Summer of Math Exposition

Nice… what I definitely liked about this is the sort of “unexpected” nature of it: When you hear people talk about areas and volumes, it is true that typically we think that area is easy, “just paint it” and don’t think it through. I think I even have posed the question of glazing a donut exactly as just simply computing some specialized integral with arclength/surface elements (washer method or cylindrical shells in single-variable integral calculus courses, or double integrals in the basic multivariable class, and parametrized surface integral in vector calc) but we don’t think twice about the actual practicality.

Anyway what would have been nice is some connection/explanation or link back to the more “normal” calculus that is taught, like, what I think here is, related rates. The reason being that sometimes the lack of that bridge leads people to see “cool visualization” and then when it comes back to their course, they may not be able to really consistently use this imagery. Also (really a nitpick) being able to render math formulas better would be nice. I don’t know what github.io offers in terms of available web tools and the level of integration it can offer, but, say, if you plan on doing exposition more regularly, I would suggest looking into using MathJax. However, gaining momentum on a creator role is important, so don’t focus on interface issues or this comment too seriously; upgrade the tools as you go. I did understand the formulas and what you meant.

is it actually ideal for the glaze to cover the entire doughnut? :) good work

That was quite interesting and well presented in itself but I didn’t feel the why and the what of it. In my opinion there should have been an introduction and conclusion. Also I’m missing the link with derivatives and infinitesimals…

Nice post! I like it, a small topic but explained in detail.

Using τ as your circle constant without any explanation makes this article entirely useless for most readers.