THREE CONVEX HULL THEOREMS ON TRIANGLES AND CIRCLES

- Journal title : Honam Mathematical Journal
- Volume 36, Issue 4, 2014, pp.787-794
- Publisher : The Honam Mathematical Society
- DOI : 10.5831/HMJ.2014.36.4.787

Title & Authors

THREE CONVEX HULL THEOREMS ON TRIANGLES AND CIRCLES

Kalantari, Bahman; Park, Jong Youll;

Kalantari, Bahman; Park, Jong Youll;

Abstract

We prove three convex hull theorems on triangles and circles. Given a triangle and a point p, let be the triangle each of whose vertices is the intersection of the orthogonal line from p to an extended edge of . Let be the triangle whose vertices are the centers of three circles, each passing through p and two other vertices of . The first theorem characterizes when via a distance duality. The triangle algorithm in [1] utilizes a general version of this theorem to solve the convex hull membership problem in any dimension. The second theorem proves if and only if . These are used to prove the third: Suppose p be does not lie on any extended edge of . Then if and only if .

Keywords

Language

English

References

1.

B. Kalantari, A characterization theorem and an algorithm for a convex hull problem, to appear in Annals of Operations Research, available online August, 2014. arxiv.org/pdf/1204.1873v2.pdf, and http://arxiv-web3.library.cornell.edu/pdf/1204.1873v4.pdf, 2012. To appear in Annals of Op erations Research, 2014.

2.

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3.

B. Kalantari, Solving linear system of equations via a convex hull algorithm, arxiv.org/pdf/1210.7858v1.pdf, 2012.

4.

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5.

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6.

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