Acute Sets

Dmitriy Zakharov

doi:10.1007/s00454-017-9947-y

Acute Sets

Dmitriy Zakharov

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

4 Scopus citations

Abstract

A set of points in R ^d is acute if any three points from this set form an acute triangle. In this note we construct an acute set in R ^d of size at least 1. 618 ^d . We also present a simple example of an acute set of size at least 2 ^d ^/ ² . Obtained bounds improve the previously best bound.

Original language	English
Pages (from-to)	212-217
Number of pages	6
Journal	Discrete and Computational Geometry
Volume	61
Issue number	1
DOIs	https://doi.org/10.1007/s00454-017-9947-y
State	Published - Jan 15 2019
Externally published	Yes

Keywords

Acute set
Danzer-Grünbaum problem
Euclidean space

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10.1007/s00454-017-9947-y

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title = "Acute Sets",

abstract = " A set of points in R d is acute if any three points from this set form an acute triangle. In this note we construct an acute set in R d of size at least 1. 618 d . We also present a simple example of an acute set of size at least 2 d / 2 . Obtained bounds improve the previously best bound.",

keywords = "Acute set, Danzer-Gr{\"u}nbaum problem, Euclidean space",

author = "Dmitriy Zakharov",

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year = "2019",

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doi = "10.1007/s00454-017-9947-y",

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AB - A set of points in R d is acute if any three points from this set form an acute triangle. In this note we construct an acute set in R d of size at least 1. 618 d . We also present a simple example of an acute set of size at least 2 d / 2 . Obtained bounds improve the previously best bound.

KW - Acute set

KW - Danzer-Grünbaum problem

KW - Euclidean space

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U2 - 10.1007/s00454-017-9947-y

DO - 10.1007/s00454-017-9947-y

M3 - Article

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EP - 217

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -

Acute Sets

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Keywords

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