Apparently, Hamilton defined quaternions as the solution to almost this exact problem. Quaternions are effectively elliptical vectors. That's a lot nicer than d

Apparently, Hamilton defined quaternions as the solution to almost this exact problem. Quaternions are effectively elliptical vectors. That's a lot nicer than defining them in terms of generators and relations. [1] - https://en.wikipedia.org/wiki/Versor https://en.wikipedia.org/wiki/Versor