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Equivalently it is the surface formed by the centers of the circles which osculate the curvature lines.
And so we would osculate (kiss).
The spiral starts at the origin in the positive x direction and gradually turns anticlockwise to osculate the circle.
Since this visitor had no freight to discharge, only a gangtube reached forth to osculate the exit for the crew.
Alternatively, real trajectories can be modeled as a sequence of Keplerian orbits that osculate ("kiss" or touch) the real trajectory.
The curves flirt and osculate with one another in some pattern that is, Waterhouse guesses, deeply fascinating and significant but too challenging for his tired mind to attack.
In mathematical invariant theory, the osculant or tacinvariant or tact invariant is an invariant of a hypersurface that vanishes if the hypersurface touches itself, or an invariant of several hypersurfaces that osculate, meaning that they have a common point where they meet to unusually high order.