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### Introduction:

The hyperbolic paraboloid is often called a saddle surface, because a person could sit on it comfortably. A monkey, however, would run into trouble because he would have nowhere to put his tail! The above surface is called a monkey saddle, because it has a convenient dip in the back to accommodate the monkey's tail. The monkey saddle is in fact a special case of the generalized monkey saddle.

### Properties:

#### Partial Derivatives:

Because z is a function of x and y, we can take partial derivatives:

#### Tangent Planes:

At u = u0, v = v0, the tangent plane to the surface is parameterized by:

#### Infinitesimal Area:

The infinitesimal area of a patch on the surface is given by

#### Gaussian Curvature:

 Gaussian curvature of the surface. Surface colored by Gaussian curvature.
Note: The jagged edge near the minimum in the graph of Gaussian curvature is not a feature of the graph; rather, it is an artifact of the plotting process.

#### Mean Curvature:

 Mean curvature of the surface. Surface colored by Mean curvature.