Necco wafers

When I was in high school, my calculus teacher liked to talk about Necco Wafers. He described them as having a thickness of dh and showed that if you integrate the area of a Necco Wafer over a roll of height h, you get the volume of the roll. We were supposed to imagine the Necco Wafers as infinitessimally thin, and the simile helped us understand that little things add up.

I use the Necco Wafer simile when I teach pottery classes. When you make a cylinder on the wheel, you do several "pulls," thinning the wall with each pull and increasing the height of the cylinder. If you pull the clay up too quickly--before the wheel has an opportunity to spin around a sufficient number of times for each wall slice dh--the cylinder wall doesn't thin evenly, and you create thin sections that coil up the pot and make the wall and rim uneven. If students don't know what I mean by dh, I tell them about my high school calculus teacher and ask them to imagine their cylinder as a stack of Necco Wafers. Usually everyone gets the idea, although sometimes I have to explain to the young'uns what Necco Wafers are.

Last week, one of my students brought me a roll of Necco Wafers that she found in the retro-candy section of a store. Turns out the only thing Necco Wafers are really good for are similes. Tip: avoid eating them, but if you feel you must, DO NOT eat the green or purple ones.