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The Writhe of Open and Closed Curves  

Mitchell A Berger   Submitted: 2006-07-02 08:27

Twist and writhe measure basic geometric properties of a ribbon or tube. While these measures have applications in molecular biology, materials science, fluid mechanics and astrophysics, they are under-utilized because they are often considered difficult to compute. In addition, many applications involve curves with endpoints (open curves); but for these curves the definition of writhe can be ambiguous. This paper provides simple expressions for the writhe of closed curves, and provides a new definition of writhe for open curves. The open curve definition is especially appropriate when the curve is anchored at endpoints on a plane or stretches between two parallel planes. This definition can be especially useful for magnetic flux tubes in the solar atmosphere, and for isotropic rods with ends fixed to a plane.

Authors: Berger, M. A. and Prior, C.
Projects: None

Publication Status: J. Phys. A: Math. and Gen. Published
Last Modified: 2006-07-02 20:39
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