Sometimes this is the math way ;) More seriously, Lie group theory puts the light exactly on the shared structure between quaternions and rotations (both are s

Sometimes this is the math way ;) More seriously, Lie group theory puts the light exactly on the shared structure between quaternions and rotations (both are smooth groups related in some way) and ignore the secondary details, so you spend time understanding what matters. It may be more abstract, but you get more from your efforts in my opinion.