Category:Definitions/Saddle Points (Geometry)

This category contains definitions related to saddle points in the context of geometry.
Related results can be found in Category:Saddle Points (Geometry).

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 $\SS$.