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Tuesday, March 27, 2007

Reading List: The Penguin Dictionary of Curious and Interesting Geometry

Wells, David. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin Books, 1991. ISBN 0-14-011813-6.
What a treat—two hundred and seventy-five diagram-rich pages covering hundreds of geometrical curiosities ranging from the problem of Apollonius to zonohedra. Items range from classical Euclidean geometry to modern topics such as higher dimensional space, non-Euclidean geometry, and topological transformations; and from classical times until the present—it's amazing how many fundamental properties of objects as simple as triangles were discovered only in the twentieth century!

There are so many wonders here I shall not attempt to list them but simply commend this book to your own exploration and enjoyment. But one example…it's obvious that a non-convex room with black walls cannot be illuminated by a single light placed within it. But what if all the walls are mirrors? It is possible to design a mirrored room such that a light within it will still leave some part dark (p. 263)? The illustration of the Voderberg tile on p. 268 is unfortunate; the width of the lines makes it appear not to be a proper tile, but rather two tiles joined at a point. This page shows a detailed construction which makes it clear that the tile is indeed well formed and rigid.

I will confess, as a number nerd more than a geometry geek, that this book comes in second in my estimation behind the author's Penguin Book of Curious and Interesting Numbers, one single entry of which motivated me to consume three years of computer time in 1987–1990. But there are any number of wonders here, and the individual items are so short you can open the book at random and find something worth reading you can finish in a minute or so. Almost all items are given without proof, but there are citations to publications for many and you'll be able to find most of the rest on MathWorld.

Posted at March 27, 2007 00:37