KCI등재
학술저널
VARIOUS CENTROIDS OF QUADRILATERALS WITHOUT SYMMETRY
- 충청수학회
- Journal of the Chungcheong Mathematical Society
- Volume 33, No. 4
- : KCI등재
- 2020.11
- 429 - 444 (16 pages)
DOI : 10.14403/jcms.2020.33.4.429
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 G₁G₂. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G₁=G₂ without symmetry.
1. Introduction
2. Preliminaries and Proposition A
3. Convex quadrilaterals with a pair of adjacent edges of equal length
4. Concave quadrilaterals with a pair of adjacent edges of equal length
References