### Math Questions On Sierpinski's Triangle

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by Cynthia Lanius

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1. Look at the triangle you made [Opens new window] in Step One. What fraction of the triangle did you NOT cut out?

2. What fraction of the triangle in Step Two is NOT cut out?

3. What fraction did you NOT cut out in the Step Three triangle?

4. Do you see a pattern here? Use the pattern to predict the fraction of the triangle you would NOT cut out in the Step Four Triangle. Confirm your prediction and explain.

5. CHALLENGE: Develop a formula so that you could calculate the fraction of the area which is NOT cut out for any step.

6. Write the fractions in the above questions in order from least to greatest. Write a statement about how their order connects to the cutting out process.

7. Find another interesting pattern in the fractal called the Sierpinski Triangle. Write a paragraph descibing this pattern.
lanius@math.rice.edu