The term derives from the Latinate root " osculate ", to kiss, because the two curves contact one another in a more intimate way than simple tangency.
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:I'm not well-versed on the mathematics involved, but you might be able to construct the parabola by treating the log as an osculating circle.
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Post release of theatrical trailer, it was revealed that the filming of ten second osculating scene between lead actors took four hours to complete after several re-takes.
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The osculating plane in the geometry of Euclidean space curves can be described in terms of the Frenet-Serret formulas as the linear span of the tangent and normal vectors.
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Or, in other words, if the torsion is zero, the curve lies completely in the same osculating plane ( there is only one osculating plane for every point ).
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Or, in other words, if the torsion is zero, the curve lies completely in the same osculating plane ( there is only one osculating plane for every point ).
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If " C " is a regular space curve then the osculating circle is defined in a similar way, using the principal normal vector " N ".
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These estimates are easiest to derive when the manifold is strongly pseudoconvex, for then one can replace the manifold by osculating it to a high enough order with the Heisenberg group.
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:: If the osculating circle has radius 1, the parabola is given by 2 " " x " 2; but this does not give a satisfactory solution.
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If the derivative of curvature ?'( " t " ) is zero, then the osculating circle will have 3rd-order contact and the curve is said to have a vertex.
