Fibonacci and Lucas Numbers with Applications, Volume 2 (Pure and Applied Mathematics: A Wiley Series of Texts, Monographs and Tracts)

The main focus of Volume One was to showcase the beauty, applications, and ubiquity of Fibonacci and Lucas numbers in many areas of human endeavor. Although these numbers have been investigated for centuries, they continue to charm both creative amateurs and mathematicians alike, and provide exciting new tools for expanding the frontiers of mathematical study. In addition to being great fun, they also stimulate our curiosity and sharpen mathematical skills such as pattern recognition, conjecturing, proof techniques, and problem-solving. The area is still so fertile that growth opportunities appear to be endless. Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio, Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication, Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers, A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology, The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Book jacket Contents......Page 7 List of Symbols......Page 12 Preface......Page 14 31. Fibonacci and Lucas Polynomials I......Page 18 32. Fibonacci and Lucas Polynomials II......Page 81 33. Combinatorial Models II......Page 103 34. Graph-Theoretic Models II......Page 141 35. Gibonacci Polynomials......Page 161 36. Gibonacci Sums......Page 211 37. Additional Gibonacci Delights......Page 248 38. Fibonacci and Lucas Polynomials III......Page 284 39. Gibonacci Determinants......Page 335 40. Fibonometry II......Page 361 41. Chebyshev Polynomials......Page 384 42. Chebyshev Tilings......Page 427 43. Bivariate Gibonacci Family I......Page 440 44. Jacobsthal Family......Page 454 45. Jacobsthal Tilings and Graphs......Page 510 46. Bivariate Tiling Models......Page 547 47. Vieta Polynomials......Page 562 48. Bivariate Gibonacci Family II......Page 600 49. Tribonacci Polynomials......Page 619 A.1. The First 100 Fibonacci and Lucas Numbers......Page 638 A.2. The First 100 Pell and Pell–Lucas Numbers......Page 641 A.3. The First 100 Jacobsthal and Jacobsthal–Lucas Numbers......Page 645 A.4. The First 100 Tribonacci Numbers......Page 649 Abbreviations......Page 651 Bibliography......Page 652 Solutions to Odd-Numbered Exercises......Page 668 Index......Page 732 Praise for the First Edition beautiful and well worth the reading with many exercises and a good bibliography, this book will fascinate both students and teachers.