Surfaces of Constant Gaussian Curvature

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I'm preparing for an exam and I would like to know what are some examples of surfaces with constant Gaussian curvature such as surfaces with $k=0, \pm1$

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HINT: try to compute the Gaussian curvature for the following objects (embedded) in $\mathbb{R}^3$ using parametrization:

  • Plane, cylinder, cone(away from the vertex)

  • Sphere

  • Tractrix, tractricoid