Ribbon theory

The Mock Turtle, a character in the mathematician Charles Lutwidge Dodgson's popular children's story Alice's Adventures in Wonderland, studied Writhing

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

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

See also

• Bollobás–Riordan polynomial
• Knots and graphs
• Knot theory
• DNA supercoil

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, 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