Gordief posted a link to a youtube which I (a jackass) think could answer the Earth/raindrop question
www.sciforums.com
In one dimension using only high school math (possibly extended slightly) .. THAT would be exciting (for a jackass).
Vector spaces and their duals
It would be hard to overestimate the importance of these guys in applications, so let's have a look. I think an entirely abstract approach is most helpful, so if anythting that folloes is not completely clear, just ask me. We suppose a set V equipped with the operation of addition which is...

