I was drawn to this project because one of my goals for taking multivariable calculus was to gain proficiency with mathematica so I chose an idea that revolved around using the software system. In the final section of our mathematica lab on parametric equations we were instructed to draw hypotrochoids using parametric equations. I enjoyed this part of the lab because I had a spirograph kit as a kid and I thought it was interesting to see the mathematical side of something that I was familiar with in an artistic sense but I hadn’t considered how the motion could be described with equations. So, I decided to expand upon what I learned in that lab for my final project.
With this project I wanted to explore how to translate a spirograph drawn from a kit into a model on mathematica. I did research to determine the “rules” for the parametric equations and I used mathematica to draw dozens of different hypotrochoids to observe the changes in shape that came from changes in the values of the constants R, r, and d. I consider calculus to be fundamentally about change so that was the broadest concept reflected in my project. Beyond that, I of course, used parametric equations extensively during this project which was the specific calculus concept I chose to work on.
