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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.
