Translations:The eikonal equation - book/3/en

Because $d\mathbf {r} /ds=\mathbf {u}$, it follows that equation 13 becomes ${dt/ds}{\ =}\ \mathrm {grad} \ {t}\cdot \mathbf {u}$ or $n{\ =}\mathrm {grad} {\textit {t}}\cdot \mathbf {u.}$ The Fermat requirement that the unit tangent u have the same direction as the vector grad $t\left(x,y\right)$ means that these two vectors are related by the scalar $n\left(x,y\right)$. Thus, the relationship can be written as