Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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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)
  • Received : 2017.05.31
  • Accepted : 2017.08.16
  • Published : 2017.09.25
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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.

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References

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