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$$\varphi(u,v)=\left( \begin{array}{c} u\\ v\\ \log\left(\dfrac{\cos u}{\cos v}\right) \end{array} \right)\qquad \begin{array}{l} u\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right)\\ v\in\left(-\dfrac{\pi}{2},\dfrac{\pi}{2}\right) \end{array} $$

Copies of this patch may be juxtaposed to form a complete minimal surface in $\mathbb{R}^3$