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Next semester, I am going to teach a small section of advanced high school students a class of Multivariable Calculus (it's about 3-4 students that have completed AP Calculus BC). Multivariable Calculus is usually a 1 semester college course, but I have the advantage of being able to teach the material over the entire school yea, which is two semesters. So I am looking for project ideas to help fill some of the time but also give the students some practical applications of calculus. I also have the great advantage that the school I work at has access to 3D printers.

I feel lucky to be in the position to work with a small and dedicated group of students and have plenty of time to get through the material and great resources to take advantage of, but on the other hand, I am relatively inexperienced with Multivariable Calculus (I know the content, but I don't know any good ideas for a projects) and I have no experience even using a 3D printer. So, what are some good project ideas for Multivariable Calculus that hopefully don't require too much of a learning curve if using the 3D printer?

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    $\begingroup$ You might be able to mimic what was done here, though I haven't read through their list of publications to see if they provide any of the learning tasks. $\endgroup$
    – Nick C
    Jun 1, 2022 at 19:29

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I have 3d printing as an extra-credit option for some projects, which are usually framed as a (fictional) business person looking for math equations to use specifically so they can then 3d print their products. My favorite is focused on Spirograph-style earrings!

The project is basically something like “I found these equations online, can you explain to me how they work and make a computer widget so I can play with them to make pretty designs?” The students turn in a report and a Mathematica file, and for extra credit they can also made prototypes using a 3d printer.

I’d be willing to share my materials if it would be helpful.

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