; Pell trees; Fibonacci-Pell hybridities; Pellnomial numbers; and advanced Fibonometry.