Mathematics in Nature: Modeling Patterns in the Natural World

Mathematics in Nature: Modeling Patterns in the Natural World

by John A. Adam
     
 

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ISBN-10: 0691114293

ISBN-13: 9780691114293

Pub. Date: 11/10/2003

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

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.

Product Details

ISBN-13:
9780691114293
Publisher:
Princeton University Press
Publication date:
11/10/2003
Pages:
416
Product dimensions:
6.48(w) x 9.22(h) x 1.18(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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