  We discuss the way in which field theory quantities assemble the spatial
geometry of three-dimensional anti-de Sitter space (AdS3). The field theory
ingredients are the entanglement entropies of boundary intervals. A point in
AdS3 corresponds to a collection of boundary intervals, which is selected by a
variational principle we discuss. Coordinates in AdS3 are integration constants
of the resulting equation of motion. We propose a distance function for this
collection of points, which obeys the triangle inequality as a consequence of
the strong subadditivity of entropy. Our construction correctly reproduces the
static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and
entanglement entropies. We discuss how these results extend to quotients of
AdS3 -- the conical defect and the BTZ geometries. In these cases, the set of
entanglement entropies must be supplemented by other field theory quantities,
which can carry the information about lengths of non-minimal geodesics.
