Global Curvature, Thickness, and the Ideal Shapes of Knots

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 char...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 1999-04, Vol.96 (9), p.4769-4773
Main Authors: Gonzalez, Oscar, Maddocks, John H.
Format: Article
Language:English
Subjects:
Biological Sciences
Circles
Curvature
Curves
Geometric shapes
Mathematical functions
Mathematics
Minimum value
Physical Sciences
Physics
Radius of curvature
Smooth curves
Space curve
Tangents
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Summary: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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.96.9.4769