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 ( X , U ) {\displaystyle (X,U)} includes a curve X {\displaystyle X} given by a three-dimensional vector X ( s ) {\displaystyle X(s)} , depending continuously on the curve arc-length s {\displaystyle s} ( a ≤ s ≤ b {\displaystyle a\leq s\leq b} ), and a unit vector U ( s ) {\displaystyle U(s)} perpendicular to ∂ X ∂ s ( s ) {\displaystyle {\partial X \over \partial s}(s)} at each point.