Twist (differential geometry)

In differential geometry, the twist of a ribbon is its rate of axial rotation. Let a ribbon ( X , U ) {\displaystyle (X,U)} be composed of a space curve, X = X ( s ) {\displaystyle X=X(s)} , where s {\displaystyle s} is the arc length of X {\displaystyle X} , and U = U ( s ) {\displaystyle U=U(s)} a unit normal vector, perpendicular at each point to ∂ X ( s ) ∂ s ( s ) {\displaystyle {\partial X(s) \over \partial s}(s)} .

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