## Fibonacci and Lucas Numbers with ApplicationsThe 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. |

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### Contents

Leonardo Fibonacci | 1 |

The Rabbit Problem | 4 |

Fibonacci Numbers in Nature | 16 |

Copyright | |

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AABC ABCD Binet's formula Bn(x Carlitz Cassini's formula Chapter coefficients column compute consecutive Fibonacci numbers continued fraction converges Corollary defined denote the number digits divides equation Euclidean algorithm example Exercise explicit formula F„_i Fibonacci and Lucas Fibonacci numbers Fibonacci polynomials Fibonacci Quarterly Fibonacci recurrence relation Fibonacci sequence Fibonacci tree Figure Find Fm+n Fn+2 following result following theorem function geometry Golden Ratio golden rectangle golden triangle graph Identity knapsack problem Koshy Lemma Likewise line segment Lucas numbers Lucas sequence mathematical induction mathematician matrix Notice Pascal's triangle pattern pentagon perfect square positive integer prime Problem Proof properties Prove real number recurrence relation recursive definition result is true rising diagonal side solution subsets Suppose Swamy Table tribonacci V. E. Hoggatt values Verify vertex vertices yields zero