MA-351 Homework 4
Due at 4:59pm in my mailbox in SAS 3151, Tuesday, November 20, 2012

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. Consider a fractal called the Sierpinski gasket. You start with an equilateral triangle of side length 1. 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 total area removed after i iterations of the procedure. Note that after 1 iteration, the removed area is 1/4 * sqrt(3)/4.
2. DMM §3.6, Problem 13, page 168. Note that your coloring also needs to include the country "11" surrounding countries 1-10.
3. DMM §3.6, Problem 19, page 169.
4. Please give a graph whose chromatic number is 2 and whose degree is 10 (cf. Problem 10, page 169).