osculating plane

An osculating plane is thus a plane which "kisses" a submanifold.

The osculating plane is the plane containing T and N.

For instance an osculating plane to a space curve is a plane that has second-order contact with the curve.

Geometrically, a ribbon is a piece of the envelope of the osculating planes of the curve.

The tangent and the normal vector at point s define the osculating plane at point r(s).

The radial component is directed from the point P to the point where the perpendicular from an arbitrary fixed origin meets the osculating plane.

The first generalized curvature χ1('t') is called 'curvature' and measures the deviance of γ from being a straight line relative to the osculating plane.

It lies in the osculating plane, the plane spanned by the tangent and principal normal vectors T and N at the point P.

There exists a circle in the osculating plane tangent to γ("s") whose Taylor series to second order at the point of contact agrees with that of "γ"("s").

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.

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.