There are so many types of hats that come in all different shapes and sizes. Just glancing at them, you’ll notice that they take on 3D shapes that can be formed with multivariable calculus equations. As hat wearers ourselves, we were fascinated by the variety in form and fit. We decided to create a variety of hats that covered a range of shapes. Beanies are similar to upward bowls and half spheres, a top hat includes a cylinder and an annulus, a snapback is a half sphere and a partial disk- the list goes on and on.
After putting on our thinking caps, we made six different hats: a beanie, a top hat, a Santa hat, a sun hat, a snapback, and a bucket hat using the computer program Mathematica. We primarily used the ParametricPlot3D command, exploring how different equations resulted in different shapes and sizes. We also used the Show command to graph the different parts of each hat into one plot. We tip our hats to the wonderful world of multivariable calculus!
