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

János Pach; Rom Pinchasi; Micha Sharir

doi:10.1145/997817.997832

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

János Pach^*, Rom Pinchasi, Micha Sharir

^*Corresponding author for this work

School of Computer Science

Research output: Contribution to conference › Paper › peer-review

Abstract

Let P be a set of n points in ℝR³, 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 - 7 different directions if n is even and at least 2n - 5 if n is odd. The bound for odd n is sharp.

Original language	English
Pages	76-85
Number of pages	10
DOIs	https://doi.org/10.1145/997817.997832
State	Published - 2004
Event	Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04) - Brooklyn, NY, United States Duration: 9 Jun 2004 → 11 Jun 2004

Conference

Conference	Proceedings of the Twentieth Annual Symposium on Computational Geometry (SCG'04)
Country/Territory	United States
City	Brooklyn, NY
Period	9/06/04 → 11/06/04

Keywords

Directions
Scott's Conjecture
Slope problem
Three dimensions
Ungar's Theorem

Access to Document

10.1145/997817.997832

Cite this

@conference{0f3425581450466a91da37ea1dbcd177,

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

abstract = "Let P be a set of n points in ℝR3, 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 - 7 different directions if n is even and at least 2n - 5 if n is odd. The bound for odd n is sharp.",

keywords = "Directions, Scott's Conjecture, Slope problem, Three dimensions, Ungar's Theorem",

author = "J{\'a}nos Pach and Rom Pinchasi and Micha Sharir",

year = "2004",

doi = "10.1145/997817.997832",

language = "אנגלית",

pages = "76--85",

note = "null ; Conference date: 09-06-2004 Through 11-06-2004",

}

TY - CONF

T1 - Solution of Scott's problem on the number of directions determined by a point set in 3-space

AU - Pach, János

AU - Pinchasi, Rom

AU - Sharir, Micha

PY - 2004

Y1 - 2004

N2 - Let P be a set of n points in ℝR3, 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 - 7 different directions if n is even and at least 2n - 5 if n is odd. The bound for odd n is sharp.

AB - Let P be a set of n points in ℝR3, 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 - 7 different directions if n is even and at least 2n - 5 if n is odd. The bound for odd n is sharp.

KW - Directions

KW - Scott's Conjecture

KW - Slope problem

KW - Three dimensions

KW - Ungar's Theorem

UR - http://www.scopus.com/inward/record.url?scp=4544329772&partnerID=8YFLogxK

U2 - 10.1145/997817.997832

DO - 10.1145/997817.997832

M3 - ???researchoutput.researchoutputtypes.contributiontoconference.paper???

AN - SCOPUS:4544329772

SP - 76

EP - 85

Y2 - 9 June 2004 through 11 June 2004

ER -

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

Abstract

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Cite this