Franklin

Mathematics in Nature : Modeling Patterns in the Natural World.

Author/Creator:
Adam, John A.
Publication:
Princeton : Princeton University Press, 2006.
Format/Description:
Book
1 online resource (349 pages)
Status/Location:
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Subjects:
Mathematical models.
Form/Genre:
Electronic books.
Summary:
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.
Contents:
Cover
Half title
Title
Copyright
Dedication
Contents
Preface The motivation for the book
Acknowledgments
Credits
Prologue Why I Might Never Have Written This Book
Chapter One The Confluence of Nature and Mathematical Modeling
Chapter Two Estimation: The Power of Arithmetic in Solving Fermi Problems
Chapter Three Shape, Size, and Similarity: The Problem of Scale
Chapter Four Meteorological Optics I: Shadows, Crepuscular Rays, and Related Optical Phenomena
Chapter Five Meteorological Optics II: A "Calculus I" Approach to Rainbows, Halos, and Glories
Chapter Six Clouds, Sand Dunes, and Hurricanes
Chapter Seven (Linear) Waves of All Kinds
Chapter Eight Stability
Chapter Nine Bores and Nonlinear Waves
Chapter Ten The Fibonacci Sequence and the Golden Ratio (τ)
Chapter Eleven Bees, Honeycombs, Bubbles, and Mud Cracks
Chapter Twelve River Meanders, Branching Patterns, and Trees
Chapter Thirteen Bird Flight
Chapter Fourteen How Did the Leopard Get Its Spots?
Appendix Fractals: An Appetite Whetter...
Bibliography
Index.
Notes:
Description based on publisher supplied metadata and other sources.
Local notes:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2021. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
Other format:
Print version: Adam, John A. Mathematics in Nature
ISBN:
9781400841011
9780691127965
OCLC:
751963486