  We represent the free energy functional by a diagrammatic series with
tensorial coefficients indexed by powers of length scale. For hard cores, we
obtain Percus' exact functional in one dimension and the Kierlik-Rosinberg form
of fundamental measures theory in three dimensions. In five dimensions, the
functional describes bulk fluids better than Percus-Yevick theory does. At
planar walls density profiles oscillate with smaller periods than in lower
dimensions. Our findings open up avenues for treating both more general
high-dimensional systems, as well as three-dimensional mixtures via dimensional
reduction.
