rambling about polar quaternions (and some clifford algebra)

I’ve wanted to make my own “how to actually understand and work with quaternions” thing for a bit now. it’d try to explain things in a way that doesn’t require any visualization, but also doesn’t try going too much into the formalities that tend to come with non-visualizations of quaternions. this isn’t that explanation, but rather some miscellaneous rambles in my journey to re-derive all of…