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Introduction to Symmetries

[Polyhedron] Pattern and symmetry are as ancient as rhythm and language, and appear in virtually every human culture (1). Symmetry surrounds us, both in the natural world and in the world of human artifact. As you walk around in the coming week or two, be aware of the patterns surrounding you-- the arrangement of needles on a pine tree, the spokes of a hubcap, the vortices in the Mississipi River, the slats in a set of blinds...

Mathematicians are relative newcomers to the symmetry game, and certainly have their own set of preoccupations, but offer an extremely useful, beautiful, and even surprising view.

[frieze]

This document, and most of the rest of the materials that make up this text, is meant to be read as a Web page. If you read only paper copies of these pages, you may miss some important links.

(1) See, for example, Dorothy Washburn and Donald Crowe's Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, University of Washington Press, 1988, an extensive and accessible survey of what might be called "geometric anthropology".

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Author: Heidi Burgiel, adapted from notes used in Math 5337, Spring 1995 by Chaim Goodman-Strauss.
Comments to: webmaster@geom.umn.edu
Created: Dec 7 1995 --- Last modified: Tue May 6 19:44:29 1997
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