Mathematics in nature : modeling patterns in the natural world
著者
書誌事項
Mathematics in nature : modeling patterns in the natural world
Princeton University Press, 2003
大学図書館所蔵 全16件
注記
Includes bibliographical references (p. [341]-355) and index
HTTP:URL=http://www.loc.gov/catdir/description/prin031/2003055616.html Information=Publisher description
内容説明・目次
内容説明
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. Professors: "A Supplementary Solutions Manual" is available for this book. It is restricted to teachers using the text in courses.
目次
- 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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