Concept Byte: Frieze Patterns

Use With Lesson 9-6

A frieze pattern is a design that repeats itself along a straight line. You can see frieze patterns in design trim. They often appear along the edges of buildings or as wallpaper borders of rooms. Every frieze pattern can be mapped onto itself by a translation.

Some frieze patterns can be mapped onto themselves by reflections.

Some frieze patterns have repeated rotational symmetry.

Some frieze patterns show glide reflections.

Exercises

For Exercises 1−4, refer to the frieze patterns above. You may find tracing paper helpful.

1. For each frieze pattern, find a portion (as small as possible) that you could translate repeatedly to form the entire pattern.
2. Which patterns show reflectional symmetry? Find their reflection lines.
3. Which patterns show rotational symmetry? Find their centers of rotation.
4. Which patterns show glide reflections? Find a glide translation and reflection line.

For each frieze pattern below, describe all transformations that map the pattern onto itself.

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