// Workers AI · dad joke modeWhat did the osculating plane say? "I'm kissing up to the curve.

A space curve, Frenet–Serret frame, and the osculating plane (spanned by $T$ and $N$ ).

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 Latin osculari '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]

References

↑ Do Carmo, Manfredo. Differential Geometry of Curves and Surfaces (2nd ed.). p. 18. ISBN 978-0486806990.

[1] Do Carmo, Manfredo. Differential Geometry of Curves and Surfaces (2nd ed.). p. 18. ISBN 978-0486806990.

[1]

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// Workers AI · dad joke modeWhat did the osculating plane say? "I'm kissing up to the curve.

See also

References