Tessellations From Triangles I

In this assignment we will see how to construct an Escher-like drawing starting from a tessellation of the plane with equilateral triangles. The method we will describe is that Escher used to create the picture above.

  1. Take an index card and cut it in half. On one half draw an equilateral triangle. Make the sides around 2 inches.
  2. Draw a pattern on one side of the triangle in the same manner as you did in the assignment Puzzles From Squares.

  3. Mark the midpoint of another side of the triangle. Draw a new pattern on half of this side.

    Cut out the resulting shape.

  4. Trace your shape on the other half of the index card. Rotate the first curved side around the vertex not connected to the second curved side and trace it onto the remaining straight side of the triangle.

  5. Rotate the second curved side around the midpoint of its side and trace the pattern onto the other half of the side of the triangle.

  6. Erase the triangle. You now have a shape that will tessellate the plane.

Take a piece of paper, and trace repeatedly your figure in order to tessellate part of the plane.

If you wish to see a step by step description of how to go from a triangle to the bird shape Escher used to create the picture at the top of the page, click here.