On Friday, a student walked into my office and asked “How do you wrap a sine curve around a circle?” It took a few minutes for the student to explain just exactly what he meant, and then a few minutes more explaining the superposition principle for parametric curves. In a few minutes, we’d hazarded a guess at a parametrization, which we verified with Maple.
I’m only bringing this up because I was a bit bored after grading Calc II quizzes, so I went and modified the Maple worksheet to wrap a pair of sine curves around a circle, together with a rotation about the origin in both the Euclidean and HSV color planes. Enjoy.
