Saddle surface

Saddle surface

A saddle surface is a smooth surface containing one or more saddle points.

The term derives of 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.

A classical third-order saddle surface is the monkey saddle.


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  • Saddle bar — Saddle Sad dle, n. [OE. sadel, AS. sadol; akin to D. zadel, G. sattel, OHG. satal, satul, Icel. s[ o][eth]ull, Dan. & Sw. sadel; cf. Russ. siedlo; all perh. ultimately from the root of E. sit.] 1. A seat for a rider, usually made of leather,… …   The Collaborative International Dictionary of English

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  • Saddle girth — Saddle Sad dle, n. [OE. sadel, AS. sadol; akin to D. zadel, G. sattel, OHG. satal, satul, Icel. s[ o][eth]ull, Dan. & Sw. sadel; cf. Russ. siedlo; all perh. ultimately from the root of E. sit.] 1. A seat for a rider, usually made of leather,… …   The Collaborative International Dictionary of English

  • saddle horse — Saddle Sad dle, n. [OE. sadel, AS. sadol; akin to D. zadel, G. sattel, OHG. satal, satul, Icel. s[ o][eth]ull, Dan. & Sw. sadel; cf. Russ. siedlo; all perh. ultimately from the root of E. sit.] 1. A seat for a rider, usually made of leather,… …   The Collaborative International Dictionary of English

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