Claim: The monkey saddle, belonging to the class of saddle surfaces, has an isolated umbilical point with zero Gaussian curvature or the product of the principal curvatures, κ1 and κ2 at the origin.
Evidence: It belongs to the class of saddle surfaces, and its name derives from the observation that a saddle for a monkey would require two depressions for the legs and one for the tail. The monkey saddle has an isolated umbilical point with zero Gaussian curvature at the origin, while the curvature is strictly negative at all other points. In differential geometry, the Gaussian curvature or Gauss curvature Κ of a surface at a point is the product of the principal curvatures, κ1 and κ2, at the given point: