Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. A saddle surface is a smooth surface containing one or more saddle points. The term derives from the peculiar shape of historical horse saddles, which curve both up and down. Classical examples of two-dimensional saddle surfaces in the Euclidean space are second order surfaces, the hyperbolic paraboloid z = x2 – y2 (which is often referred to as the saddle surface or "the standard saddle surface") and hyperboloid of one sheet. Saddle surfaces have negative Gaussian curvature which distinguish them from convex/elliptical surfaces which have positive Gaussian curvature.

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