Homework #4

Reading: pg. 37-62; 112-134; 153-167

1. a.(Refer to pg. 48 of the text.) Attempt to duplicate Table 1.27 on your calculator. (Include your results.) Comment.

b. (Refer to pg. 49-50 of the text.) Attempt to duplicate Table 1.28 and Figure 1.29. (Include your results.) Comment.

2. Let X be the real plane. Consider the metric space (X,Euclidean). Show that the Koch curve and Koch island are elements of H(X).

3. Find the Hausdorff distance between the Sierpinski gasket with vertices at (0,0), (1,0), and (0,1), and the circle of unit radius centered at (5,5).

4. Find the Hausdorff distance between the triangle with vertices at (0,0), (1,0), and (0,1), and the first (n=1) Sierpinski gasket pre-fractal (formed by removing one open triangle from the solid triangle). Comment.

5. Find the Hausdorff distance between the square with vertices at (0,0), (1,0), (0,1), and (1,1), and the first (n=1) Sierpinski carpet pre-fractal (formed by removing one open square from the solid square). Would your answer change if the original square had vertices at (10,10), (10,11), (11,10), (11,11)?