there's my question:

Given 2 regular plane curves (let's say $\mathcal{C}^1$) in the 3D space, is there always a developable surface which contains both curves ?

Thanks, anders

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Sure. If you have parametric equations for both your curves, and the parameter ranges for both curves are the same, you can then consider the surface drawn out by a moving straight line whose endpoints are at the two curves. – J. M. Jul 26 '12 at 16:44
Do you really want the surface to contain the curves, or to have them as parts of the boundary? Are the curves disjoint? Is the surface required to be embedded (without self-intersections)? – user31373 Jul 26 '12 at 21:16
@Ｊ.Ｍ.: It seems to me you are proving that you can build a ruled surface from two curves, but nothing proves such built surface is developable. – anderstood Oct 13 '13 at 16:39