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
R3 to be paths (i.e., simple open curves).
We also show two contrasting results: the three shadows of a path in R3 can all be cycles (although not all convex) and, for every d≥1,
there exists a d-sphere embedded in Rd+2 whose d+2 shadows
have no holes (i.e., they deformation-retract onto a point).Comment: 6 pages, 10 figure