• Honam Mathematical Journal
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• v.39 no.3
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• pp.431-442
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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. 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.4
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• pp.105-112
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• 1984

In horizontal positioning, various methods of adjustment have been studied and developed to improve accuracy. This paper aims to present the best effective adjustment in horizontal positioning. In this study, by observation of lengths and angles, Quadrilaterals and center-point pentagon are formed and analysed with Triangulation, Trilateration and combined method.

• Journal for History of Mathematics
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• v.33 no.3
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• The Mathematical Education
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• v.53 no.3
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• pp.383-397
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• 2014

This study aims to explore secondary students' thinking while doing proof in geometry. Two secondary students were interviewed and the interview data were analyzed. The results of the analysis suggest that the two students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles to solve a given problem, b) being confused about the rules of similar and congruent triangles, and c) being confused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the results revealed that a relatively low achieving student has tendency to rely on intuitive information such as visual representations.

• International Journal of CAD/CAM
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• v.1 no.1
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• pp.11-21
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• 2002

This paper presents a triangular-to-quadrilateral mesh conversion method that can control the directionality of the output quadrilateral mesh according to a user-specified vector field. Given a triangular mesh and a vector field, the method first scores all possible quadrilaterals that can be formed by pairs of adjacent triangles, according to their shape and directionality. It then converts the pairs into quadrilateral elements in order of the scores to form a quadrilateral mesh. Engineering analyses with finite element methods occasionally require a quadrilateral mesh well aligned along the boundary geometry or the directionality of some physical phenomena, such as in the directions of a streamline, shock boundary, or force propagation vectors. The mesh conversion method can control the mesh directionality according to any desired vector fields, and the method can be used with any existing triangular mesh generators.

• Research in Mathematical Education
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• v.18 no.2
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• pp.103-128
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• 2014

This paper presents the Global van Hiele (GVH) questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. The questionnaire facilitates identification of the respondents' mastery of the first three levels of thinking according to van Hiele theory with regard to key geometrical topics. Teacher-educators can apply this questionnaire for checking preliminary knowledge of mathematics teaching candidates or pre-service teachers. Moreover, it can be used when planning a course or granting exemption from studying in basic geometry courses. The questionnaire can also serve high school mathematics teachers who are interested in exposing their students to multiple-choice questions in geometry.

• Bulletin of the Society of Naval Architects of Korea
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• v.18 no.4
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• pp.1-11
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• 1981

A flow problem around a ship hull with the nonlinear free surface boundary condition has been considered within the potential flow assumption. The Green's function based on the hull boundary condition is constructed numerically and used to satisfy the free surface boundary condition. This singularity to be distributed ideally on the undulating free surface is put actually, for practical reasons, on the flat water surface with the assumption of linear variation of velocities between the two positions. The surfaces of singularity distribution are approximated by Hess and Smith type quadrilaterals. The radiation condition is only crudely satisfied and this produced one of the major difficulties arising in the present way of attacking the problem.

• Steel and Composite Structures
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• v.51 no.3
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• pp.261-270
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• 2024

This paper proposes an effective method for optimizing the structure of functionally graded isotropic and incompressible linear elastic materials. The main emphasis is on utilizing a specialized polytopal composite finite element (PCE) technique capable of handling a broad range of materials, addressing common volumetric locking issues found in nearly incompressible substances. Additionally, it employs a continuum model for bi-directional functionally graded (BFG) material properties, amalgamating these aspects into a unified property function. This study thus provides an innovative approach that tackles diverse material challenges, accommodating various elemental shapes like triangles, quadrilaterals, and polygons across compressible and nearly incompressible material properties. The paper thoroughly details the mathematical formulations for optimizing the topology of BFG structures with various materials. Finally, it showcases the effectiveness and efficiency of the proposed method through numerous numerical examples.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.491-510
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• 2017

This study analyzes on conjecturing tasks in elementary mathematics textbook. We adopted Peircean semiotic perspective and variation theory to analyze conjecturing tasks in elementary mathematics textbook. We specifically analyzed mathematical tasks designed to support students' inquiries into definitions and properties of quardrilaterals. As a result, we found that conjecturing tasks in textbooks do not focus on supporting students' diagrammatic reasoning and inductive verification on provisional abductions. These tasks were mainly designed to support students' conjecturing on commonalities of mathematical objects rather than differences between objects.

• Journal of KIISE:Software and Applications
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• v.30 no.1_2
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• pp.31-39
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• 2003

It is often assumed that text regions in images are characterized by some distinctive or characteristic spatial frequencies. This feature is highly intuitive, and thus appealing as much. We propose a method of detecting horizontal texts in natural scene images. It is based on the use of two features that can be employed separately or in succession: the frequency of edge pixels across vertical and horizontal scan lines, and the fundamental frequency in the Fourier domain. We confirmed that the frequency features are language independent. Also addressed is the detection of quadrilaterals or approximate rectangles using Hough transform. Since texts that is meaningful to many viewers usually appear within rectangles with colors in high contrast to the background. Hence it is natural to assume the detection rectangles may be helpful for locating desired texts correctly in natural outdoor scene images.