Mathematics in Nature: Modeling Patterns in the Natural World
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.
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The Confluence of Nature and Mathematical Modeling
Estimation The Power of Arithmetic in Solving Fermi Problems
Shape Size and Similarity The Problem of Scale
Meteorological Optics I Shadows Crepuscular Rays and Related Optical Phenomena
Meteorological Optics II A Calculus I Approach to Rainbows Halos and Glories
Clouds Sand Dunes and Hurricanes
Linear Waves of All Kinds
Bores and Nonlinear Waves