1. Stage 0 is one shaded triangle. You create Stage 1, by using macro M1 and clicking the three vertex points that gives the frame for the triangle.

2. To create Stage 2, by using macro M2 and clicking the three vertex points.

3. To create Stage 3, create a triangle by using macro M0 (macro tool image) and clicking the three vertex points that gives the frame for the triangle. Then use a macro M2 three times, clicking on a vertex and two midpoints.

1. Does the Sierpinski triangle have the property of self-similarity? Explain.
2. How many reduced copies of a Stage 0 triangle would you need to make a Stage 1 triangle? How many copies of Stage 1 are needed to make Stage 2?
3. How many copies of a Stage n triangle make up a Stage n + 1 triangle?
4. Copy and complete this table of the number of triangles in each successive stage of the Sierpinski triangle. Can you find a pattern that helps you to fill in the table?

5. What would happen to the number of triangles if you could infinitely increase the stage number?

Suppose the Stage 0 triangle has area 1. Find the shaded area in Stage 1. Copy and complete this table by looking at the areas of Stages 2 and 3, and finding a pattern.

What would happen to the shaded area if you could infinitely increase the stage number?

Suppose the Stage 0 triangle has perimeter 6. Find the perimeter of the shaded area in Stage 1. Copy and complete this table by looking at the perimeters for the next two stages and finding a pattern.

What would happen to the perimeter if you could infinitely increase the stage number?