The basic idea:

Build an interesting surface and measure something about it.
 

A little more detail:

Using materials of your choice, actually construct a surface (probably the graph of some function
of two variables, but I'm very willing to consider other options). You get to pick the surface, the
materials, everything. Once you've got it built, measure something about it that has relevance to
what we've done -- a directional derivative at some point, the direction of a gradient, volume,
surface area, or whatever else interests you.

Ideally, you should measure two different ways: First, physically measuring the actual object, and
second, using math. Compare the answers you get these two different ways.
 

What actually to turn in:

• Your surface, if it's transportable, otherwise a photograph or other likeness of it
• A brief writeup describing:
• How you made it
• How you made it conform as closely as possible to the formula (or whatever it was you were trying to represent)
• How your measurement was carried out and how accurate you think it was

Grading:

• Up to 10 points for the ambitiousness of the project
• Up to 10 points for how well it was carried out (including accuracy)
• Up to 10 points for how well it is presented