Mathematics in Nature : : Modeling Patterns in the Natural World / / John A. Adam.

• Superior document: Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013
• VerfasserIn: Adam, John A.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2011]; ©2003
• Year of Publication: 2011
• Edition: Course Book
• Language: English
• Physical Description: 1 online resource (392 p.) :; 24 color illus. 84 line illus. 9 tables.

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.

Table of Contents

Frontmatter -- Contents -- Preface -- 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