  The variance of the position operator is associated with how wide or narrow a
wave-packet is, the momentum variance is similarly correlated with the size of
a wave-packet in momentum space, and the angular-momentum variance quantifies
to what extent a wave-packet is non-spherically symmetric. We examine an
interacting three-dimensional trapped Bose-Einstein condensate at the limit of
an infinite number of particles, and investigate its position, momentum, and
angular-momentum anisotropies. Computing the variances of the three Cartesian
components of the position, momentum, and angular-momentum operators we present
simple scenarios where the anisotropy of a Bose-Einstein condensate is
different at the many-body and mean-field levels of theory, despite having the
same many-body and mean-field densities per particle. This suggests a way to
classify correlations via the morphology of 100\% condensed bosons in a
three-dimensional trap at the limit of an infinite number of particles.
Implications are briefly discussed.
