Classification of Patterns -

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:

• ROTATION: To rotate is to turn about a point. When you make a left-hand turn at a corner, we say you are rotating 90 degrees about the corner.
  

  
  

• REFLECTION: When you look in a mirror, your image is reflected back at you. If you imagine that your image actually exists on the other side of the mirror, you get some idea of the mathematical definition of reflection or mirror image. We can reflect figures by folding along the mirror line as you see below.
  

  
  

• TRANSLATION: Translate means to slide. A translation moves a figure a given distance in a given direction. You can think of a translation as sliding an image across a piece of paper.
  

  
  

• GLIDE REFLECTION: This transformation combines translations and reflections. A glide reflection occurs when you slide an image in one direction and then reflect it over a line.
  

  
  

• ROTATIONAL SYMMETRY: We say a pattern has rotational symmetry when we can turn it by some degree about a point and the pattern looks exactly the same.
• REFLECTIVE SYMMETRY: In the same way, we say a pattern has reflective symmetry when we can fold it across a mirror line so that one half lies on top of the other.
• TRANSLATION SYMMETRY: Translation symmetry occurs only in patterns that cover a plane. If you can move a copy of a pattern a specific distance in a specific direction so that it lies exactly on top of the original pattern, then the pattern is said to have translational symmetry.
• GLIDE REFLECTIVE SYMMETRY: Glide Reflective symmetry, like translational symmetry, only occurs in patterns that cover a plane. When you move a pattern a given distance in a given direction and then reflect it over a mirror line so that it lies exactly on top of the original pattern, that pattern has glide reflective symmetry.

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.

• Pattern 1
  
• Pattern 2
  
• Pattern 3
  
• Pattern 4
  
• Pattern 5
  
• Pattern 6
  
• Pattern 7
  
• Pattern 8
  
• Pattern 9
  
• Pattern 10
  
• Pattern 11
  
• Pattern 12
  
• Pattern 13
  
• Pattern 14
• Pattern 15
• Pattern 16
• Pattern 17

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