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osculating plane
In mathematics, particularly in differential geometry, an osculating plane is a plane in a Euclidean space or affine space which meets a submanifold at a point in such a way as to have a second order of contact at the point. The word ''osculate'' is from the Latin ''osculatus'' which is a past participle of ''osculari'', meaning ''to kiss''. An osculating plane is thus a plane which "kisses" a submanifold.
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.
== See also ==
* Osculating circle
* Differential geometry of curves#Special Frenet vectors and generalized curvatures
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