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Rectifying plane

From Encyclopedia of Mathematics
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The plane of the Frénet frame (cf. Frénet trihedron) of a given point $ A $ on a curve $ \mathbf r = \mathbf r ( t) $( cf. Line (curve)) which is spanned by the tangent (cf. Tangent line) $ \mathbf t $ and the binormal $ \mathbf b $ to the curve at this point. The equation of the rectifying plane can be written in the form

$$ \left | or $$ ( \mathbf R - \mathbf r ) \mathbf r ^ \prime [ \mathbf r ^ \prime , \mathbf r

^ {\prime\prime} ]  =  0,

$$

where $ \mathbf r ( t) = \mathbf r ( x( t), y( t), z( t)) $ is the equation of the curve.

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References

[a1] M. Spivak, "A comprehensive introduction to differential geometry" , 2 , Publish or Perish (1970) pp. 1–5
How to Cite This Entry:
Rectifying plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Rectifying_plane&oldid=18907
This article was adapted from an original article by L.A. Sidorov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article