I was interested to learn more about mathematical knots, and since I knew that knots are quite prevalent in Celtic artwork, I decided to connect these two. I chose to focus on the trefoil knot. I researched its history and the symbolism behind it. I also expanded on the material in a Mathematica assignment about parameterized curves and knots, finding several ways to create representations of a trefoil knot in Mathematica.
I also explored the concept of the velocity vector, considering the velocity of the parameterized equation of the trefoil hypotrochoid I’d graphed. I visualized this as the speed and magnitude at which a person might draw a 2-dimensional trefoil hypotrochoid with a pencil, and I used that equation to calculate the velocity of the parameterization of the hypotrochoid trefoil.
