Saddle point

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In mathematics, a saddle point is a point in the domain of a function where the slopes (derivatives) of orthogonal function components defining the surface become zero (a stationary point) but are not a local extremum on both axes. The saddle point will always occur at a relative minimum along one axial direction (between peaks) and where the crossing axis is a relative maximum.


Mathematical discussion[edit]




The plot of y = x3 with a saddle point at 0


Saddle surface [edit]

A model of an elliptic hyperboloid of one sheet


Classical examples of two-dimensional saddle surfaces in the Euclidean space are second order surfaces, the hyperbolic paraboloid (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.


The PhD thesis of Grigori Perelman, titled "Saddle surfaces in Euclidean spaces," was devoted to saddle surfaces.[1]

Other uses[edit]





See also[edit]


  1. ^ Перельман, Григорий Яковлевич (1990). Седловые поверхности в евклидовых пространствах: Автореф. дис. на соиск. учен. степ. канд. физ.-мат. наук (in Russian). Ленинградский Государственный Университет.  [Perelman, Gregory (1990). Saddle surfaces in Euclidean spaces: Author. Dis. on soisk. scientists. step. cand. Sci. Science (in Russian). Leningrad State University.]
  2. ^ von Petersdorff 2006


Further reading[edit]