A saddle point is a point in the range of a smooth function every neighbourhood of which contains points on each side of its tangent plane.
a saddle
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On the horse top right
what way did point B move relative to point A?
Eight point four. Eight point four. Eight point four. Eight point four.
An inflection point is not a saddle point, but a saddle point is an inflection point. To be precise, a saddle point is both a stationary point and an inflection point. An inflection point is a point at which the curvature changes sign, so it is not necessary to be a stationary point.
cyl
A saddle.
The pommell
A saddle.
There will be no saddle point; no point in the table will be an optimum.
In the liquid drop model, excitation energy in a nucleus gives rides to modes of motion or oscillations. On a potential energy surface, the saddle point corresponds to the critical deformation of unstable equilibrium in the nucleus.
When looking at a horse saddle, the saddle point (i.e. the centre) is the lowest point on the structure in the longitudinal plane whilst also being the highest point on the structure in the lateral plane. Therefore it can be considered geometrically to simultaneously be a point of maximum and minumum height in space. This describes well the equilibrium situation in game theory where the agent tries tominimize the maximum possible loss. Alternatively, it can be thought of as maximizing the minimum gain (maximin).
A saddle
A saddle
saddle
A saddle