Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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VARIOUS CENTROIDS OF QUADRILATERALS WITHOUT SYMMETRY

  • Kim, Incheon (Department of Mathematics Chonnam National University) ;
  • Kim, Dong-Soo (Department of Mathematics Chonnam National University)
  • Received : 2020.08.22
  • Accepted : 2020.10.05
  • Published : 2020.11.15
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Abstract

For a quadrilateral P, we consider the centroid G0 of the vertices of P, the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P, respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

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References

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