Ribbon (mathematics)
In mathematics by a ribbon is meant a smooth space curve given by a three-dimensional vector, depending continuously on the curve arc-length , together with a smoothly varying unit vector perpendicular to at each point.
The ribbon is called simple and closed if is simple 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 linking number, denotes the total writhing number and is the total twist number.
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.
