Google: Curve Stitching
You say that you like sewing? You like art? I have the answer. This is really cool. My 5th grade teacher had everyone in my class do something like this, and I remember it fondly to this very day. At the time, I didn't realize that it had anything to do with math, so it should satisfy your professor's fun requirement.http://www.montessoriworld.org/Handw...h/stitch1.html
Will give you an idea of what I'm talking about. You could just use pencil and pen, without the embroidery floss, but it is absolutely stunningly gorgeous if you do needle and thread, specifically colored embroidery floss. You don't have to do it with exactly the same equipment that they say. In fifth grade, we didn't do the two straight lines at an angle that you see above. We did a circle.
In fifth grade, what we did is we took a piece of cardstock (thick paper), used a compass to draw a circle about 2 inches radius, and then used a pencil to mark tick marks all the way around the curve of the circle in order to subdivide the circumference into a lot (don't remember, maybe 100) equal arcs. Then we took something sharp (used the dangerous end of the compass), and poked the 100 holes, evenly spaced all the way around the rim of the circle. Then we used the pencil to label each hole, numbered from 1 to 100. Then, we threaded a needle with embroidery floss. I THINK we stitched from hole number 1 to hole number 2, then on the wrong side, we went back to number 1, then we stitched from hole number 1 to hole number 3, etc, until we stitched from hole number 1 to hole number 100. Then I THINK we started at hole number 2, and stitched to each of the other 98 holes in this manner, then started at hole number 3, etc. In the end we ended up with an gorgeous design. I think it was a cardioid (heart shape).
Now, doing this took us days, but we did this while multitasking. (While listening to teacher read a book to us, for example.) So you could do this anytime you would normally knit or have a spare moment, like watching TV or wait in line. It would only take 5 minutes to show the final product in class and explain what you did.
To round out your project, google Mary Everest Boole (1832 - 1916). She was an Englishwoman mathematician who invented this technique in 1904.