Center of mass for two particle's equal and opposite 4 momenta or for the separation of a system's internal motion from its external motion.
The not allowed hydrogen atom.
Does hydrogen in its ground state occur naturally, ideally, experimentally? Is it stable? Is this like asking, "Does a center of mass occur naturally, ideally, experimentally? Is it stable?"
Judge Judgement
I understand the comparison with Artin, but I'm not able to judge
your judgement. Anyway, who is the most famous; Hamilton or
Hestenes? Fame is fickle so let's get some criteria down to inform
judgement, all the while expecting these to run like sand between
our fingers.
viewing is seeing
Your view is more precise than mine, I'm more coarse. Working on a ferris wheel in the rain puts me real \textit{e} off. An old carny needs some help with this question. A convex polygon in a plane is specified by the ordered set of points \{x_{0},x_{1},\,.\,.\,.\,,x_{n}\}...
It also suggests to me a feeling, a way to invent or learn. I first approached this associative "geometric product" reading, http://www.mrao.cam.ac.uk/%7Eclifford/publications/abstracts/imag_numbs.html". Following this paper; "to see what is going on" and to make it feel satisfying and natural...