In
mathematics, a
saddle point is a point in the
domain of a
function that is a
stationary point but not a
local extremum. The name derives from the fact that the prototypical example in two dimensions is a
surface that
curves up in one direction, and
curves down in a different direction, resembling a
saddle or a
mountain pass. In terms of contour lines, a saddle point in two dimensions gives rise to a contour that appears to intersect itself.