  Consider a random geometric graph over a random point process in
$\mathbb{R}^d$. Two points are connected by an edge if and only if their
distance is bounded by a prescribed distance parameter. We show that projecting
the graph onto a two dimensional plane is expected to yield a constant-factor
crossing number (and rectilinear crossing number) approximation. We also show
that the crossing number is positively correlated to the stress of the graph's
projection.
