One of our faculty members teaching Calc 2 was absent for some days, so I volunteered to step up and cover 2 of his classes, the topic: areas and lengths in polar coordinates.
In all of my many decades of using calculus in physics and math, I never really needed these tools, so I have often said less priority should be given to them, BUT math is also about fun, so I wanted to not only present some really simple examples to show how one calculates with these ideas, but also something that could catch the imagination with a computer algebra system (CAS). The spaghetti curves (it seemed a natural nickname for a pasta lover like bob) seemed to hold promise, but little did I know that pulling on them would open up interesting mathematical questions. The result shows how a CAS can really spark someone with a love of mathematics to inspire them to discover on their own, armed with this powerful tool.
Alas, no one was inspired. Oh well. I enjoyed it.