Ribbon

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 includes a curve given by a three-dimensional vector , depending continuously on the curve arc-length, and a unit vector perpendicular to at each point. Ribbons have seen particular application as regards DNA. Properties and implications The ribbon is called simple if is a simple curve (i.e. without self-intersections) and closed and if and all its derivatives agree at and . For any simple closed ribbon the curves given parametrically by are, for all sufficiently small positive , simple closed curves disjoint from . The ribbon concept plays an important role in the Călugăreanu-White-Fuller formula, 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.