Global curvature, thickness, and the ideal shapes of knots (original) (raw)

1Département de Mathématiques, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland

Edited by Nicholas R. Cozzarelli, University of California at Berkeley, Berkeley, CA, and approved February 16, 1999

Copyright © 1999, The National Academy of Sciences

Abstract

The global radius of curvature of a space curve is introduced. This function is related to, but distinct from, the standard local radius of curvature and is connected to various physically appealing properties of a curve. In particular, the global radius of curvature function provides a concise characterization of the thickness of a curve, and of certain ideal shapes of knots as have been investigated within the context of DNA.