Osculating Plane

The plane spanned by the three points x(t), x(t+h_1), and x(t+h_2) on a curve as h_1,h_2->0. Let z be a point on the osculating plane, then


where [A,B,C] denotes the scalar triple product. The osculating plane passes through the tangent. The intersection of the osculating plane with the normal plane is known as the (principal) normal vector. The vectors T and N (tangent vector and normal vector) span the osculating plane.

See also

Normal Vector, Osculating Sphere, Scalar Triple Product, Tangent Vector

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Cite this as:

Weisstein, Eric W. "Osculating Plane." From MathWorld--A Wolfram Web Resource.

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