Dimension of Sierpi skis Triangle Problem: Figure 11-6f shows the pre-image and the first iteration of Sierpi skis triangle. The original pre-image triangle is transformed into three self-similar triangles, each of which has sides one-half the length of the sides in the pre-image. a. For iterations 0 through 4, make a table of values showing the iteration number (n), the number of triangles (N), the ratio of the side length of each triangle to the side length of the pre-image (r), and . b. Calculate the dimension D of the Sierpi skis triangle using iterations 1 and 4. Show that you get the same value of D using the values for N and r from either iteration 1 or 4. What word is used to describe the fact that the dimension is not an integer? function of log . Plot the points and the equation on the same screen. Show numerically that the slope of the line equals the dimension of Sierpi skis triangle. d. If the pre-image is an equilateral triangle with sides 16 cm long, calculate the total perimeter of the images in each iteration, 1 through 4. Use the pattern you observe to calculate the total perimeter of the images in the 50th iteration. Explain why the total perimeter of Sierpi skis triangle approaches infinity as the iterations continue.

Week 3 The legislative branch: the congress and the Texas legislature chapter 6 o The concept of representation The first meaningful use of concept of representation was in the American and French revolutions; it was an important issue when the U.S. Constitution was written The...