Definition:Saddle Point (Geometry)

This page is about saddle point in the context of geometry. For other uses, see Saddle Point.

Definition

Let $\SS$ be a surface defined by the Cartesian equation $z = \map f {x, y}$.

Let $P$ be a point on $\SS$ such that:

the partial derivatives $\dfrac {\partial z} {\partial x}$ and $\dfrac {\partial z} {\partial y}$ are both zero

but:

there is no local maximum or local minimum at $P$.

Then $P$ is a saddle point of $\SS$.

Also see

• Results about saddle points in the context of geometry can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): saddle point: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): saddle point: 1.