In differential geometry, a ribbon (or strip) is the combination of a smooth space curve and its corresponding normal vector.
More formally, a ribbon denoted by
, depending continuously on the curve arc-length
[1] Ribbons have seen particular application as regards DNA.
is a simple curve (i.e. without self-intersections) and closed and if
For any simple closed ribbon the curves
are, for all sufficiently small positive
, simple closed curves disjoint from
The ribbon concept plays an important role in the Călugăreanu formula,[3] [4] that states that where
is the asymptotic (Gauss) linking number, the integer number of turns of the ribbon around its axis;
denotes the total writhing number (or simply writhe), a measure of non-planarity of the ribbon's axis curve; and
is the total twist number (or simply twist), the rate of rotation of the ribbon around its axis.
Ribbon theory investigates geometric and topological aspects of a mathematical reference ribbon associated with physical and biological properties, such as those arising in topological fluid dynamics, DNA modeling and in material science.