  We construct a family of spectral triples for the Sierpinski Gasket $K$. For
suitable values of the parameters, we determine the dimensional spectrum and
recover the Hausdorff measure of $K$ in terms of the residue of the volume
functional $a\to$ tr$(a\,|D|^{-s})$ at its abscissa of convergence $d_D$, which
coincides with the Hausdorff dimension $d_H$ of the fractal. We determine the
associated Connes' distance showing that it is bi-Lipschitz equivalent to the
distance on $K$ induced by the Euclidean metric of the plane, and show that the
pairing of the associated Fredholm module with (odd) $K$-theory is non-trivial.
When the parameters belong to a suitable range, the abscissa of convergence
$\delta_D$ of the energy functional $a\to$
tr$(|D|^{-s/2}|[D,a]|^2\,|D|^{-s/2})$ takes the value
$d_E=\frac{\log(12/5)}{\log 2}$, which we call energy dimension, and the
corresponding residue gives the standard Dirichlet form on $K$.
