• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.27-32
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• 2017

In this paper we consider the two tangent lines of isogonal and isotomic conjugates of the line at both vertices of a given triangle. We find the necessary and sufficient condition for the two tangent lines of isogonal or isotomic conjugates of the line at both vertices and the median line to be concurrent. We also prove that every line whose isogonal conjugate tangent lines at both vertices are concurrent with the median line intersects at a unique point. Moreover, we show that the three intersection points correspond to the vertices of triangle are collinear.

• East Asian mathematical journal
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• v.29 no.4
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• pp.425-447
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• 2013

Since the center of mass of mathematics curriculum in middle school is dealt with only on triangle and it is defined as just an intersection point of median lines without any physical experiments, students sometimes have misconception of the centroid as well as it is difficult to promote divergent thinking that enables students to think the centroids of various figures. To overcome these problems and to instruct effectively the centroid unit in middle school mathematics classroom, this study suggests a teaching and learning method for the unit which uses physical experiments, drawing, and calculation methods sequentially based on the investigation of students' understanding on the centroid of triangle and the analysis of the mathematics textbooks.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.539-540
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• 2007

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.925-933
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• 2015

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.27 no.4
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• pp.94-104
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• 2004

This paper proposed a new method to evaluate service quality attribute of perceived service quality in public sectors, using triangle fuzzy numbers and hamming distance. Our method measured the ratio of the expected and perceived service for the customers' perceived service quality. By using fuzzy numbers, This method not only overcomes linguistic variable problems but also provides more objective and direct information for service quality attributes. The discrepancy rate between expected service and perceived service that is perceived service quality is evaluated by hamming distance. To evaluate the discrepancy rate from hamming distance, we induced general solutions to compute the intersection area between two triangle fuzzy numbers and the weak or strong attributes in public sectors are clarified.

• Journal for History of Mathematics
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• v.34 no.4
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• pp.137-149
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• 2021

The center of gravity of a triangle is the center of a physical shape. This is the content in the second grade of middle school, 'The Use of Similarity'. Unlike the cases of circumcenter and incenter, which are easily recognized visually, it is not easy for teachers to guide students with the visual meaning of center of gravity. According to the survey results, students, regardless of academic achievement, grade, and major, perceived the center of gravity of various plane figure as the center of their shape within a limited area through visual judgment. With reference to the results and contents of this process, it is hoped that the point of the three medians is meaningful not only in argumentative definition that the intersection of the triple line is the center of gravity of the triangle, but also in the center of a figure.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1995.04a
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• pp.603-616
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• 1995

Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, and to generate NC tool path in CAD/CAM system.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 1998.03a
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• pp.129-134
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• 1998

STL which is used in Rapid Prototyping is composed of a lot of triangular facets. The number of triangles and the shapes of these triangles determine the quality of STL. Therefore, proper algorithm is necessary to enhance the quality of triangular patch. In this paper we used the Delaunay triangulation method to apply to following processes. 1) On processing for reducing sharp triangles which cause errors on intersection. 2) On processing for connecting two or more collinear edges. 3) On processing for deleting unnecessarily inserted points in coplanar polygon.

• Journal of Korean Institute of Industrial Engineers
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• v.21 no.4
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• pp.493-506
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• 1995

Presented in this paper is an algorithm to obtain the intersections of a polyhedral surface composed of triangle facets with a series of parallel planes for extracting machining information from the surface. The change of the topology of the intersection curves is caused by characteristic points of the surface when sectioning the surface with parallel planes. The characteristic points are internal maximum, internal minimum, internal saddle, boundary maximum, boundary minimum, boundary max-saddle, and boundary min-saddle points. The starting points of the intersects are found efficiently and robustly using the characteristic points. The characteristic points as well as the intersection contours can be used to evaluate the machining information for process planning, and to generate NC tool path in CAD/CAM system.

• Journal of the Korea Society of Computer and Information
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• v.29 no.8
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• pp.59-65
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• 2024

In this paper, we present a GPU-based acceleration of computationally intensive self-collision processing in triangular mesh-based cloth simulation. For Compute Unified Device Architecture (CUDA)-based parallel optimization, we propose 1) an efficient way to build, update, and traverse the Bounding Volume Hierarchy (BVH) tree on the GPU, and 2) optimize the Representative-Triangle (R-Triangle) technique on the GPU to minimize primitive collision checking in triangular mesh-based cloth simulations. As a result, the proposed method can handle self-collisions and object collisions of cloth simulation in GPU environment faster and more efficiently than CPU-based algorithms, and experiments on various scenes show that it can achieve simulation results that are 5x to 10x faster. Since the proposed method is optimized for BVH on GPU, it can be easily integrated into various algorithms and fields that utilize BVH.