Solution of Scott's problem on the number of directions determined by a point set in 3-space

Let <i>P</i> be a set of <i>n</i> points in ℝ<sup>3</sup>, not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of <i>P</i> assume at least 2<i>n</i>-7 different directions if <i>n</i> is even and at least 2<i>n</i>-5 if <i>n</i> is odd. The bound for odd <i>n</i> is sharp.

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