Sierpinski's Carpet Exploration Questions Run several stages of the Sierpinski's Carpet Activity, and answer the following questions: Fill in the table: Iteration 1 2 3 4 Number of Shaded Squares Area of one Shaded Square Total Shaded Area What patterns do you see in the numbers for the number of shaded squares? Can you build a formula for the number of shaded squares at the n-th stage? What patterns do you see in the numbers for the area of one shaded square? Can you build a formula for the area of one shaded square 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? What do you think happens to these numbers as the number of stages approaches infinity? Compare these results to those for the Sierpinski's Triangle. Does the "three-ness" of a triangle and the "four-ness" of a square seem to play a role in these numbers?