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Normal plane

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to a curve in space at a point

The plane passing through and perpendicular to the tangent at . The normal plane contains all normals (cf. Normal) to the curve passing through . If the curve is given in rectangular coordinates by the equations

then the equation of the normal plane at the point corresponding to the value of the parameter can be written in the form

If the equation of the curve has the form , then the equation of the normal plane is


Comments

References

[a1] M.P. Do Carmo, "Differential geometry of curves and surfaces" , Prentice-Hall (1976) pp. 142
How to Cite This Entry:
Normal plane. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Normal_plane&oldid=32595
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article