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Wallpaper Groups (Plane Symmetry Groups)

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Visit this site: http://aleph0.clarku.edu/~djoyce/wallpaper/

Author:David Joyce; Dept. of Mathematics & Computer Science, Clark University
Description: Mathematicians classify plane patterns such as wallpaper patterns by means of symmetry groups - groups of transformations of the plane that leave the pattern invariant. A transformation slides, rotates, and reflects the plane into another position. Such a transformation moves the pattern around, and we say the transformation leaves the pattern invariant if the transformed pattern matches the original pattern exactly. Some Plane symmetry groups include rotations and/or reflections, and some don't. A mathematical analysis of these groups shows that there are exactly 17 different plane symmetry groups. Table, images.

Levels: High School (9-12), College
Languages: English
Resource Types: Graphics
Math Topics: Transformational Geometry, Symmetry/Tessellations

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