Here are some sites that explain what cycloids and spirographs are, as well as different types of spirographs called hypotrochoids and epritochoids.

http://en.wikipedia.org/wiki/Spirograph

http://en.wikipedia.org/wiki/Cycloid

http://en.wikipedia.org/wiki/Hypotrochoid

http://en.wikipedia.org/wiki/Epitrochoid

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