In the fall of 1997, during my first year of teaching at Kenyon, I wrote a MAPLE lab for my Multivariable Calculus class that served as an introduction to parametric equations. My idea at the time was that students would gain a deeper understanding of parameterizations if they were encouraged to “get their hands dirty” by experimenting with the equations. I encouraged them to make small changes to various parameterizations -- starting out with circles and ellipses, and moving up to lines and functions -- so they could see for themselves what the effects were.
At the end of the project, I threw in a final exercise asking students “to have some fun” by creating a picture. I included a simple smiley face as an example and told the students that I would offer a gourmet pizza dinner (made by my husband) for the best picture.
At the time, this final exercise was just an afterthought -- I hadn’t anticipated the level of excitement that would emerge. As it turned out, the students saw the initial exercises about circles and lines as merely “warm-up” for the final exercise. The final exercise became the project for them, as they spent amazing amounts of time on the pictures -- sometimes creating hundreds of curves. Indeed, one of my colleagues complained to me about our joint students who had decided not to do their homework in his class in order to allow more time for my project!
Since that first semester at Kenyon, the parametric plots project has continued to evolve. The current version, Parametric Plots: A Creative Outlet , was co-authored with my colleague Keith Howard. Keith wrote MAPLETs for the project, making it more user-friendly and more appropriate for use on the Internet. The current version also includes a larger repertoire of curves.
After 14 consecutive semesters of using the project at Kenyon, I am happy to report that the level of student excitement remains high. Students continually try to outdo the work of previous students, and my husband is now quite famous across campus for his gourmet pizza pies. The winning entry for the spring semester of 2004 is shown in Figure 1.
Figure 1. A parametric rendition of Bill Watterson's Calvin and Hobbes comic strip. The cartoon was recreated by Kenyon student Christopher White in the Spring of 2004 using 234 lines of code. Skeptical? Check out the MAPLE file.