Ribbon theory

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


  • 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 Călugăreanu, White and Brock Fuller led to the Călugăreanu–White–Fuller theorem that Link = Writhe + Twist.[2]

See also


  • Adams, Colin (2004), The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, ISBN 0-8218-3678-1
  • Călugăreanu, G. 1959 'L’intégral de Gauss et l’analyse des nœuds tridimensionnels', Rev. Math. Pures Appl. 4, 5–20.
  • Călugăreanu, G. 1961 'Sur les classes d’isotopie des noeuds tridimensionels et leurs invariants', Czech. Math. J. 11, 588–625.
  • Fuller F. B. 1971 'The writhing number of a space curve', Proc Natl Acad Sci U S A. Apr;68(4):815–9.
  • White, J. H. 1969 'Self-linking and the Gauss integral in higher dimensions', Am. J. Math. 91, 693–728
  1. ^ Topology and physics of circular DNA by Aleksandr Vadimovich Vologodskiǐ, CRC Press Inc, 1992, p49
  2. ^ The geometry of twisted ribbons, Mark Dennis Homepage, University of Bristol, Accessed 18 July 2010, Inaccessible 27 February 2018
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