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http://dx.doi.org/10.5831/HMJ.2017.39.3.431

PERIMETER CENTROIDS OF QUADRILATERALS  

Kim, Wonyong (Department of Mathematics, Chonnam National University)
Kim, Dong-Soo (Department of Mathematics, Chonnam National University)
Kim, Sangwook (Department of Mathematics, Chonnam National University)
Lim, So Yeon (Department of Mathematics, Chonnam National University)
Publication Information
Honam Mathematical Journal / v.39, no.3, 2017 , pp. 431-442 More about this Journal
Abstract
For a quadrilateral P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. We denote by M the intersection point of two diagonals of P. If P is a parallelogram, then we have $G_0=G_1=G_2=M$. Conversely, one of $G_0=M$ and $G_2=M$ implies that P is a parallelogram. In this paper, we show that $G_1=M$ is also a characteristic property of parallelograms.
Keywords
Centroid; perimeter centroid; rhombus; parallelogram; quadrilateral;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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