  A "shadow" of a subset $S$ of Euclidean space is an orthogonal projection of
$S$ into one of the coordinate hyperplanes. In this paper we show that it is
not possible for all three shadows of a cycle (i.e., a simple closed curve) in
$\mathbb R^3$ to be paths (i.e., simple open curves).
  We also show two contrasting results: the three shadows of a path in $\mathbb
R^3$ can all be cycles (although not all convex) and, for every $d\geq 1$,
there exists a $d$-sphere embedded in $\mathbb R^{d+2}$ whose $d+2$ shadows
have no holes (i.e., they deformation-retract onto a point).
