Differential Form of Arc Length on Curved Surface

Theorem
The first fundamental form for the element of arc length on a curved surface is given by:
 * $\mathrm d s^2 = E \, \mathrm d u^2 + 2 F \, \mathrm d u \, \mathrm d v + G \, \mathrm d v^2$

where $E$, $F$ and $G$ are the coefficients of the first fundamental form.