Sierpinski's Triangle

You will need a ruler or straightedge for these activity.

1. Find the midpoint of each side of the triangle.

2. Connect these 3 points to make four smaller equilateral triangles.

3. Leave the center triangle alone-the process will continue with the three outside triangles. This is called Stage 1.

4. Repeat steps 1-3 with the three outside triangles. This makes a stage 2 triangle.

5. Continue this process with the outside triangles until you run out of dots to use for midpoints. You should be able to do this two more times, getting a stage 4 triangle.

6. You should end up with grouping of 4 triangles (each group looks like a stage 1). In each group, shade the three outside triangles. The triangles you shade should all be facing up.

  

stage	0
number of shaded triangles	1
area of each triangle	1
total area of triangles	1