What Shape is a Snowflake?

Rating:
Summary: Mathematics deserves four colour
Review: 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.

Rating:
Summary: A Universe Full of Mathematics
Review: 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.

Rating:
Summary: A Universe Full of Mathematics
Review: 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.