Try for yourself—before you read much further—to construct configurations of points in the plane that determine “relatively few” slopes. For this we assume, of course, that the n ≥ 3 points do not all lie on one line. Recall from Chapter 11 on “Lines in the plane” the theorem of Erdős and de Bruijn: the n points will determine at least n different lines. But of course many of these lines may be parallel, and thus determine the same slope.
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