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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.
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참고문헌 (15)
참고문헌 신청
B. Khorshidi / 2009 / A new method for finding the center of gravity of polygons / J. Geom 96 (1-2) : 81 ~ 91
D.-S. Kim / 2012 / Some characterizations of spheres and elliptic paraboloids / Linear Algebra Appl 437 (1) : 113 ~ 120
D.-S. Kim / 2013 / Some characterizations of spheres and elliptic paraboloids II / Linear Algebra Appl 438 (3) : 1356 ~ 1364
D.-S. Kim / 2015 / Ellipsoids and elliptic hyperboloids in the Euclidean space En+1 / Linear Algebra Appl 471 : 28 ~ 45
Edmonds / 2009 / The center conjecture for equifacetal simplices / Adv. Geom 9 (4) : 563 ~ 576
D.-S. Kim / 2012 / Some characterizations of spheres and elliptic paraboloids / Linear Algebra Appl 437 (1) : 113 ~ 120
D.-S. Kim / 2013 / Some characterizations of spheres and elliptic paraboloids II / Linear Algebra Appl 438 (3) : 1356 ~ 1364
D.-S. Kim / 2015 / Ellipsoids and elliptic hyperboloids in the Euclidean space En+1 / Linear Algebra Appl 471 : 28 ~ 45
Edmonds / 2009 / The center conjecture for equifacetal simplices / Adv. Geom 9 (4) : 563 ~ 576
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