  In $\mathbb{R}^3$, a hyperbolic paraboloid is a classical saddle-shaped
quadric surface. Recently, Elser has modeled problems arising in Deep Learning
using rectangular hyperbolic paraboloids in $\mathbb{R}^n$. Motivated by his
work, we provide a rigorous analysis of the associated projection. In some
cases, finding this projection amounts to finding a certain root of a quintic
or cubic polynomial. We also observe when the projection is not a singleton and
point out connections to graphical and set convergence.
