Friday, 19 August 2011
Solids and Shadows
An Adventure in Multidimensional Space: The Art and Geometry of Polygons, Polyhedra, and Polytopes, Koji Miyazaki
Two, three, four – or rather, two, three, ∞. Polygons are closed shapes in two dimensions (for example, the square), polyhedra closed shapes in three dimensions (the cube), and polytopes closed shapes in four or more (the hypercube). You could spend a lifetime exploring any one of these geometries, but unless you take psychedelic drugs or brain-modification becomes much more advanced, you’ll be able to see only two of them: the geometries of polygons and polyhedra. Polytopes are beyond imagining but you can glimpse the shadows of their wonder and beauty here – literally, because we can represent polytopes by the shadows they cast in 3-space or by the shadows of their shadows in 2-space.
ElsewhereThe slightly odd English there is another example of what I like about this book, because it proves the parochialism of language and the universality of mathematics.
doesn’t have to convey wonder and beauty by shadows: not only is this book full of beautiful shapes, it’s beautifully designed too and the way it alternates black-and-white pages with color actually increases the power of both. It isn’t restricted to pure mathematics either: Miyazaki also looks at the modern and ancient art and architecture inspired by or reflecting the influence of geometry, and at geometry in nature: the dodecahedral pollen of Gypsophilum elegans, for example, and the tetrahedral seeds of the Water Chestnut, which the Japanese spies and assassins called the ninja used as natural caltrops. A regular tetrahedron always lies on a flat surface with a vertex facing directly upward, and when a pursued ninja scattered the sharply pointed tetrahedral seeds of the Water Chestnut, they were regular enough to injure “the soles of feet of his pursuers”. Miyazaki
Posted by Feral Beacon at 01:47