The Number of Directions Determined by Points in the Three-Dimensional Euclidean Space
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Let X be a set of n points in the three-dimensional Euclidean space such that no three points in X are on the same line and there is no plane containing all points in X . An old conjecture states that pairs of points in X determine at least 2n-3 directions. We prove the weaker result that X determines at least 1.75n-2 directions.
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