By the equivalence principles of relativity you do NOThave to choose a stationary point as a reference, Any point in space may be chosen as no point is truly "stationary" and a point that is stationary in one reference frame will be moving in another.

There is really no such thing as an absolute stationary point. By convention one can be picked as any point in the observer's frame of reference (i.e. any point stationary relative to the observer).

The fulcrum

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.

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