  The geometry conjecture, which was posed nearly a quarter of a century ago,
states that the fixed point set of the composition of projectors onto nonempty
closed convex sets in Hilbert space is actually equal to the intersection of
certain translations of the underlying sets.
  In this paper, we provide a complete resolution of the geometry conjecture.
Our proof relies on monotone operator theory. We revisit previously known
results and provide various illustrative examples. Comments on the numerical
computation of the quantities involved are also presented.
