CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS

- Journal title : Communications of the Korean Mathematical Society
- Volume 31, Issue 3, 2016, pp.637-645
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.c150165

Title & Authors

CENTROIDS AND SOME CHARACTERIZATIONS OF PARALLELOGRAMS

Kim, Dong-Soo; Lee, Kwang Seuk; Lee, Kyung Bum; Lee, Yoon Il; Son, Seongjin; Yang, Jeong Ki; Yoon, Dae Won;

Kim, Dong-Soo; Lee, Kwang Seuk; Lee, Kyung Bum; Lee, Yoon Il; Son, Seongjin; Yang, Jeong Ki; Yoon, Dae Won;

Abstract

For a polygon P, we consider the centroid of the vertices of P, the centroid of the edges of P and the centroid of the interior of P, respectively. When P is a triangle, the centroid always coincides with the centroid . For the centroid of a triangle, it was proved that the centroid of a triangle coincides with the centroid of the triangle if and only if the triangle is equilateral. In this paper, we study the relationships between the centroids , and of a quadrangle P. As a result, we show that parallelograms are the only quadrangles which satisfy either $G_0

Keywords

center of gravity;centroid;polygon;triangle;quadrangle;parallelogram;

Language

English

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