The French mathematicians Joseph Alfred Serret and Jean Frédéric Frenet found a way to represent a parametrized curve by intrinsic equations. At each point

of the curve (parametrized by arclength

), three mutually perpendicular unit vectors are defined (called a TNB frame). The tangent

shows the direction of motion of the point, the normal

points toward the direction in which the curve bends, and the binormal

is a vector perpendicular to both

. Another two quantities are introduced: curvature to measure how quickly the curve is changing its direction, and torsion to measure how quickly the curve is leaving the

**TN** plane. In this Demonstration, the functions

(kappa, for curvature) and

(tau, for torsion) can be adjusted using the parameters

and

and can be chosen to build a ribbon-like surface (in fact, a ruled surface) of a selected width and length, in discrete steps

applied

times. This is possible because the other edge has the same TNB frame, but displaced.