We chose to model a chess set both in Mathematica and via 3D printing. We were drawn to chess specifically because the pieces seemed to be of shapes that would be interesting to graph. It was also a good project in that the work was easy to split up equally, with each of us taking on the design of two pieces. The process of modeling these shapes in Mathematica was relatively straightforward. Each shape was either a function of two variables, a contour plot of a function of three variables, or a parametric plot. We then had Mathematica “show” all of the functions together to have a complete piece visible all at once.
We feel that the principal multivariable calculus topic that is being highlighted in our project is the graphing of functions in 3 space. This general idea was expressed in several forms, as I have described already. By graphing with parameterized functions, functions of two variables, and contour plots of functions of three variables we were able to explore and dive in to many areas of multivariable calculus.
