Lets have a regular surface $S$ and $p \in S$. I have to prove that:
$K(p) = \lim_{r \to 0} \frac{12}{\pi} \frac{\pi r^2 - A}{r^4}$
where $A$ is the area of the geodesic disc with center in $p$ and radius $r$. Any clue? I've tried Fermi coordinates but I don't understand them.