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

Janos Pach; Rom Pinchasi; Micha Sharir

doi:10.1007/s00454-007-1344-5

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

Janos Pach^*, Rom Pinchasi, Micha Sharir

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	399-441
Number of pages	43
Journal	Discrete and Computational Geometry
Volume	38
Issue number	2
DOIs	https://doi.org/10.1007/s00454-007-1344-5
State	Published - Sep 2007

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

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