Symmetry

Symmetry can be found in islamic design, chineese bronzes, and quilting. Symmetry exists in architecture, music and nature.

There are four symmetry operations: Translation, Rotation, Reflection, and Glide Reflection.


Translation

Translation is simply the placing of mutiple instances of a figure or shape in the same space. Examining the three examples reveals that each shape and occupy the space of the other.

Rotation

In Rotation, there is no translation. As you rotate one of the shapes around the center dot, it would eventually cover the other shape. In each othe pairs the point of rotation is different. The point of rotation for each shape in each example is the same. Imagine this as the 0,0 point.

Reflection

Reflection is different from both translation and rotation in that one shape is the exact mirror image of the other. The examples to the left are as if we were to place a mirror along the line running between them.

Glide Reflection

Glide Reflection is simmilar to reflection where there is a mirror image and that there is translation. The images are reflected but there is an offset to their position.

Using these four operations, we are able to create Symmerty Groups.

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