The rotation groups $SO(n)$ are generated by the rotations in every pair of planes in ${\mathbb R}^n$. The unitary groups $SU(n)\subset SO(2n)$ can be interpreted as correlated rotations of pairs of planes in ${\mathbb R}^{2n}$. We describe a graphical representation of these rotations at the Lie algebra level, and discuss the extent to which it generalizes to groups over the quaternions or octonions. Our results are not new, but their presentation is somewhat nontraditional.