Ribbon (mathematics)

In mathematics (differential geometry) by a ribbon (or strip) ${\displaystyle (X,U)}$ is meant a smooth space curve ${\displaystyle X}$ given by a three-dimensional vector ${\displaystyle X(s)}$, depending continuously on the curve arc-length ${\displaystyle s}$ (${\displaystyle a\leq s\leq b}$), together with a smoothly varying unit vector ${\displaystyle U(s)}$ perpendicular to ${\displaystyle X}$ at each point (Blaschke 1950).

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