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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.^{[1]}