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.
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
Mathematics in Nature is an excellent resource for bringing a greater variety of patterns into the mathematical study of nature, as well as for teaching students to think about describing natural phenomena mathematically... [T]he breadth of patterns studied is phenomenal. -- Will Wilson American Scientist John Adam has combined his interest in the great outdoors and applied mathematics to compile one surprising example after another of how mathematics can be used to explain natural phenomena. And what examples! ... [He] has done a great deal of reading and exposition, indulging his passions to create this compilation of mathematical models of natural phenomena, and the sheer number of examples he manages to cram into this book is testament to his efforts. There are other texts on the market which explore the connection between mathematics and nature ... but none this wide-ranging. -- Steven Morics MAA Online Adam has laced his mathematical models with popular descriptions of the phenomena selected... Mathematics in Nature can accordingly be read for pleasure and instruction by the select laity who are not afraid of reading between the lines of equations. -- Philip J. Davis SIAM News John Adam's quest is a very simple one: that is, to invite one to look around and observe the wonders of nature, both natural and biological; to ponder them; and to try to explain them at various levels with, for the most part, quite elementary mathematical concepts and techniques. -- Brian D. Sleeman Notices of the American Mathematical Association Reading this book progressively creates a course in mathematical modeling built around familiar, tangible, human-scale examples, with a trajectory that takes readers from dimensional estimates through geometrical modeling, linear and nonlinear dynamics, to pattern formation. Choice John Adam's Mathematics in Nature illustrates how, in a friendly and lucid manner, mathematicians think about nature. Adam lets us see how mathematics is not only an ally, but is perhaps the very language that nature uses to express the beautiful... This is a book that will challenge while it intrigues and excites. -- Stanley David Gedzelman Weatherwise
John A. Adam is Professor of Mathematics at Old Dominion University, coeditor of "A Survey of Models for Tumor-Immune System Dynamics", and a regular contributor to leading journals in applied mathematics.