## 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, math educators Alfred Posamentier and Ingmar Lehmann take us on a fascinating tour of the many ramifications of the Fibonacci numbers. The authors begin with a brief history of their 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.Alfred S. Posamentier (New York, NY) is dean of the School of Education and professor of mathematics education at The City College of the City University of New York. He has published over 40 books in the area of mathematics and mathematics education, including Pi: A Biography of the World's Most Mysterious Number and Math Charmers: Tantalizing Tidbits for the Mind.Ingmar Lehmann (Berlin, Germany) is on the mathematics faculty at Humboldt University in Berlin and the coauthor of Pi: A Biography of the World's Most Mysterious Number. |

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#### LibraryThing Review

User Review - fpagan - LibraryThingCould double as a rival to Livio's book on the golden ratio [phi, (sqrt(5)+1)/2, 1.618...], so intimately is the latter entwined with the Fibonacci sequence. E.g., there's a proof that (1/sqrt(5)) (phi^n - (- 1/phi)^n) is a direct formula for the nth Fibonacci number. Thorough and enjoyable. Read full review

### Contents

Acknowledgments | 9 |

The Fibonacci Numbers in Nature | 59 |

The Fibonacci Numbers and | 77 |

The Fibonacci Numbers and | 107 |

The Fibonacci Numbers | 161 |

A Potpourri of Fibonacci Number | 177 |

The Fibonacci Numbers Found in | 231 |

The Fibonacci Numbers | 271 |

The Famous Binet Formula for Finding | 293 |

The Fibonacci Numbers | 307 |

Epilogue | 327 |

List of the First 500 Fibonacci Numbers | 343 |

Proofs of Fibonacci Relationships | 349 |

371 | |

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### Common terms and phrases

ABCD angle appendix approximation artist begin bers Binet formula Bonacci bulb calculate chapter circle column common factor consecutive Fibonacci numbers consider construction continued fraction Corbusier diagonal digits divides Elliott equation example F n+1 famous Fibo Fibonacci Quarterly Fibonacci sequence Figure Fk+1 Fn+1 fractal Fx is divisible geometric golden angle golden ratio golden rectangle golden section golden triangle Grossman truss hexagon induction inspection irrational number iteration kilometers Le Corbusier 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 sides sonata spirals square number tion true