MATH 7030 Extra Assignment 1 : For each of the following problems, (a) solve the problem and (b) reflect on the problem from a mature, "bigger picture" perspective. For example, you could write about how the problem is related to one or more mathematical topics, or you could write about ways to modify the problem and how these modifications might be helpful in teaching mathematical ideas to students. Other ways of reflecting on the problem can also be suitable as long as you use this writing opportunity to deepen your thinking about the math involved. Please type your answers (pictures and mathematical expressions/equations may be added by hand).

1) Refer to problem 3 on page 249 of the Activity Manual. Consider an extension of problem 3: what if you have 4 lines in the plane, 5 lines in the plane, in general n lines in the plane, in each case, what is the largest number of disjoint regions into which that many lines can divide the plane? Try to find a formula in terms of n, the number of lines in the plane. See if you can explain why that formula is true for all n.

2) Problem 15 on page 416 of the textbook. (If you know how to use Geometer's Sketchpad, you could use this program to help you investigate the problem.)

3) Problem 18 on page 418 of the textbook. (If you know how to use Geometer's Sketchpad, you could use this program to help you investigate the problem.)