  State space geometry is obtained for the one dimensional Blume Emery
Griffiths model and the associated scalar curvature(s) investigated for various
parameter regimes, including the Blume-Capel limit and the Griffiths model
limit. For the one-dimensional case two complementary geometries with their
associated curvatures $R_m$ and $R_q$ are found which are related to the
fluctuations in the two order parameters, namely the magnetic moment and the
quadrupole moment. An excellent agreement is obtained in significant regions of
the parameter space between the two curvatures and the two corresponding
correlation lengths $\xi_1$ and $\xi_2$. The three dimensional scalar curvature
$R_g$ is also found to efficiently encode interactions. The scaling function
for the free energy near critical points and the tricritical point is obtained
by making use of Ruppeiner's conjecture relating the inverse of the singular
free energy to the thermodynamic scalar curvature.
