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Wallpaper Objectives

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Wallpaper Objectives

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    1. Wallpaper Objectives Be able to classify a wallpaper pattern using centers of rotation and lines of reflection and glide reflection Be able to construct wallpaper patterns given a classification Be able to analyze cultural tilings using the classification

    2. Locating centers and lines Tips for finding centers of rotation You should have a center of rotation at any point where lines of reflection meet. Look halfway between pairs of lines or pairs of rotation centers.

    3. Locating centers and lines Tips for finding lines Check lines connecting rotation centers and lines between lines Look in all n directions around an n-gon

    4. Classification Wallpaper patterns are classified using a four character string (just like frieze patterns). Rather than memorizing the rules for each character, we use the flow chart on page 163 and the table on page 162.

    5. Examples

    6. Double-checking your work Once you have identified a classification, you can check it at http://www.xahlee.org/Wallpaper_dir/c5_17WallpaperGroups.html

    7. Generating a wallpaper pattern The image on the right shows how to generate a cmm pattern (the motif is placed in the shaded area; the double lines stand for reflection).

    8. Generating a wallpaper pattern Repeat the process with this generator for p4g.

    9. Exam on Friday Covers dimensions of fractals using replacement rules and measurement building fractals using area analysis of artwork using fractals regular and semiregular tilings creating irregular tilings frieze patterns

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