• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.263-287
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• 2010

The purposes of the study were to investigate how children define a triangle, their reasoning types in identifying examples and non-examples of a triangle, and the relationship between their reasoning types and geometrical levels. Twenty-nine students consisted of 3th to 6th grades were involved in the study. Using the van Hiele levels of geometrical thought, children's reasoning types for identifying a figure as a triangle or non-triangle were categorized into visual reasoning, reasoning based on the figure's attributes and formal reasoning. The figure's attributes were further divided into critical and non-critical attributes. Most children identified a figure as a triangle or non-triangle based on critical attributes of the figure(e.g. closed figure, three, vertices, straight sides etc.) Some children identified a figure based on non-critical attributes of the figure(e.g. the length of the sides, the measurement of the angles, or the orientation of the figure). Particularly, some children who had lower levels of geometry identified a figure using visual reasoning, taking in the whole shape without considering that the shape is made up of separate components.

• The Mathematical Education
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• v.46 no.4
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• pp.493-502
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• 2007

What is a foundational element of plane geometry? Isn't it possible to constitute the contents of plane geometry from that element? In this paper, we suggest a view point that triangle is a foundational element of plane geometry. And take some examples of reconstruction of usually given contents and mathematical activity centered on the triangle in plane geometry.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.637-645
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• 2016

For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. When P is a triangle, the centroid $G_0$ always coincides with the centroid $G_2$. For the centroid $G_1$ of a triangle, it was proved that the centroid $G_1$ of a triangle coincides with the centroid $G_2$ of the triangle if and only if the triangle is equilateral. In this paper, we study the relationships between the centroids $G_0$, $G_1$ and $G_2$ of a quadrangle P. As a result, we show that parallelograms are the only quadrangles which satisfy either $G_0=G_1$ or $G_0=G_2$. Furthermore, we establish a characterization theorem for convex quadrangles satisfying $G_1=G_2$, and give some examples (convex or concave) which are not parallelograms but satisfy $G_1=G_2$.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.886-889
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• 2004

A simple macro triangle with drilling d.o.f.'s is proposed for plane stress problems based on IET(Individual element test) and finite element template. Three-node triangular element has geometrical advantages in preprocessing but suffers from bad performance comparing to other shapes of elements -especially quadrilateral. Main purpose of this study is to construct a high-performance linear triangular element with limited supplementary d.o.f.'s. A triangle is divided by three sub-triangles with drilling d.o.f.'s. The sub-triangle stiffness come from IET passing force-lumping matrix, so this assures the consistency of the element. The macro element strategy takes care of the element‘s stability and accuracy like higher-order stiffness in the F.E. template. The resulting element fits on the uses of conventional three-node. Benchmark examples show proposed element in closed form stiffness from CAS (Computer algebra system) gives the improved results without more computational efforts than others.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.41-44
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• 2001

In reverse engineering, the whole surfaces of the three-dimensional(3D) product are measured using 3D positional scanners. The raw triangle meshes constructed from a scanned point set are not well suited for direct use in the downstream activities. This is because the amount of triangle meshes may be very large(from millions to hundreds of millions) and usually distorted by scanning error. Furthermore, the triangle meshes may contain several holes that must be filled. Thus, several solutions have to be addressed and implemented before a complete CAD models can be acquired. This paper discusses on the algorithms of decimation, smoothing, and hole-filling that are crucial to refine the triangle meshes. Several examples are also given and discussed to validate the system.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2007.06a
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• pp.37-50
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• 2007

What is a foundational element of plane geometry? Isn't it possible to constitute the contents of plane geometry from that element? In this paper, we suggest a view point that triangle is a foundational element of plane geometry. And take some examples of reconstruction of usually given contents and mathematical activity centered on the triangle in plane geometry.

• The Mathematical Education
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• v.46 no.1 s.116
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• pp.69-79
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• 2007

Students experience many problem solving activities in school mathematics. These activities have focused on finding the solution whose existence was known, and then again conjecture about existence of solution or posing of problems has been neglected. It needs to put more emphasis on conjecture and problem posing activities in school mathematics. To do this, a model and examples of designing mathematical activities centered on conjecture and problem posing are needed. In this article, we introduce some examples of designing such activities (from the pythagorean theorem, the determination condition of triangle, and existing solved-problems in textbook) and examine suggestions for mathematics education. Our examples can be used as instructional materials for mathematically able students at middle school.

• Journal of the Korean Data and Information Science Society
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• v.20 no.2
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• pp.411-423
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• 2009

In the current paper, by extending Verall (1990)'s work, we propose a new Bayesian model for analyzing run-off triangle data. While Verall's (1990) work only account for the calendar year and evolvement time effects, our model further accounts for the "absolute time" effects. We also suggest a Markov Chain Monte Carlo method that can be used for estimating the proposed model. We apply our proposed method to analyzing three empirical examples. The results demonstrate that our method significantly reduces prediction error when compared with the existing methods.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.6
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• pp.929-937
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• 2011

This thesis is intended for addressing issues of the local expropriation committee system by drawing the policy suggestion through theoretical considerations on the land expropriation system of the UK and of the US, and for finding a plan to improve the system by focusing on the examples of land expropriation of local governments. The US' Takings utilize a public hearing and the jury system. When property is expropriated through eminent domain, stakeholders and citizens share the necessity of the expropriation and its awareness through a public hearing, and project institutes (administrative organizations) file a lawsuit to a law court to exercise takings. In the case of Compulsory Purchase in the UK, the system should be based on laws established by the Parliament, and the resolution to use CPO is also decided by district councils. So the system is able to prevent power abuse. As a plan to improve the land expropriation committee of local governments, it is necessary ${\triangle}$ to enhance the professionality of the local land expropriation committee, ${\triangle}$ to expropriate lands by the analysis of land type, and ${\triangle}$ to come up with alternative measures to prevent the rights of the expropriated.

• Journal of the Korean Society for Precision Engineering
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• v.21 no.4
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• pp.140-147
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• 2004

In reverse engineering, the whole surfaces of the three-dimensional product are measured using 3D positional scanners. The raw triangle meshes constructed from a scanned point set are not well fitted for direct use in the downstream engineering or graphic activities. No object can be fully described by a single scan. Although multiple scans are usually taken and aligned to achieve a complete model, a set of scanned points does not entirely wrap the whole object. This is because some surfaces may be inaccessible to the scanner, so some portion of the scanned surface may be missing. This paper discusses the algorithms of a hole-filling that are crucial to refine the triangle meshes. In this paper, the holes are filled with flat triangles first by subdivision operation and then smoothed with neighboring triangles. This process continues until it converges to a certain user-defined iteration number. Examples are given and discussed to validate the system.