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The straight line passing through a point of a curve perpendicular to the osculating plane to at . If is a parametrization of , then the vector equation of the binormal at corresponding to the value of the parameter has the form


This definition holds for space curves for which does not depend linearly on , i.e. the curvature should not vanish.

For curves in a higher-dimensional Euclidean space, the binormal is generated by the second normal vector in the Frénet frame (cf. Frénet trihedron), which is perpendicular to the plane spanned by and and depends linearly on (cf. [a1]).


[a1] M. Spivak, "A comprehensive introduction to differential geometry" , 2 , Publish or Perish (1970) pp. 1–5
How to Cite This Entry:
Binormal. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by E.V. Shikin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article