I encourage the participants to develop a taxonomy of symmetry so that we can compare the blocks according to the symmetries present/absent. Using the example in Figure 2, I ask, “What would we call this if we were to classify it according to its symmetries?” Usually, some- one will say something like, “Diagonal, Diagonal, and 180.” I argue that it might be easier to attach an algebraic representation such as D-D-180. Tis leads to a classifica- tion scheme that might look something like:


• 90: 90-degree rotational symmetry • 180: 180-degree rotational symmetry • 270: 270-degree rotational symmetry • H: reflective symmetry in a horizontal line; inter- changeable with V


• V: reflective symmetry in a vertical line; interchange- able with H


• D: reflective symmetry in a diagonal line; two possible


Using this scheme, I ask participants to identify the dif- ferent “types” of quilts they had constructed, an activity that leads naturally to the question, "Are there more?"


Are There More? At this point, I hand out a set of 28 quilt blocks for fur- ther investigation. Organized into small groups, partici- pants are encouraged to use the classification scheme to “type” each quilt according to the symmetries present. Tese 28 quilt blocks are displayed in Figure 4. Te reader is encouraged to attempt this classification task before reading on. A tool that may be useful in completing the activity


is the Mira, a small plastic device that helps with the concept of reflective symmetry. Te sorting activity takes time and invariably leads to conflict. Encourage groups to settle conflicts by presenting their reasoning or by critiquing the reasoning of others. Groups should come to the consensus that there are seven different symmetry classes, each containing four distinct quilt blocks:


• D • H-V-D-D-90-180-270 (also called “ALL”) • D-D-180 • H • H-V-180 • 180 • 90-180-270


In Figure 4, members of these classes are found in the seven rows. Tis sorting activity usually adds several new Figure 4. Twenty-eight quilts to sort by symmetry


⊆ 06 MTCircular · Summer/Autumn 2016 · American Institute of Mathematics


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