Article
Article
Helix
Article By:
Blumenthal, Leonard M. Formerly, Department of Mathematics, University of Missouri, Columbia, Missouri.
Last reviewed:January 2020
DOI:https://doi.org/10.1036/1097-8542.312400
Any nonplanar curve all of whose tangents make the same angle with a fixed line. Other characteristic properties are that all principal normals are parallel to a plane and that the ratio of torsion to curvature is constant. If a helix has constant curvature (and hence constant torsion), it is a circular helix; it lies on a circular cylinder whose elements it cuts at a constant angle (see illustration). Parametric equations for a circular helix (the curve of an untapered screw) are x = a cos t, y = a sin t, z = kt, a > 0, k ≠ 0, and −∞ < t < ∞. See also: Analytic geometry; Differential geometry; Parametric equation
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