## The Fabulous Fibonacci NumbersThe most ubiquitous, and perhaps the most intriguing, number pattern in mathematics is the Fibonacci sequence. In this simple pattern beginning with two ones, each succeeding number is the sum of the two numbers immediately preceding it (1, 1, 2, 3, 5, 8, 13, 21, ad infinitum). Far from being just a curiosity, this sequence recurs in structures found throughout nature - from the arrangement of whorls on a pinecone to the branches of certain plant stems. All of which is astounding evidence for the deep mathematical basis of the natural world. With admirable clarity, two veteran math educators take us on a fascinating tour of the many ramifications of the Fibonacci numbers. They begin with a brief history of a distinguished Italian discoverer, who, among other accomplishments, was responsible for popularizing the use of Arabic numerals in the West. Turning to botany, the authors demonstrate, through illustrative diagrams, the unbelievable connections between Fibonacci numbers and natural forms (pineapples, sunflowers, and daisies are just a few examples). In art, architecture, the stock market, and other areas of society and culture, they point out numerous examples of the Fibonacci sequence as well as its derivative, the "golden ratio." And of course in mathematics, as the authors amply demonstrate, there are almost boundless applications in probability, number theory, geometry, algebra, and Pascal's triangle, to name a few. Accessible and appealing to even the most math-phobic individual, this fun and enlightening book allows the reader to appreciate the elegance of mathematics and its amazing applications in both natural and cultural settings. |

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### Contents

Acknowledgments | 9 |

The Fibonacci Numbers in Nature | 59 |

The Fibonacci Numbers and | 77 |

Copyright | |

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ABCD angle appendix approximation artist beauty begin bers Binet formula Bonacci bulb calculate chapter circle column common factor consecutive Fibonacci numbers consider construction continued fraction Corbusier diagonal digits divides equation example famous Fibo Fibonacci Quarterly Fibonacci sequence fractal Fx is divisible geometric golden angle golden ratio golden rectangle golden section golden spiral golden triangle Grossman truss hexagon induction inspection intersect irrational number iteration kilometers length Liber Abaci line segment logarithmic spiral look Lucas numbers Mandelbrot set mathematician mathematics measure minor modulus multiply nacci numbers natural numbers notice numbers appear pairs Pascal triangle pattern petals phyllotaxis Pinus Pisa positive integer problem proof proportions Pythagorean theorem Pythagorean triple quence radius recursive regular pentagon relationship relatively prime result right triangle sequence of numbers shown in figure sides sonata spirals square number tion true