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)?

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