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How can we use transformations to produce patterns?

Have you ever glanced around at the buildings that surround you and noticed beautiful patterns? Some patterns of brick or glass repeat, producing amazing architectural accents. Look at the examples below.

Take a close look at this doorway. There are several beautiful patterns that repeat all around the door. One looks like peacock feathers stacked one on top of the other. Can you see any other patterns? This is a window from a Thai temple. There is an intricate pattern that repeats on the front of the door. Here is another beautiful pattern on a the side of a building. Can you spot the repeating pattern?

These are examples of what are called frieze patterns. These patterns are created by the transformations that you have already studied. Let's begin our discussion of frieze patterns by reviewing those transformations.