Alternatively, a line can be given by two points, which yields a slightly different definition:

Given two curves ${\bf X}(t)$ and ${\bf Y}(t)$, a ruled surface is the image of the function $$ f(s,t) = (1-s) {\bf X}(t) + s{\bf Y}(t). $$

This corresponds to Olivier's process of threading a string through holes in two brass "curves".