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k = \frac{\frac{\partial^{2} z}{\partial x^{2}} \frac{\partial^{2} z}{\partial y^{2}} - {(\frac{\partial^{2} z}{\partial x \partial y})}^{2}}{{(1 + {(\frac{\partial z}{\partial x})}^{2} + {(\frac{\partial z}{\partial y})}^{2})}^{2}}