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I vaguely remember from my youth a result concerning scrolls or ruled surfaces. Here is what I remember:

A ruled surface containing at least $n$ non-parallel lines is a plane

In my memory $n=27$, but I am not very sure. Does this remind someone of a correctly stated theorem, does it have a name?

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The generic smooth cubic surface has 27 lines on it (working in $\Bbb CP^3$). However, it is not a ruled surface. On the other hand, a nonsingular quadric (working over $\Bbb R$ we need a saddle surface or a hyperboloid of one sheet) has *two* infinite families of pairwise skew lines on it. So I’m not quite sure what the result you’re remembering might be.

Now, if you talk about smooth (real analytic) *flat* ruled surfaces in $\Bbb R^3$, they must be either planes, cones, cylinders, or tangent developables. Cylinders are ruled by parallel lines, but cones and tangent developables have infinitely many non-parallel rulings.

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