Creating Symmetry by Farris Frank A

Author:Farris, Frank A.
Language: eng
Format: epub, pdf
Publisher: Princeton University Press
Published: 2015-03-14T16:00:00+00:00

Figure 16.2. A function invariant under cm, turned sideways, with colors from a late summer day in the University of Minnesota arboretum.

By now, we expect to see repetitions of the single mirror symmetry our recipe forces on the image, so this is no surprise. Can you see a different type of symmetry in this diagram—one that we have not mentioned in this chapter? Draw a vertical line halfway between mirror axes—two nearest ones, so that they are not related by horizontal translation. When we flip about that line and slide half a unit up, the pattern falls into coincidence with itself. This pattern has glide symmetry.

As usual, we ask: Is this a necessary feature of cm patterns, or did my choices introduce it as an accidental symmetry? Even though the image has vertical mirrors, we persist with our horizontal notation. A computation left as an exercise shows that

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