  We study the average number of simplices $N'(r)$ at geodesic distance $r$ in
the dynamical triangulation model of euclidean quantum gravity in four
dimensions. We use $N'(r)$ to explore definitions of curvature and of effective
global dimension. An effective curvature $R_V$ goes from negative values for
low $\kappa_2$ (the inverse bare Newton constant) to slightly positive values
around the transition $\kappa_2^c$. Far above the transition $R_V$ is hard to
compute. This $R_V$ depends on the distance scale involved and we therefore
investigate a similar explicitly $r$ dependent `running' curvature $R_{\rm
eff}(r)$. This increases from values of order $R_V$ at intermediate distances
to very high values at short distances. A global dimension $d$ goes from high
values in the region with low $\kappa_2$ to $d=2$ at high $\kappa_2$. At the
transition $d$ is consistent with 4. We present evidence for scaling of $N'(r)$
and introduce a scaling dimension $d_s$ which turns out to be approximately 4
in both weak and strong coupling regions. We discuss possible implications of
the results, the emergence of classical euclidean spacetime and a possible
`triviality' of the theory.
