I choose to model Rapunzel’s tower from the Disney animated movie in Mathematica as my project for Multivariable Calculus. I did this by breaking the tower into sections that resemble the equations of surfaces that were covered in class. These equations included those of cylinders, cones, spheres, disks, and hyperboloids of one sheet. I chose this topic as my project as I knew that I wanted to reproduce a building from a Disney movie in Mathematica and Rapunzel’s tower seemed the most possible to me. For example, I also briefly looked at modeling the castle from Cinderella, but that seemed very overwhelming and too complicated. This was due to that fact that the middle portion of the structure was hidden from view and I would have had to use rectangular prisms, while with Rapunzel’s tower I could visibly see all the surfaces I would need to use and all the of these surfaces would be ones that were covered in class.
I created the actual tower portion by using a level set of a three variable function which formed a hyperboloid of one sheet. The main upper portion of the tower was created by using as cylinder, specifically with cylindrical coordinates. The smaller turret on the side was also created with the same surface or shape. Cones were employed to form the main roof of the tower and also the smaller roof of the turret. I could have created the cones by using level sets, but in the end, I chose to use spherical coordinates. A less notable feature of the tower is the spires that are on top of both of the roofs. The spires were devised by using very skinny cylinders and spheres. I also used the bottom half of a sphere to create that bottom portion of the turret.
