# Points and triangles in the plane and halving planes in space

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.

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Author

Aronov, Boris;
Chazelle, Bernard;
Edelsbrunner, Herbert

^{ISTA}^{}; Guibas, Leonidas; Sharir, Micha; Wenger, RephaelAbstract

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.

Publishing Year

Date Published

1990-01-01

Proceedings Title

Proceedings of the 6th annual symposium on Computational geometry

Publisher

ACM

Page

112 - 115

Conference

SCG: Symposium on Computational Geometry

Conference Location

Berkley, CA, United States

Conference Date

1990-06-07 – 1990-06-09

ISBN

IST-REx-ID

### Cite this

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:10.1145/98524.98548Aronov, 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/10.1145/98524.98548Aronov, 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.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.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.