In 2D there's an alternative. One can rotate purely synthetically, by that I mean with compass and straight edge. This avoids getting into transcendentals. Of

In 2D there's an alternative. One can rotate purely synthetically, by that I mean with compass and straight edge. This avoids getting into transcendentals. Of course I am not suggesting building synthetic graphics engines :) but the synthetic approach is sufficient to show that the operation is linear.