Mathematics in Nature: Modeling Patterns in the Natural World / Edition 1

Mathematics in Nature: Modeling Patterns in the Natural World / Edition 1

by John A. Adam
     
 

ISBN-10: 0691127964

ISBN-13: 9780691127965

Pub. Date: 08/21/2006

Publisher: Princeton University Press

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

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Overview

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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Product Details

ISBN-13:
9780691127965
Publisher:
Princeton University Press
Publication date:
08/21/2006
Edition description:
New Edition
Pages:
416
Sales rank:
760,729
Product dimensions:
6.10(w) x 9.10(h) x 1.20(d)

Table of Contents

Preface: The motivation for the book; Acknowledgments; Credits xiii

Prologue: Why I Might Never Have Written This Book xxi

CHAPTER ONE: The Confluence of Nature and Mathematical Modeling 1

CHAPTER TWO: Estimation: The Power of Arithmetic in Solving Fermi Problems 17

CHAPTER THREE: Shape, Size, and Similarity: The Problem of Scale 31

CHAPTER FOUR: Meteorological Optics I: Shadows, Crepuscular Rays, and Related Optical Phenomena 57

CHAPTER FIVE: Meteorological Optics II: A "Calculus I" Approach to Rainbows, Halos, and Glories 80

CHAPTER SIX: Clouds, Sand Dunes, and Hurricanes 118

CHAPTER SEVEN: (Linear) Waves of All Kinds 139

CHAPTER EIGHT: Stability 173

CHAPTER NINE: Bores and Nonlinear Waves 194

CHAPTER TEN: The Fibonacci Sequence and the Golden Ratio 213

CHAPTER ELEVEN: Bees, Honeycombs, Bubbles, and Mud Cracks 231

CHAPTER TWELVE: River Meanders, Branching Patterns, and Trees 254

CHAPTER THIRTEEN: Bird Flight 295

CHAPTER FOURTEEN: HowDid the Leopard Get Its Spots? 309

APPENDIX: Fractals: An Appetite Whetter... 336

BIBLIOGRAPHY 341

INDEX 357

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