In groups of two (or at most three), come up with a "good" surface z = f(x,y). A good surface should have at least one valley and at least one hill and not be unbounded. Experiment with different functions (perhaps trigs or the like) and graphing the surface using software to make certain you have one that looks good. Once you have decided on a surface to use, check with the instructor to be certain it is not very close to a surface already chosen by another group.

The goal of this project is to construct a decent model of the surface using level curves. To do this:

Using software, :

• draw a number of level curves. You will need to determine how to scale these and to choose appropriate step sizes
• paste onto some type of thicker material and cut out appropriate parts so that the surface looks right when assembled
• arrange your level curves into a 3D structure that models your original function z = f(x,y). Do NOT permanently fasten the parts together.

Save the parts of your project to disk or usb drive just in case something needs to be redone. Successful completion of this project will count as two homework grades.

Deadline: February 6, 2012