Osculating plane

File:Frenet.svg

A space curve, Frenet–Serret frame, and the osculating plane (spanned by Template:Math and Template:Math).

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 Template:Ety; 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

• Normal plane (geometry)
• Osculating circle
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