Example 6.11 Define $u(x,y)=-y\sinh 2x$ and $v=y-{\textstyle\frac{1}{2}}\cosh 2x$ on the half-plane $y\geqslant 0$ in $\mathbin{\mathbb{R}}^{2}$. Then $u,v$ satisfy (32). So equation (31), with the additional condition that $y=\mathop{\rm Im}(z_{1}z_{2})\geqslant 0$, defines an explicit special Lagrangian 3-fold $N$ in $\mathbin{\mathbb{C}}^{3}$. It turns out (surprisingly) that $N$ is nonsingular, and is equivalent to one of the SL 3-folds constructed in [12, Ex. 7.4] by evolving paraboloids in $\mathbin{\mathbb{C}}^{3}$.