On sets of points that determine only acute angles

Eyal Ackerman; Oren Ben-Zwi

doi:10.1016/j.ejc.2008.07.020

On sets of points that determine only acute angles

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

Abstract

We show that for every integer d there is a set of points in E^d of size Ω ((frac(2, sqrt(3)))^d sqrt(d)) such that every angle determined by three points in the set is smaller than π / 2. This improves the best known lower bound by a Θ (sqrt(d)) factor.

Original language	English
Pages (from-to)	908-910
Number of pages	3
Journal	European Journal of Combinatorics
Volume	30
Issue number	4
DOIs	https://doi.org/10.1016/j.ejc.2008.07.020
State	Published - May 2009
Externally published	Yes

Bibliographical note

Funding Information:
We thank Guy Wolfovitz for helpful discussions, specifically, for suggesting using [6] instead of [8] in order to simplify the proof of Theorem 1 . The first author was supported by a fellowship from the Alexander von Humboldt Foundation.

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2008.07.020

Cite this

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title = "On sets of points that determine only acute angles",

abstract = "We show that for every integer d there is a set of points in Ed of size Ω ((frac(2, sqrt(3)))d sqrt(d)) such that every angle determined by three points in the set is smaller than π / 2. This improves the best known lower bound by a Θ (sqrt(d)) factor.",

author = "Eyal Ackerman and Oren Ben-Zwi",

note = "Funding Information: We thank Guy Wolfovitz for helpful discussions, specifically, for suggesting using [6] instead of [8] in order to simplify the proof of Theorem 1 . The first author was supported by a fellowship from the Alexander von Humboldt Foundation.",

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AB - We show that for every integer d there is a set of points in Ed of size Ω ((frac(2, sqrt(3)))d sqrt(d)) such that every angle determined by three points in the set is smaller than π / 2. This improves the best known lower bound by a Θ (sqrt(d)) factor.

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On sets of points that determine only acute angles

Abstract

Bibliographical note

ASJC Scopus subject areas

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