  The projection of a compact oriented submanifold M^{n-1} in R^{n+1} on a
hyperplane P^{n} can fail to bound any region in P. We call this ``projecting
to zero.'' Example: The equatorial S^1 in S^2 projects to zero in any plane
containing the x_3-axis. Using currents to make this precise, we show: A
lipschitz (homology) (n-1)-sphere embedded in a compact, strictly convex
hypersurface cannot project to zero on n+1 linearly independent hyperplanes in
R^{n+1}. We also show, using examples, that all the hypotheses in this
statement are sharp.
