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Global curvature, thickness, and the ideal shapes of knots
Open accessAbstract
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.
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Citations
Cited by
Optimal shapes of compact strings
Maritan, A., Micheletti, C., Trovato, A., & Banavar, J. R. (2000) · Nature · doi:10.1038/35018538 · Cited by 275
Kim, D., Wang, S., Keum, H., Ghaffari, R., Kim, Y., Tao, H., Panilaitis, B., Li, M., Kang, Z., Omenetto, F., et al. (2012) · Small · doi:10.1002/smll.201200933 · Cited by 170
Knot tightening by constrained gradient descent
Ashton, T., Cantarella, J., Piatek, M., & Rawdon, E. J. (2011) · Experimental Mathematics · doi:10.1080/10586458.2011.544581 · Cited by 71
Curvature and torsion of the tight closed trefoil knot
Baranska, J., Przybyl, S., & Pieranski, P. (2008) · The European Physical Journal B · doi:10.1140/epjb/e2008-00443-y · Cited by 20
Metadata
- Authors
- Gonzalez, O., & Maddocks, J. H.
- Venue
- Proceedings of the National Academy of Sciences
- Published
- 1999-04-27
- Volume
- 96
- Issue
- 9
- Pages
- 4769-4773
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- OpenAlex
- W2153292122
- Cited by
- 246
- References
- 0
- FWCI
- 10.21
- Type
- journal article
- Language
- en
- Open access
- green
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- Gonzalez, O., & Maddocks, J. H. (1999). Global curvature, thickness, and the ideal shapes of knots. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.96.9.4769
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
