• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.429-444
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• 2020

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.

• Bulletin of the Korean Mathematical Society
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• v.39 no.1
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• pp.97-111
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• 2002

We show that an analog of the age-Grayson-Hamilton Theorem for curves moving according to their mean curvature holds for the motion of quadrilaterals according to their Menger curvature.

• Education of Primary School Mathematics
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• v.11 no.2
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• pp.141-159
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• 2008

The purpose of this study id to delve into how elementary mathematics textbook deal with the quadrilaterals from a view of Didactic Transposition Theory. Concerning the instruction period and order, we have concluded the following: First, the instruction period and order of quadrilaterals were systemized when the system of Euclidian geometry was introduced, and have been modified a little bit since then, considering the psychological condition of students. Concerning the definition and presentation methods of quadrangles, we have concluded the following: First, starting from a mere introduction of shape, the definition have gradually formed academic system, as the requirements and systemicity were taken into consideration. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Concerning the contents and methods of instruction, we have concluded the following: First, the subject of learning has changed from textbook and teachers to students. Second, when presenting and introducing the definition, quadrilaterals were connected to real life. Third, when instructing the characteristics and inclusive relation, students could build up their knowledge by themselves, by questions and concrete operational activities. Fourth, constructions were aimed at understanding of the definition and characteristics of the figures, rather than at itself.

• Journal of Elementary Mathematics Education in Korea
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• v.9 no.2
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• pp.161-180
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• 2005

The purpose of this study is to delve into how elementary mathematics textbooks deal with the areas of triangles and quadrilaterals from a viewpoint of the Didactic Transposition Theory. The following conclusion was derived about the teaching of the area concept: The area concept started to be taught perfectly in the 7th curricular textbook, and the focus of area teaching was placed on the area concept, since learners were gradually given opportunities to compare and measure areas. As to the area formulae of triangles and quadrilaterals, the following conclusions were made: First, the 1st curricular, the 2nd curricular and the 3rd curricular textbooks placed emphasis on transposition by textbooks, and the 4th curricular, the 5th curricular and the 6th curricular textbooks accentuated transposition by teachers. The 7th curricular textbooks put stress on knowledge construction by learners; Second, the focus of teaching shifted from a measurement of area to inducing learners to make area formula. Namely, the utilization of area formula itself was accentuated, while algorithm was emphasized in the past; Third, the way to encourage learners to produce area formula changed according to the curricula and in light of learners' level, but a wide range of teaching devices related to the area formulae were removed, which resulted in offering less learning chances to students; Fourth, what to teach about the areas of triangles and quadrilaterals was gradually polished up, and the 7th curricular textbooks removed one of the overlapped area formula of triangle.

• Education of Primary School Mathematics
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• v.26 no.4
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• pp.237-255
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• 2023

At a time when the textbooks publishing system is changing from government-administered to certified, it is necessary to analyze textbooks published in both systems. This study analyzed one government textbook and three certified textbooks on quadrilaterals based on the instructional components that must be taught in the area of 2-D shapes. As a result of the analysis, it was found that concept exploration was implemented appropriately, but classification activities were not presented in some lessons. In Defining Concepts, the definition of the concept was presented appropriately, but there were differences depending on the textbooks. In addition, it was found that there was little activity in talking about the components of shapes or shapes. In applying concepts, more diverse activities were presented in certified textbooks than in government textbooks. Knowing relationships are rarely presented in textbooks due to its influence on the curriculum. Based on the results of this analysis of quadrilaterals, this study provides textbook writers with implications on what to further consider is dealing with quadrilaterals.

• Honam Mathematical Journal
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• v.39 no.2
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• pp.247-258
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• 2017

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. It is well known that P satisfies $G_0=G_1$ or $G_0=G_2$ if and only if it is a parallelogram. In this note, we investigate various quadrilaterals satisfying $G_1=G_2$. As a result, for example, we show that among circumscribed quadrilaterals kites are the only ones satisfying $G_1=G_2$. Furthermore, such kites are completely classified.

• Korean Journal of Computational Design and Engineering
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• v.20 no.4
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• pp.357-366
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• 2015

We review recent research results on coupled line cameras (CLC) as a new geometric tool to reconstruct a scene quadrilateral from image quadrilaterals. Coupled line cameras were first developed as a camera calibration tool based on geometric insight on the perspective projection of a scene rectangle to an image plane. Since CLC comprehensively describes the relevant projective structure in a single image with a set of simple algebraic equations, it is also useful as a geometric reconstruction tool, which is an important topic in 3D computer vision. In this paper we first introduce fundamentals of CLC with reals examples. Then, we cover the related works to optimize the initial solution, to extend for the general quadrilaterals, and to apply for cuboidal reconstruction.

• Journal of the Society of Naval Architects of Korea
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• v.54 no.1
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• pp.26-33
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• 2017

In this study, the surface marker method, one of the particle tracking methods, used to track the free surface is extended to cover the more general cases easily including the collision and separation of the free surface. In surface particle method to redistribute particles effectively using the grid system, the free surface is composed of the sum of quadrilaterals having four curves where fixed markers are placed at ends of each curve. Fixed markers are used to know how curves are connected to each other. The position of fixed markers can move as the free surface deforms but all fixed markers cannot be deleted during all time of simulation to keep informations of curve connection. In the case of the collision or separtion of the free surface where several curves can be intersected disorderly, severe difficulties can occur to define newly states of curve connection. In this study, the adaptable surface parTicle method without fixed markers is introduced. Intersection markers instead of the fixed markers are used to define quadrilaterals. The position of the intersection markers is defined to be the intersection point between the free surface and the edge of the grid and it can be added or deleted during the time of simulation to allow more flexibilities. To verify numerical schemes, two flow cases are simulated and the numerical results are compared with other's one and shown to be valid.

• Transactions of Materials Processing
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• v.4 no.1
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• pp.69-78
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• 1995

The arbitrary Lagrangian-Eulerian(ALE) finite element analysis is applied to the axisymmetric hot extrusion through continuous dies. In order to simulate hot forming problems, an ALE scheme for temperature analysis is proposed. The computed results are compared with experimental results as with those by pure Lagrangian method. In the present study mesh control is accomplished by the use of isoparametric mapping of quadrilaterals.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.249-260
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• 2008

In this work we propose a mixed finite volume method for the Signorini problem which are based on the idea of Keller's finite volume box method. The triangulation may consist of both triangles and quadrilaterals. We choose the first-order nonconforming space for the scalar approximation and the lowest-order Raviart-Thomas vector space for the vector approximation. It will be shown that our mixed finite volume method is equivalent to the standard nonconforming finite element method for the scalar variable with a slightly modified right-hand side, which are crucially used in a priori error analysis.