Sierpinski Triangle
Run several stages of the Sierpinski's Triangle and answer the following questions:
- Write down for each Stage:
- Number of Shaded Triangles
- Area of one Shaded Triangle
- Total Shaded Area
- What patterns do you see in the numbers for the number of shaded triangles? Can you build a formula for the number of shaded triangles at the n-th stage?
- What patterns do you see in the numbers for the area of one shaded triangle? Can you build a formula for the area of one shaded triangle at the n-th stage?
- What patterns do you see in the numbers for the total shaded area? Can you build a formula for the total area at the n-th stage?