Ribbon theory

Ribbon theory is a strand of mathematics within topology that has seen particular application as regards DNA.[1]

## Contents

* 1 Concepts
* 2 See also
* 3 References
* 4 Notes

## Concepts

* Link is the integer number of turns of the ribbon around its axis;
* Twist is the rate of rotation of the ribbon around its axis;
* Writhe is a measure of non-planarity of the ribbon's axis curve.

Work by Gheorghe Călugăreanu, James H. White, and F. Brock Fuller led to the Călugăreanu–White–Fuller theorem that Link = Writhe + Twist.[2][3]

## See also

* Bollobás–Riordan polynomial
* Knots and graphs
* Knot theory
* DNA supercoil
* Möbius strip

## References

* Adams, Colin (2004), The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, ISBN 0-8218-3678-1
* Călugăreanu, Gheorghe (1959), "L'intégrale de Gauss et l'analyse des nœuds tridimensionnels", Revue de Mathématiques Pure et Appliquées 4: 5–20
* Călugăreanu, Gheorghe (1961), "Sur les classes d'isotopie des noeuds tridimensionels et leurs invariants", Czechoslovak Mathematical Journal 11: 588–625, doi:10.21136/CMJ.1961.100486
* Fuller, F. Brock (1971), "The writhing number of a space curve", Proceedings of the National Academy of Sciences of the United States of America 68 (4): 815–819, doi:10.1073/pnas.68.4.815, PMID 5279522
* White, James H. (1969), "Self-linking and the Gauss integral in higher dimensions", American Journal of Mathematics 91 (3): 693–728, doi:10.2307/2373348

## Notes

1. ↑ Vologodskiǐ, Aleksandr Vadimovich (1992). Topology and Physics of Circular DNA (First ed.). Boca Raton, FL. p. 49. ISBN 978-1138105058. OCLC 1014356603.
2. ↑ Dennis, Mark R.; Hannay, J.H (2005). "Geometry of Călugăreanu's theorem". Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461 (2062): 3245–3254. doi:10.1098/rspa.2005.1527. https://royalsocietypublishing.org/doi/10.1098/rspa.2005.1527.
3. ↑ Dennis, Mark. "The geometry of twisted ribbons". University of Bristol. http://www.phy.bris.ac.uk/people/dennis_mr/highlights.html.

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