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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.

We live in a world of optical marvels - from the commonplace but beautiful rainbow, to the rare and eerie superior mirage. But how many of us really understand how a rainbow is formed, why the setting sun is red and flattened, or even why the sky at night is not absolutely black? This beautiful and informative guide provides clear explanations to all naturally occurring optical phenomena seen with the naked eye, including shadows, halos, water optics, mirages and a host of other spectacles. Separating myth from reality, it outlines the basic principles involved, and supports them with many figures and references. A wealth of rare and spectacular photographs, many in full color, illustrate the phenomena throughout. In this new edition of the highly-acclaimed guide to seeing, photographing and understanding nature's optical delights, the authors have added over 50 new images and provided new material on experiments you can try yourself.

This book presents in a concise way the Mie theory and its current applications. It begins with an overview of current theories, computational methods, experimental techniques, and applications of optics of small particles. There is also some biographic information on Gustav Mie, who published his famous paper on the colour of Gold colloids in 1908. The Mie solution for the light scattering of small spherical particles set the basis for more advanced scattering theories and today there are many methods to calculate light scattering and absorption for practically any shape and composition of particles. The optics of small particles is of interest in industrial, atmospheric, astronomic and other research. The book covers the latest developments in divers fields in scattering theory such as plasmon resonance, multiple scattering and optical force.