Changes

It's easy enough to do this: each border vector will have some small ''x'' component, some small ''y'' component, and some small ''z'' component.  By choosing our surface elements <math>S_k \ </math> to be in line with the curves of constant ''u'' and curves of constant ''v'' on the surface, these small components will then be

It's easy enough to do this: each border vector will have some small ''x'' component, some small ''y'' component, and some small ''z'' component.  By choosing our surface elements <math>S_k \ </math> to be in line with the curves of constant ''u'' and curves of constant ''v'' on the surface, these small components will then be

<math>\vec{u}=\begin{pmatrix}\frac{dx}{du}\\\frac{dy}{du}\\\frac{dz}{du}\end{pmatrix}</math>, <math>\vec{v}=\begin{pmatrix}\frac{dx}{dv}\\\frac{dy}{dv}\\\frac{dz}{dv}\end{pmatrix}</math>

<math>\vec{u}=\begin{pmatrix}\partial_u x\\\partial_u y\\\partial_u z\end{pmatrix}</math>, <math>\vec{v}=\begin{pmatrix}\partial_v x\\\partial_v y\\\partial_v z\end{pmatrix}</math>

{{MVCalc}}

{{MVCalc}}