Function for finding the length of a curve connecting two points in a two-dimensional sphere I am trying to study differential geometry.
I am confused with regards to the following function for finding the length of
a curve $\gamma$ connecting two points $p, q ∈ S^2$
$$L(γ) = \int^1_0|\dot{γ}(t)| dt,γ(0) = p, γ(1) = q$$
Where $S^2$ is a 2-dimensional sphere sitting in the three dimensional Euclidean space $R^3$
I am unfamiliar with the "dot above function" notation (dot above $\gamma$), what does it mean? And from where is this function derived or what is it called?

As @math.pr said the dot shows drive function. But about formula, if you take an eleman on curve and assume to be straight, so its length can be computed by euclidean meter as below:
$$dL=\sqrt{dx^2+dy^2+dz^2} \Longrightarrow \int dL = \int \frac{\sqrt{dx^2+dy^2+dz^2}}{dt} \ dt \Longrightarrow$$
$$L = \int \sqrt{\frac{dx^2+dy^2+dz^2}{dt^2}} \ dt = \int \sqrt{\frac{dx^2}{dt^2}+\frac{dy^2}{dt^2}+\frac{dz^2}{dt^2}} \ dt = \int \sqrt{(\frac{dx}{dt})^2+(\frac{dy}{dt})^2+(\frac{dz}{dt})^2} \ dt$$
$$= \int \left|\left(\frac{dx}{dt},\frac{dy}{dt},\frac{dz}{dt}\right)\right| dt = \int \left| \overset{.}{\gamma}(t) \right| dt \Longrightarrow L = \int \left| \overset{.}{\gamma}(t) \right| dt$$
And the limits show the start and end points.
