Rectifying Plane

rectifying plane

[′rek·tə‚fī·iŋ ‚plān]
(mathematics)
The plane that contains the tangent and binormal to a curve at a given point on the curve.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Rectifying Plane

 

The rectifying plane of a space curve L at a point M on L is the plane of the tangent and binormal to L at M. The envelope of the family of rectifying planes of L is a developable surface called the rectifying developable of L (seeRULEDSURFACE). On this surface, L is a geodesic. When the rectifying developable is developed on a plane, L becomes a straight line. In other words, L is “rectified”; this fact accounts for the term “rectifying plane.”

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
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When does the position vector of a space curve always lie in its rectifying plane? Amer.
It is also known that if all rectifying planes of the curve in [E.sub.3] pass through a particular point, then the ratio of torsion and curvature of the curve is a non-constant linear function [2].
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At each of the curve, the planes spanned by {T, N}, {T, B} and {N, B} are known respectively as the osculating plane, the rectifying plane and the normal plane[5].
Chen, When does the position vector of a space curve always lie in its rectifying plane?, Amer.
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Both the rectifying planes of [gamma] and [gamma] are timelike.
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