Surfaces: Explorations with Sliceforms
Many people will be familiar with John Sharp’s Sliceform models, from ATM (or other) conferences, and his book published by Tarquin in 1995 (reviewed in MT156 p.41). Any introduction necessarily focuses on practicalities, but his latest book is much more extensive. Of course it starts with detailed instructions on basic techniques, with recipes for some simple models, and some general advice that is the result of John’s long experience in making Sliceforms, as well as teaching others to make them. If you intend doing either read this advice, even if you read nothing else in the book.
As the title indicates this book is meant to be about surfaces. Sliceforms just happen to be one of the easiest ways of displaying them, and they have a long history. Many museums across the world still have collections of mathematically important surfaces modelled as Sliceforms, although usually not on display. Often they no longer exist. This historical context is given its proper prominence, along with reference to some related artwork, for example Renaissance perspective, and the early work of Naum Gabo.
The bulk of the book explores a wide variety of different types of surface, and different ways of displaying them as Sliceforms: quadrics, surfaces of revolution, ruled surfaces and polyhedra all get a chapter each. As well as many familiar classical mathematical surfaces there are several ideas for generating new ones, usually algebraically, allowing the natural application computer graphical techniques. The last main chapter provides a useful introductory survey of appropriate software packages, with ideas about how they can be used.
Sadly the pressures of the National Curriculum at all levels, and an emphasis on conceptual development (what Gardner would call logical-mathematical intelligence) at the expense of other aspects of human development, mean that there will be little opportunity in most classrooms for time-consuming practical activities, such as making Sliceforms. This is a pity, because even quite young children would be able to make some very pleasing models, using nothing more than thin card, pencil, ruler and scissors, and begin to get ideas and intuitions about space in the process. I remember a sculptor at an ATM conference some years ago commenting on the lack of 3-D awareness in most art students. I doubt if this can have improved in the current educational climate.
For more advanced students, at sixth-form level and beyond, Sliceforms provide accessible introductions to range of difficult mathematics, and teachers might well want to make their own models as visual aids, even if their students do not have the time to make their own. Some, I am sure, would find the time, and learn a lot in the process.
This book could well become a classic. I often come across people who tell me about how they have been affected by Cundy and Rollett’s Mathematical Models. Although it has a much narrower focus, Surfaces: Explorations with Sliceforms has the potential to make the same kind of impact on anyone interested in space and visual thinking.
Paul Gailiunas
Surfaces: Explorations with Sliceforms
John Sharp
QED Books 2004
ISBN 1 85853 201 9
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