Ok so I have known about imaginary numbers for quite some time now. I also understand why we want them to exist (to have a solution for $x^2=-1$). I also remember reading that the complex numbers are ...
Is there a specific name and/or representation for the group of distinguishable orientations of a given shape?
Consider a 3-dimensional body $B$. The space of all orientations of $B$ in 3-space is the rotation group $SO(3)$, and is often represented in computer science applications as the quaternions with $q$ ...