  Angular momentum is traditionally taught as a (pseudo)vector quantity, tied
closely to the cross product. This approach is familiar to experts but
challenging for students, and full of subtleties. Here, we present an
alternative pedagogical approach: angular momentum is described using
bivectors, which can be visualized as "tiles" with area and orientation and
whose components form an antisymmetric matrix. Although bivectors have
historically been studied in specialized contexts like spacetime classification
or geometric algebra, they are no more complicated to understand than cross
products. The bivector language provides a more fundamental definition for
rotational physics, and opens the door to understanding rotations in relativity
and in extra dimensions.
