Editing Saddle point (section)

== Saddle surface {{anchor|Surface}} ==
[[Image:HyperbolicParaboloid.svg|thumb|right|[[Hyperbolic paraboloid]]]]
[[Image:Ruled hyperboloid.jpg|thumb|right|A model of an [[elliptic hyperboloid]] of one sheet]]
[[Image:Monkey_saddle_surface.svg|thumb|right|A [[monkey saddle]]|300px]]

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

Classical examples of two-dimensional saddle surfaces in the [[Euclidean space]] are second order surfaces, the [[hyperbolic paraboloid]] <math>z=x^2-y^2</math> (which is often referred to as "''the'' saddle surface" or "the standard saddle surface") and the [[hyperboloid of one sheet]]. The [[Pringles]] potato chip or crisp is an everyday example of a hyperbolic paraboloid shape.

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]].<ref>{{cite book |first = R. Creighton |last=Buck |author-link=Robert Creighton Buck |year=2003 |title = Advanced Calculus |location = Long Grove, IL |publisher=[[Waveland Press]] |edition=3rd |isbn = 1-57766-302-0 |page=160 |url = https://books.google.com/books?id=7cYQAAAAQBAJ&pg=PA160 }}</ref>