Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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Session 7, Part C:
Translation Symmetry and Frieze Patterns

In This Part: Translation Symmetry | Frieze Patterns | Classifying Frieze Patterns

Note that the point of the following problems is not to memorize the classification system, but rather to be able to make sense of this kind of a system, interpret what the symbols mean, and apply it to new situations.

Mathematicians have developed a two-character notation to denote each possible frieze pattern.

 • The first character is m or 1 according to whether there is reflection over a vertical line or not. • The second character is m if there is a reflection over a horizontal line, g if there is a glide reflection, 2 if there is a rotation, and 1 if none of these exist.

 Problem C4 Classify each of the seven frieze patterns from the previous page according to this system.

Problem C5

The symbol m2 was not part of the classification you used. (It was the only combination of the two symbols missing.)

 a. What would m2 represent in terms of symmetries? b. Create a simple frieze pattern with m2 symmetry. c. What is another name for the symmetry in your pattern?

 Problem C6 Using the codes for frieze patterns, classify each of the following designs. Assume the designs are really infinite.

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