Osculating plane | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-02

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Osculating_plane


00:00:38 See also



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SUMMARY
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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.