---
_id: '4077'
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 of S there exists a point (not necessarily of S) contained in at
least n3-3α/(512 log25 n) of the triangles. This implies that any set of n points
in three - dimensional space defines at most 6.4n8/3 log5/3 n halving planes.
article_processing_charge: No
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. In: *Proceedings of
the 6th Annual Symposium on Computational Geometry*. ACM; 1990:112-115. doi:10.1145/98524.98548'
apa: 'Aronov, B., Chazelle, B., Edelsbrunner, H., Guibas, L., Sharir, M., &
Wenger, R. (1990). Points and triangles in the plane and halving planes in space.
In *Proceedings of the 6th annual symposium on Computational geometry* (pp.
112–115). Berkley, CA, United States: ACM. https://doi.org/10.1145/98524.98548'
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.” In *Proceedings of the 6th Annual Symposium on Computational
Geometry*, 112–15. ACM, 1990. https://doi.org/10.1145/98524.98548.
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,” in *Proceedings
of the 6th annual symposium on Computational geometry*, Berkley, CA, United
States, 1990, pp. 112–115.
ista: 'Aronov B, Chazelle B, Edelsbrunner H, Guibas L, Sharir M, Wenger R. 1990.
Points and triangles in the plane and halving planes in space. Proceedings of
the 6th annual symposium on Computational geometry. SCG: Symposium on Computational
Geometry, 112–115.'
mla: Aronov, Boris, et al. “Points and Triangles in the Plane and Halving Planes
in Space.” *Proceedings of the 6th Annual Symposium on Computational Geometry*,
ACM, 1990, pp. 112–15, doi:10.1145/98524.98548.
short: B. Aronov, B. Chazelle, H. Edelsbrunner, L. Guibas, M. Sharir, R. Wenger,
in:, Proceedings of the 6th Annual Symposium on Computational Geometry, ACM, 1990,
pp. 112–115.
conference:
end_date: 1990-06-09
location: Berkley, CA, United States
name: 'SCG: Symposium on Computational Geometry'
start_date: 1990-06-07
date_created: 2018-12-11T12:06:48Z
date_published: 1990-01-01T00:00:00Z
date_updated: 2022-02-17T09:42:27Z
day: '01'
doi: 10.1145/98524.98548
extern: '1'
language:
- iso: eng
main_file_link:
- url: https://dl.acm.org/doi/10.1145/98524.98548
month: '01'
oa_version: None
page: 112 - 115
publication: Proceedings of the 6th annual symposium on Computational geometry
publication_identifier:
isbn:
- 978-0-89791-362-1
publication_status: published
publisher: ACM
publist_id: '2045'
quality_controlled: '1'
scopus_import: '1'
status: public
title: Points and triangles in the plane and halving planes in space
type: conference
user_id: ea97e931-d5af-11eb-85d4-e6957dddbf17
year: '1990'
...