Saturday, April 19, 2008

John A. Adam's "Mathematics in Nature"

John A. Adam is professor of mathematics at Old Dominion University. His new book, with Lawrence Weinstein, is Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin.

Adam applied the "Page 99 Test" to his award-winning book Mathematics in Nature: Modeling Patterns in the Natural World, and reported the following:
On page 99 of this book, the reader might be very distressed to find two very complicated-looking equations, in addition to several innocuous-looking ones. But reader, fear not: these equations are present 'merely' to illustrate some of the underlying mathematical features of one of nature's most beautiful (and common) sights: a 22-degree ice-crystal halo around the sun. Still puzzled? Well, allow me to explain. When those highest of all clouds are seen in an otherwise clear blue sky, a ring, tinged faintly red on the inside, may be noticed around the sun. Those whispy, feather-like clouds known as cirrus, or cirro-stratus, are composed entirely of ice crystals, and sunlight refracted through myriads of these crystals produces this beautiful sight. Similar halos also can been seen around the moon when conditions are favorable.

[Warning: never look directly at the sun - when looking for halos always block off the solar disk with your hand, someone's head, or a conveniently located chimney on a neighbor's house, before examining the region near the sun.]

But this book is not just about halos. 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, and this book is designed to introduce readers to the beauty of nature as revealed by mathematics and the beauty of mathematics as revealed in nature. Illustrated with many color photographs and line drawings, written in an informal style, and replete with examples from everyday life, Mathematics in Nature is an 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 how to interpret the solutions. In the process, it teaches such topics as the art of estimation and 'the problem of scale', that is, what happens as things get bigger. Each chapter has a non-mathematical introduction to the topic at hand. I hope that as a result, readers will develop 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.
Read an excerpt from Mathematics in Nature, and learn more about the book at the Princeton University Press website.

The Page 99 Test: Guesstimation.

--Marshal Zeringue