aka strip

A ribbon refers to the mathematical object consisting of a Curve and an associated 1d unit perpendicular Vector field on it. Formally it is a pair $(X,U)$, of a smooth Curve $X$ together with a smoothly varying Unit Vector field $U(t)$ perpendicular to to $X$ (perpendicular to the Tangent vector of $X$). The ribbon is called simple and closed if $X$ is simple and closed and if $U$ and its derivatives agree at $a$ and $b$.

http://mathworld.wolfram.com/Twist.html

https://en.wikipedia.org/wiki/Ribbon_theory

Ways of measuring the number of times "U goes around X"

• Linking number $Lk$
• Twist $Tw$

The linking number and twist are in general different. However, their difference only depends on $X$ (and not in $U$). We can therefore define the writhing number as this difference

Sur les classes d'isotopie des noeuds tridimensionnels et leurs invariants

The self-linking number of a closed space curve – pdf

The writhing number of a space curve