Abstract
Let P be a set of n points in R3, not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n - 5 different directions if n is odd and at least 2n - 7 if n is even. The bound for odd n is sharp.
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Pach, J., Pinchasi, R. & Sharir, M. Solution of Scott's Problem on the Number of Directions Determined by a Point Set in 3-Space. Discrete Comput Geom 38, 399–441 (2007). https://doi.org/10.1007/s00454-007-1344-5
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DOI: https://doi.org/10.1007/s00454-007-1344-5