---
_id: '4062'
abstract:
- lang: eng
text: We prove that for any set S of n points in the plane and n3-α triangles spanned
by the points in S there exists a point (not necessarily in S) contained in at
least n3-3α/(c log5 n) of the triangles. This implies that any set of n points
in three-dimensional space defines at most {Mathematical expression} halving planes.
acknowledgement: "Work on this paper by Boris Aronov and Rephael Wenger has been supported
by DIMACS under NSF Grant STC-88-09648. Work on this paper by Bernard Chazelle has
been supported by NSF Grant CCR-87-00917. Work by Herbert Edelsbrunner has been
supported by NSF Grant CCR-87-14565. Micha Sharir has been supported by ONR Grant
N00014-87-K-0129, by NSF Grant CCR-89-01484, and by grants from the U.S.-Israeli
Binational Science Foundation, the Israeli National Council for Research and Development,
and the Fund for Basic Research administered by the Israeli\r\nAcademy of Sciences"
article_processing_charge: No
article_type: original
author:
- first_name: Boris
full_name: Aronov, Boris
last_name: Aronov
- first_name: Bernard
full_name: Chazelle, Bernard
last_name: Chazelle
- first_name: Herbert
full_name: Edelsbrunner, Herbert
id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
last_name: Edelsbrunner
orcid: 0000-0002-9823-6833
- first_name: Leonidas
full_name: Guibas, Leonidas
last_name: Guibas
- first_name: Micha
full_name: Sharir, Micha
last_name: Sharir
- first_name: Rephael
full_name: Wenger, Rephael
last_name: Wenger
citation:
ama: Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. Points
and triangles in the plane and halving planes in space. Discrete & Computational
Geometry. 1991;6(1):435-442. doi:10.1007/BF02574700
apa: Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., & Wenger,
R. (1991). Points and triangles in the plane and halving planes in space. Discrete
& Computational Geometry. Springer. https://doi.org/10.1007/BF02574700
chicago: Aronov, Boris, Bernard Chazelle, Herbert Edelsbrunner, Leonidas Guibas,
Micha Sharir, and Rephael Wenger. “Points and Triangles in the Plane and Halving
Planes in Space.” Discrete & Computational Geometry. Springer, 1991.
https://doi.org/10.1007/BF02574700.
ieee: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, and R. Wenger,
“Points and triangles in the plane and halving planes in space,” Discrete &
Computational Geometry, vol. 6, no. 1. Springer, pp. 435–442, 1991.
ista: Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1991.
Points and triangles in the plane and halving planes in space. Discrete &
Computational Geometry. 6(1), 435–442.
mla: Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes
in Space.” Discrete & Computational Geometry, vol. 6, no. 1, Springer,
1991, pp. 435–42, doi:10.1007/BF02574700.
short: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger,
Discrete & Computational Geometry 6 (1991) 435–442.
date_created: 2018-12-11T12:06:43Z
date_published: 1991-12-01T00:00:00Z
date_updated: 2022-02-24T15:39:25Z
day: '01'
doi: 10.1007/BF02574700
extern: '1'
intvolume: ' 6'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/article/10.1007/BF02574700
month: '12'
oa: 1
oa_version: Published Version
page: 435 - 442
publication: Discrete & Computational Geometry
publication_identifier:
eissn:
- 1432-0444
issn:
- 0179-5376
publication_status: published
publisher: Springer
publist_id: '2063'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Points and triangles in the plane and halving planes in space
type: journal_article
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
volume: 6
year: '1991'
...