Mathematics in Nature: Modeling Patterns in the Natural World [Paperback]

John A. Adam (Author)

Book Description

Publication Date: August 21, 2006

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.

Editorial Reviews

Review

Mathematics in Nature is an excellent resource for bringing a greater variety of patterns into the mathematical study of nature, as well as for teaching students to think about describing natural phenomena mathematically. . . . [T]he breadth of patterns studied is phenomenal. -- Will Wilson, American Scientist



John Adam has combined his interest in the great outdoors and applied mathematics to compile one surprising example after another of how mathematics can be used to explain natural phenomena. And what examples! . . . [He] has done a great deal of reading and exposition, indulging his passions to create this compilation of mathematical models of natural phenomena, and the sheer number of examples he manages to cram into this book is testament to his efforts. There are other texts on the market which explore the connection between mathematics and nature . . . but none this wide-ranging. -- Steven Morics, MAA Online



Adam has laced his mathematical models with popular descriptions of the phenomena selected. . . . Mathematics in Nature can accordingly be read for pleasure and instruction by the select laity who are not afraid of reading between the lines of equations. -- Philip J. Davis, SIAM News



John Adam's quest is a very simple one: that is, to invite one to look around and observe the wonders of nature, both natural and biological; to ponder them; and to try to explain them at various levels with, for the most part, quite elementary mathematical concepts and techniques. -- Brian D. Sleeman, Notices of the American Mathematical Association



Reading this book progressively creates a course in mathematical modeling built around familiar, tangible, human-scale examples, with a trajectory that takes readers from dimensional estimates through geometrical modeling, linear and nonlinear dynamics, to pattern formation. -- Choice



John Adam's Mathematics in Nature illustrates how, in a friendly and lucid manner, mathematicians think about nature. Adam lets us see how mathematics is not only an ally, but is perhaps the very language that nature uses to express the beautiful. . . . This is a book that will challenge while it intrigues and excites. -- Stanley David Gedzelman, Weatherwise



Although Mathematics in Nature has not been written as a textbook, availability of such a manual shall help instructors who choose this delightful book for teaching a course in applied mathematics or mathematical modeling. -- Yuri V. Rogovchenko, Zentralblatt Math



Spanning a range of mathematical levels, this book can be used as an undergraduate textbook, a source of high school math enrichment, or can be read for pleasure by folks with an appreciation of nature but without advanced mathematical background. -- Southeastern Naturalist

Review

Have you wondered how rainbows or sand dunes form? Does it puzzle you why drying mud forms polygonally shaped cracks? Can you explain the patterns on a butterfly's wings or how birds fly? In this delightful book, John Adam invites us to question and to share his enthusiasm for developing mathematical models to explore a wide range of everyday natural phenomena. Mathematics in Nature can be used as a text on mathematical modeling or as a book to dip into and encourage us to observe and wonder at the beauty of nature. It has the potential of becoming a classic.
(Brian Sleeman, University of Leeds ) --This text refers to an out of print or unavailable edition of this title.

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Product Details

• Paperback: 416 pages
• Publisher: Princeton University Press (August 21, 2006)
• Language: English
• ISBN-10: 0691127964
• ISBN-13: 978-0691127965
• Product Dimensions: 9.2 x 6.1 x 1 inches
• Shipping Weight: 1.6 pounds (View shipping rates and policies)
• Average Customer Review: 4.2 out of 5 stars  See all reviews (5 customer reviews)
• Amazon Best Sellers Rank: #526,647 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

25 of 26 people found the following review helpful:

5.0 out of 5 stars Seeing beauty through numbers, February 3, 2004

By 

S. Goodman (Los Angeles) - See all my reviews
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This review is from: Mathematics in Nature: Modeling Patterns in the Natural World (Hardcover)

For those of us who admire nature and see it as a product of processes both beautiful and rational, Adam's book is the perfect bedside long-termer for anyone more than casually interested in math or the intricate patterns in nature.

This book is chock full of ponderous examples of mathematical simplicity and complexity in nature, and reading it I was constantly reading only one topic and then putting the book down for days to think about and tinker with the question myself.

Good pictures, solid math (I prefer clean, modelistic equations to numerical approximations anyday), and a charming, conversational writing style make this book highly readable and highly inspiring in the way it makes you reexamine your perception of nature as unintegrated or inelegant. The very repetition of mathematical themes throughout nature - such as the omnipresent Golden Ration - proves otherwise.

For me, this is staying on my "constantly referenced" shelf.

24 of 29 people found the following review helpful:

5.0 out of 5 stars Excellent, January 4, 2004

By 

David (NJ) - See all my reviews

This review is from: Mathematics in Nature: Modeling Patterns in the Natural World (Hardcover)

I disagree strongly with the previous reviewer. The book is well presented, with some lovely photos, and is nicely produced and attractive. The actual content of the book is equally good. Some of the material is familiar, but the author always seems to take a good fresh look at these topics so I still enjoyed them. There was some new material too, which I particularly enjoyed. This is an excellent book, and I hope that the negative review on Amazon will not discourage potential readers from buying a copy.

1 of 1 people found the following review helpful:

5.0 out of 5 stars Discover math in nature, May 14, 2011

By 

Pichierri Fabio (Japan) - See all my reviews
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This review is from: Mathematics in Nature: Modeling Patterns in the Natural World (Paperback)

Gauss, the famous math genius, once said that mathematics is "the Queen of the Sciences". However, as a non-mathematician I find quite boring opening those books that are crammed with abstruse theorems and demonstrations. To me, the special place math occupies among the sciences emerges when we apply it to modeling nature. It is amazing how the n-fold symmetry in flowers, the pattern exhibited by sand dunes, and optical effects such as rainbows and glories can be mathematically described in a very concise manner. These are but a few natural phenomena and objects that are described in Adam's book. Upon turning each page you will discover an equation or mathematical model of the natural world; for instance, why do honey bees built their honeycombs using hexagonal cells? This has to do with maximizing the region of space covered by such biological structures (the 7-hexagon honeycomb) while minimizing the perimeter. Hence, does nature possess a mathematical struture?
Another important aspect of this beautiful book is that it teaches us how to develop mathematical models of complex, natural systems and phenomenas while selecting only the most important variables (the great physicist Enrico Fermi was a master of mathematical estimations based on simple reasoning). Obviously, this type of exercise requires years of practice as well as a good knowlege of physics and its basic laws. Another nice book written by the same author is "A Mathematical Nature Walk".