The way this is presented in the blog post is as if this is a really insightful but now under-appreciated gem of mathematics.

But all that description is saying is, when a 2D shape is made by rotation, its area is the multiple of the 1D generator and the 1D path it takes? You don't say! And then volumes! when a 3D volume is made, its a 2D shape going through 1D path ...wow.

Forgive me if I am not impressed. This is not an unknown theorem but a trivial mathematical fact that one learns somewhere around Grade 7 in school. Of course, Pappus deserves credit for discovering in 300 AD, and the paper by the Goodmans is nice to have a general formal proof of. But even that paper concedes that they are simply proving a general proof for completeness.