## Mathematics in Nature: Modeling Patterns in the Natural WorldFrom rainbows, river meanders, and shadows to spider webs, honeycombs, and the markings on animal coats, the visible world is full of patterns that can be described mathematically. Examining such readily observable phenomena, this book introduces readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Generously illustrated, written in an informal style, and replete with examples from everyday life, Developed out of a university course, this book makes an ideal supplemental text for courses in applied mathematics and mathematical modeling. It will also appeal to mathematics educators and enthusiasts at all levels, and is designed so that it can be dipped into at leisure. |

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### Contents

The Confluence of Nature and Mathematical Modeling | 1 |

Estimation The Power of Arithmetic in Solving Fermi Problems | 17 |

Shape Size and Similarity The Problem of Scale | 31 |

Meteorological Optics I Shadows Crepuscular Rays and Related Optical Phenomena | 57 |

Meteorological Optics II A Calculus I Approach to Rainbows Halos and Glories | 80 |

Clouds Sand Dunes and Hurricanes | 118 |

Linear Waves of All Kinds | 139 |

Stability | 173 |

The Fibonacci Sequence and the Golden Ratio 964 | 213 |

Bees Honeycombs Bubbles and Mud Cracks | 231 |

River Meanders Branching Patterns and Trees | 254 |

Bird Flight | 295 |

How Did the Leopard Get Its Spots? | 309 |

Fractals An Appetite Whetter | 336 |

341 | |

356 | |