Tiling the Plane with Triangles (Method 1)
- David Chandler
Two ways to tile the plane with triangles. This is Method 1.
Methods 1 and 2 show two ways to tile the plane with a triangle. The point is to manipulate the original triangle to show that no matter what the shape, the tiling pattern works. In Method 1, note that the green triangles are simply shifted copies of the original and the orange triangles are 180 degree rotations of the original. Each green-orange pair creates a parallelogram. Copies of the parallelogram can be lined up to form a strip with parallel sides. Duplicate strips can be laid side-by-side to cover the plane. In Method 2, the first strip is created as before, then the strip is turned over (reflected) to form the next strip. Again, manipulate the corner points and note that the validity of the pattern does not depend on the shape of the triangle. Can you find other ways?