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
     
 

"Have you wondered how rainbows or sand dunes form? Does it puzzle you why drying mud forms polygonally shaped cracks? Can you explain the patterns on a butterfly's wings or how birds fly? In this delightful book, John Adam invites us to question and to share his enthusiasm for developing mathematical models to explore a wide range of everyday natural phenomena. See more details below

Overview

"Have you wondered how rainbows or sand dunes form? Does it puzzle you why drying mud forms polygonally shaped cracks? Can you explain the patterns on a butterfly's wings or how birds fly? In this delightful book, John Adam invites us to question and to share his enthusiasm for developing mathematical models to explore a wide range of everyday natural phenomena. Mathematics in Nature can be used as a text on mathematical modeling or as a book to dip into and encourage us to observe and wonder at the beauty of nature. It has the potential of becoming a classic."—Brian Sleeman, University of Leeds

"This is a book that I will want to keep close to hand so that I will not be stumped by all those seemingly simple yet subtle questions about nature: Why can fleas jump so high? Why is visibility better in rain than in fog? Why does a river meander? How high can trees grow? But it is much more than a compendium of useful facts and explanations. It is the clearest guide I have seen to the art of conceptualizing, simplifying, and modeling natural phenomena—no less than an exegesis on how good quantitative science is done."—Phillip Ball, Consultant Editor, Nature

"Mathematics in Nature leads the calculus-literate reader on a vigorous tour of nature's visible patterns—from the radiator-sailed dinosaur Dimetrodon to fracturing of dried mud and ceramic glazes, from the dispersion of rainbows and iridescence of beetles to the pearling of spider silk. Eschewing phenomena that are too small to see or too large to grasp, Adam shows how elementary college mathematics, rigorously applied, can give precise expression to everyday natural phenomena. His extraordinary range of examples and meticulous explanations document mathematics' wonderful capacity to describe and explain nature's patterns."—Lynn Arthur Steen, St. Olaf College

"This work is outstanding! The color photographs are beautiful. The writing style is splendid."—Robert B. Banks, author of Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics

"This is a unique, even great book. It is in the spirit of a number of books on topics like symmetry and chaos that look at mathematics in the context of visually striking natural and other phenomena but is more broadly based. The author leads with the phenomena and follows with the math, making the book accessible to a wider audience while still appealing to math students and faculty."—Frank Wattenberg

"This is one of the best contemporary texts on the subject, appealing to a very broad audience that will definitely love this excellent book."—Yuri V. Rogovchenko, Zentralblatt Math (European Mathematical Society)

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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:
1,332,599
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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