MA-351 Homework 4

Tuesday, Nov 16, 11:30am (at the end of class).

All solutions must be submitted in hardcopy either to me in class or placed in my mailbox. Note my office hours on my schedule.

1. What is the Alabama paradox? Please explain.
2. Consider a fractal called the Sierpinski gasket. You start with an equilateral triangle. Remove the equilateral triangle formed by the midpoints of the three edges. This leaves 3 equilateral triangles of the same size at the corners. Recur the procedure with these triangles.

   

   Compute the remaining area (drawn in black in the above picture) after i iterations of the procedure as a fraction of the initial area.
3. DMM §3.6, Problem 13, page 168. Note that your coloring also needs to include the country "11" surrounding countries 1-10.
4. DMM §3.6, Problem 19, page 169.