Ribbon (mathematics)

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 ${\displaystyle (X,U)}$ includes a curve ${\displaystyle X}$ given by a three-dimensional vector ${\displaystyle X(s)}$, depending continuously on the curve arc-length ${\displaystyle s}$ (${\displaystyle a\leq s\leq b}$), and a unit vector ${\displaystyle U(s)}$ perpendicular to ${\displaystyle X}$ at each point. Ribbons have seen particular application as regards DNA.