  We prove that the multiplication maps $\mathbb{s}^n \times \mathbb{s}^n
\rightarrow \mathbb{s}^n$ ($n = 1, 3, 7$) for unit complex, quaternion and
octonion numbers are, up to isometries of domain and range, the unique
Lipschitz constant minimizers in their homotopy classes. Other geometrically
natural maps, such as projections of Hopf fibrations, have already been shown
to be, up to isometries, the unique Lipschitz constant minimizers in their
homotopy classes, and it is suspected that this may hold true for all
Riemannian submersions of compact homogeneous spaces.
