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

See alsoEdit


  • Adams, Colin (2004), The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots, American Mathematical Society, ISBN 0-8218-3678-1
  • Călugăreanu, Grigore (1959), "L'intégrale de Gauss et l'analyse des nœuds tridimensionnels", Rev. Math. Pures Appl., 4: 5–20, MR 0131846
  • Călugăreanu, Grigore (1961), "Sur les classes d'isotopie des noeuds tridimensionels et leurs invariants", Czechoslovak Mathematical Journal, 11: 588–625, MR 0149378
  • 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: 815–819, doi:10.1073/pnas.68.4.815, MR 0278197, PMC 389050
  • White, James H. (1969), "Self-linking and the Gauss integral in higher dimensions", American Journal of Mathematics, 91: 693–728, doi:10.2307/2373348, MR 0253264
  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