Classification of Patterns -

Student Lesson

If you have not done so already, sort these wallpaper patterns by any method you like. You might classify them by color, size, shape, use, etc. BE CREATIVE!

Classification systems are used in many different areas. When you look on store shelves, you have a classification system that sorts products. In a filing cabinet you have a classification system that sorts files, and in a library you have a classification system that sorts books based on their genre. What other examples of classification have you seen?

You have already sorted patterns according to your own classification system. In this lesson you will learn symmetries of repeated patterns. In addition you will learn about a system for sorting these patterns according to their symmetries as mathematicians do. Before we start, here are some terms you need to know.

TRANSFORMATIONS - The terms you need to know:

SYMMETRY: Thus to summarize, when you take a copy of an image or a shape in a repeated pattern and move it in some way so that it lies exactly on top of the original, that figure is said to have symmetry. Symmetry means "the same" or "identical." The terms we defined above are examples of different types of symmetry on a flat surface (planar symmetry).

The patterns you have already classified have the above types of symmetry. We call patterns like these which can be repeated to cover the entire plane, "wallpaper patterns." Why do you think mathematicians use this term?

Now that you have looked at examples of the four different types of symmetry, return to your collection of patterns and classify them according to their types of symmetry. Create a chart or a Venn Diagram of your own that will help you in classifying your patterns. Do any of your patterns have more than one type of symmetry? Can you create a table of your patterns' symmetries? How can you fit this information into a Venn Diagram? For hints on how to determine what type of symmetry a pattern has, see our hint book

Web sites:

Listed below is a collection of WWW sites which will link you to other patterns. Your task is to choose 12 patterns by linking to their Web sites and classify them in the same type of chart or Venn Diagram as you did the earlier patterns.

Caution!! Because you are linking to other sites, you will need to use the BACK button (at the top of this page) to return to this document. Classroom time has not been allotted to browse entire documents. Please restrict yourself to the pattern you have been linked to and then return to this document by using the BACK button.

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