Tiling the Plane.

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Do all Plane Figures Tile a Plane?

With the slider at its default position, n = 3, move the blue triangle by holding the white circle to tesselate the plane.
Use the red circle to rotate the figure.
With the slider now at 4, move the figure to tesselate the plane.
Repeat the steps with n taking different values up to 10 .
Complete the following table; (Yes if it tiles the plane, and No if it doesn’t.)

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Which Regular Plane Figures Tile a Plane?

Move the “vertices” slider in the applet below to start at 3.
Use the red circle to rotate the figure to form a tessellation. Any direction you choose is ok.
Repeat the steps with different number of sides up to 15. (Note: For tiling to occur, there must be no gaps or overlaps.)

From the activity above, the triangle, square, and hexagon are the only polygons that will tile the plane.

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Can Different Shapes be Jointly Used to Tile the Plane ?

Play around with the polygons and observe which ones could be used jointly to create a nice pattern for your floor or rug.

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