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http://dx.doi.org/10.4134/CKMS.c160023

VARIOUS CENTROIDS OF POLYGONS AND SOME CHARACTERIZATIONS OF RHOMBI  

Kim, Dong-Soo (Department of Mathematics Chonnam National University)
Kim, Wonyong (Department of Mathematics Chonnam National University)
Lee, Kwang Seuk (Yeosu Munsoo Middle School)
Yoon, Dae Won (Department of Mathematics Education and RINS Gyeongsang National University)
Publication Information
Communications of the Korean Mathematical Society / v.32, no.1, 2017 , pp. 135-145 More about this Journal
Abstract
For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P. When P is a triangle, (1) we always have $G_0=G_2$ and (2) P satisfies $G_1=G_2$ if and only if it is equilateral. For a quadrangle P, one of $G_0=G_2$ and $G_0=G_1$ implies that P is a parallelogram. In this paper, we investigate the relationships between centroids of quadrangles. As a result, we establish some characterizations for rhombi and show that among convex quadrangles whose two diagonals are perpendicular to each other, rhombi and kites are the only ones satisfying $G_1=G_2$. Furthermore, we completely classify such quadrangles.
Keywords
center of gravity; centroid; perimeter centroid; rhombus; kite; polygon; quadrangle;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
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