Math Questions on the Sierpinski Triangle
- Look at the triangle you made in Step One. What fraction of the triangle did you NOT shade?
- What fraction of the triangle in the Step Two triangle is NOT shaded?
- What fraction did you NOT shade in the Step Three triangle?
- In the Step Four Triangle?
- Do you see a pattern here? Use the pattern to predict the fraction of the triangle you would NOT shade if you made a Step Five Triangle.
- CHALLENGE: Develop a formula so that you could calculate the fraction of the area which is NOT shaded for any step.
- Write the fractions in the above questions in order from least to greatest. What can you conclude about the area of the triangles from this?
- Find another interesting pattern in the fractal called the Sierpinski Triangle. Write a paragraph descibing this pattern.
These pages were developed through GirlTECH '96, a teachertraining and student technology council program sponsored bythe Center for Research onParallel Computation (CRPC), a NationalScience Foundation Science and Technology Center. Copyright June, 1996 Cynthia Lanius