# Mathematics in Nature: Modeling Patterns in the Natural World

Princeton University Press, Sep 10, 2006 - Mathematics - 360 pages

From 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, Mathematics in Nature is an excellent and undaunting introduction to the ideas and methods of mathematical modeling. It illustrates how mathematics can be used to formulate and solve puzzles observed in nature and to interpret the solutions. In the process, it teaches such topics as the art of estimation and the effects of scale, particularly what happens as things get bigger. Readers will develop an understanding of the symbiosis that exists between basic scientific principles and their mathematical expressions as well as a deeper appreciation for such natural phenomena as cloud formations, halos and glories, tree heights and leaf patterns, butterfly and moth wings, and even puddles and mud cracks.

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 BIBLIOGRAPHY 341 INDEX 356

 Bores and Nonlinear Waves 194