Tessellating a Circle

 

Here are some definitions of to tessellate found on the Web:

(1) to cover the plane with a pattern in such a way as to leave no region uncovered.

(2) to decompose a curve or surface into polygonal faces.

(3) to break an image into small, square regions for processing or output.

(4) to tile with tesserae (small pieces used in mosaic work); "tessellate the kitchen floor".

In school mathematics we generally think of tessellating a plane with congruent shapes. But what about tessellating a circle? We could cover it with congruent sectors, which is not very interesting. Below we give a non-trivial way to tessellate a circle with congruent shapes that are not sectors. When cut out, the pieces make a nice puzzle.

It is fun to start by having students use the twelve congruent shapes to try to make a circle.  Click here for a sheet of the pieces that can be used for this task.  We Xerox them on cardstock so they are sturdier.

Here are some tessellated circles:

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Here are some designs you can make with tessellated pieces:

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Click on the Flash animation below to view step-by-step how to tessellate a circle:

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Webpage and Flash Animation Developed by Aous Manshad
Last Modified: April 22, 2007