What Shape is a Snow Flake?: Magic Numbers in Nature [Hardcover]

Ian Stewart (Author)

Book Description

Publication Date: November 6, 2001

The stripes of a zebra...the complexities of a spider's web...the waves of the ocean...and the shape of a snowflake. These and other natural patterns have been recognized by scientists for centuries. What do they have in common? They can all be accounted for mathematically.
In What Shape is a Snowflake? internationally acclaimed mathematician Ian Stewart shows how life on earth develops not simply from genetic processes, but also from the principles of mathematics. Starting with the simplest symmetrical patterns, each chapter looks at a different kind of patterning system and the key scientific issues that underlie it. Patterns can embrace chaos, fractals, dislocations, even statistical regularities, and are found in many things that at first seem irregular or featurless. A constant wind blowing over a flat expanse of sand, for example will develop ripples, which eventually lead to sand dunes that are often arranged in long parallel rows or other geometric forms. And the smooth surface of a growing organism will develop beautiful patterns, of spots, stripes and colors.
Beautifully illustrated, What Shape is a Snowflake? is an illuminating and engaging vision of how the apparently cold laws of mathematics find organic expression in the beauty of nature.

Editorial Reviews

From the Back Cover

PRAISE FOR STEWART'S FLATTERLAND

The most exciting book I have read this year...truly amazing.
--A.S. Byatt

A book in which the hard science is as gripping as the fiction...one for anyone with an interest in where science comes from.
--The Times

...an accurate, informative portrayal of contemporary mathematics without a single equation in sight.
--Nature

A provocative, ambitious, and enjoyable attempt to ask and answer some of the most interesting Big Questions of modern science.
--New Scientist

About the Author

Ian Stewart is Professor of Mathematics at the University of Warwick, England. He broadcasts regularly on television and radio , and has written articles for Nature, New Scientist, Scientific American and many other periodicals. He is the author or co-author of over 60 books including the best-selling Does God Play Dice?, Life's Other Secret, Fearful Symmetry and Nature's Numbers, which was shortlisted for the 1996 Rhone-Poulenc Science Prize. In 1995 he was awarded the Michael Faraday Medal by the Royal Society for the year's most significant contribution to the public understanding of science.

Product Details

• Hardcover: 224 pages
• Publisher: W. H. Freeman (November 6, 2001)
• Language: English
• ISBN-10: 0716747944
• ISBN-13: 978-0716747949
• Product Dimensions: 9 x 7.8 x 0.9 inches
• Shipping Weight: 1.8 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (4 customer reviews)
• Amazon Best Sellers Rank: #1,886,914 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

30 of 30 people found the following review helpful:

5.0 out of 5 stars A Universe Full of Mathematics, November 6, 2001

By 

R. Hardy "Rob Hardy" (Columbus, Mississippi USA) - See all my reviews
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This review is from: What Shape is a Snow Flake?: Magic Numbers in Nature (Hardcover)

In _What Shape is a Snowflake? Magical Numbers in Nature_ (W. H. Freeman), Ian Stewart has managed to write a wonderfully comprehensive and colorful mathematical tour of the universe from top to bottom without putting a single equation into his book. In fact, there aren't really many numbers. He gets to show what happens when a mathematician looks at the infinite aspects of the world. He writes, "I am a mathematician. I experience these wonders through a mind that has spent a lifetime learning how to detect patterns, how to understand patterns, how to find new patterns... I stand on the shoulders (and lean on the elbows) of giants, on five thousand years of mathematical history that has been groping toward such understanding. I see what all humans see, and in a few respects perhaps I see more. I see clues to rules, laws, regularities."

The snowflake is key to his tour, and there is plenty to learn specifically from it, but since Stewart is keen to draw on patterns all over the place, the range of his book is amazing. In well connected chapters, looking closely at snowflakes takes him to the leafy patterns of frost on the window, the organization of leaves around spirals and Fibonacci numbers, the spiral of the nautilus shell, the stripes and amazing triangle patterns on other sea shells, the patterns of stripes on zebras and fish, the grooves in sand dunes and the lines of dunes themselves, the lines a sidewinder leaves in the sand, the synchrony of a millipede's legs and a horse's at different gaits, the oscillations of the legs of robots, the ups and downs of animal populations, the chaotic variations of weather and of the planets in the solar system, and the shape of the universe. It is clear that Stewart sees connections everywhere, and is only using the snowflake as an excuse to look at the foundations of physical laws, the nature of time, space, and matter, and why patterns in one field give clues to patterns in something entirely different. "I'm going on a journey in search of the snowflake's secret," he says, "and, with it, the deeper secrets of our astonishing universe. And you're coming with me." It's a beguiling invitation from a masterful guide.

Naturally a tour of this type, with all it encompasses, is not going to be long on detail, and anyway, one would have to start getting into equations for that. There is a useful list for further reading at the back of the book, for those who insist on stronger doses of such stuff. Stewart's book, however, is an exhilarating, accessible, vividly illustrated voyage through classic and current mathematical ideas. By the end of it, a reader will understand that the snowflake's shape is determined by phase transition, bifurcation, symmetry-breaking, chaos, fractals, and other complexities. Oh, and the book does eventually reveal what shape a snowflake is.

3 of 3 people found the following review helpful:

5.0 out of 5 stars Required reading for everyone learning math., August 23, 2005

By 

Joseph Biskup (Sunnyvale, ca United States) - See all my reviews
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This review is from: What Shape Is a Snowflake? (Hardcover)

Rob Hardy's review is an excellent summation of this excellent book. "What Shape is a Snowflake?" is a book about the big picture, about the meanings behind and the connections between big ideas. This book is not about details of applying or calculating under these frameworks. As has been stated before, this is an excellently illustrated and formatted book. The pictures and text dance with each other, nicely balancing and building interest in each other.

As Mr. Stewart says, he sees mathematics and beauty as attached ideas and this book is an effort to show the beauty of mathematics. "Most people's mental image of mathematics is page upon page of complicated `sums' - not an especially beautiful sight. I sympathize, believe me. But that's arithmetic, not mathematics (I'm quite passionate about this). Those symbols on the page come no closer to the subject's true beauty than the staves and semiquavers of musical notation come to a Beethoven symphony." As such, this is definitely a book about mathematics and definitely not about arithmetic. There are many references in the book to original publications and theories, and there is a short section at the end for further reading so anyone who wants more detail has a place to start looking. For me this book provided a clear and concise description of the ideas at the foundation of various mathematical principles. Mr. Stewart focuses his book on patterns and their implications. He talks about the different dimensions, scale, and symmetry of patterns, he talks about bifurcation, fractals, chaos, randomness, complexity and phase transitions. He also showed how these ideas and principles thread their way through literally everything in the universe.

This book should be approachable for any child in junior high or high school. Additionally, I think it is an excellent introduction for any adult interested in understanding the world around us.

7 of 9 people found the following review helpful:

5.0 out of 5 stars Mathematics deserves four colour, July 18, 2002

By 

"thirteenthfairy" (, N.S.W. Australia) - See all my reviews

This review is from: What Shape is a Snow Flake?: Magic Numbers in Nature (Hardcover)

I must admit I was looking for more detail from this book than it contains. I was looking for more detail on hexagonal systems.
Instead there is less detail and less formal mathematics. I found it to be rather similar to other publications by Ian Stewart, such as the book Fearful Symetry which contains many of the same ideas.

Despite my personal desires I am glad to see that Ian has finally been granted lots and lots of expensive four colour illustrations with which to explain how interesting mathmatics really is.

I immediately found a use for it in the workshops I run for children. It is the best illustrated book Mr Stewart has yet produced.