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To celebrate Halloween, last year we discussed what you can do with 1,818 pounds of pumpkin. It was a popular blog post, and it put an awful lot of smiles on peoples’ faces. An entire lamina (filled shape) of smiles, in fact.
We at Wolfram|Alpha were recently inspired to make a lamina out of everything possible. That said, Halloween is—to me, at least—about making jack-o’-lanterns. Before we can delve into jack-o’-lantern laminae, first you need to find a quality pumpkin. One that, if it were a curved parametric surface made by extending the epicycloid into 3D via spherical coordinates, would look like this:
A typical jack-o’-lantern usually has triangles for eyes and a nose and angled teeth (because angles are scary). For the jack-o’-lantern lamina, we give closed forms for the area, centroid, and area moment of inertia tensor, which is sure to earn us some street cred.
Of course, some people prefer to avoid that kind of imagery altogether, opting instead for something a bit sillier. One of Wolfram’s most talented mathematicians/artists put together a pirate jack-o’-lantern lamina that we simply had to share with you.
If you want to check out how to make a jack-o’-lantern of your own using other Wolfram technology, I strongly recommend Yu-Sung Chang’s blog post “Industrial Pumpkin Carving with Mathematica.” It’s just terrific, and you should read it.
We here at Wolfram|Alpha hope you have a happy Halloween! And stay tuned to our blog, because we have a whole series of new shapes, curves, and laminae to show off coming soon.