Reueaux Polygons

There are an infinite number of Reueaux polygons that share a very interesting property.  See the links below to explore a part of geometry not covered in your basic high school geometry course.  I don’t think you will be disappointed.
See the following links for some ideas:
http://commons.wikimedia.org/wiki/File:Rouleaux_triangle_Animation.gif

http://www.china.org.cn/china/photos/2009-05/07/content_17738257.htm

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