Mathematicians can describe the balance or symmetry of something by using the idea of rigid motion or isometry. A rigid motion is a transformation in space or in a plane in which the original figure and the image of the original figure are congruent. There are four kinds of rigid motions in the plane. These four rigid motions are a) reflection in a line, b) rotation, c) translation and, d) glide reflection.

The simplest isometry, called bilateral symmetry, or mirror-symmetry, is reflection across a line. A figure with bilateral symmetry looks the same on both sides of a line except that the two sides of the figure are mirror images of each other. Figure 1a shows an example of a figure with a vertical line of symmetry. Figure 1b shows an example of a figure with a horizontal line of symmetry. Figure 1c shows an example of a figure with both vertical and horizontal lines of symmetry.

A simple flow chart can be used to easily classify any strip pattern with this 4-character code. This flow chart is presented by Dorothy K. Washburn and Donald W. Crowe, and is more completely described in Symmetries of Culture: Theory and Practice of Plane Pattern Analysis, published by the University of Washington Press.

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Symmetry Patterns of the Wisconsin Woodland Indians

Kim Nishimoto and Bernadette Berken

St. Norbert College

## Saturday, 2 June 2012

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