• The Mathematical Education
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• v.15 no.1
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• pp.5-7
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• 1976

Euclid 기하학이 성립하는 공간은 우리들과 가장 밀접한 공간이다. Descartes의 해석기하학은 Euclid의 3차원공간에서 성립한다. 이 경우 점이라 해도 그것은 3개의 실수의 순서쌍(x, y, z)에 의해 표현되는 것으로 생각해도 좋다. 일반의 n차원 Euclid 공간 R$^n$에 대해서도 같은 생각으로 정의할 수 있다. 이 경우 n=1은 수치선, n=2는 평면, n=3은 소위 3차원의 공간으로서 직관적으로 상상할 수 있으나 n(equation omitted)4인 경우는 상상하기 어렵다. 여기서는 거리의 성질과 추상공간을 논하고 Euclid 공간의 거리에서 출발하여 그 성질중 삼각부등식을 계산을 통하여 증명하므로서 공간의 확장화가 이루워짐을 보였다.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2020.11a
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• pp.322-324
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• 2020

본 논문에서는 스테레오 영상으로부터 얻은 특징점들을 활용하여 기초행렬(Fundamental matrix)을 추정하는 실험을 한다. 획득한 영상들은 보정이 되어 있으며, 특징점 추출 후 매칭은 RANSAC 등의 기존 알고리즘을 활용한다. 기초 행렬을 얻기 위해 스테레오 영상으로부터 정의되는 에피폴라 점, 에피폴라 선, 에피폴라 평면을 정의하고, 이들로부터 얻을 수 있는 기하학적 관계식을 활용하여 기초행렬을 수학적으로 추정해 보고, 실험으로 수학적 이론을 검증해 본다.

• The Mathematical Education
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• v.61 no.1
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• pp.47-62
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• 2022

This study investigated the contents related to the plane figures in the geometry domains of Joseon-Sanhak in the late 18th century and focused on changes in explanations and calculation methods related to plane figures, the rigor of mathematical logic in the problem-solving process, and the newly emerged mathematical topics. For this purpose, We analyzed , and written in the late 18th century and and written in the previous period. The results of this study are as follows. First, an explanation that pays attention to the figures as an object of inquiry, not as a measurement object, and a case of additional presentation or replacing the existing solution method was found. Second, descriptions of the validity of calculations in some problems, explanations through diagrams with figure diagrams, clear perceptions of approximations and explanations of more precise approximation were representative examples of pursuing the rigor of mathematical logic. Lastly, the new geometric domain theme in the late 18th century was Palsun corresponding to today's trigonometric functions and example of extending the relationship between the components of the triangle to a general triangle. Joseon-Sanhak cases in the late 18th century are the meaningful materials which explain the gradual acceptance of the theoretical and argumentative style of Western mathematics

• International Journal of Highway Engineering
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• v.10 no.1
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• pp.1-9
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• 2008

Five bases for of highways are sight distance, vehicle stability, driver comfort, drainage and aesthetics. Among these bases, the sight distance is the most critical one in the highway alignment design. It is certain that highways and drivers' observation actions are 3-dimensional in nature. But, the highway alignment design and the sight distance analysis have been performed on 2-dimensional planes because of various constraints and complexity of calculating 3-dimensional sight distance. The purpose of this study is to derive a model for determining exact available sight distance in 3-D combined horizontal and vertical alignments. Application of the model is illustrated using numerical examples. The proposed model should be useful in quantifying the criteria for 3-D highway alignments.

• Journal of Educational Research in Mathematics
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• v.25 no.2
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• pp.177-188
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• 2015

In this paper, I investigated the historical development process for the product of two vectors in the plane and space, and draw implications for educational guidance to internal and external product of vectors based on it. The results of the historical analysis show that efforts to define the product of the two line segments having different direction in the plane justified the rules of complex algebraic calculations with its length of the product of their lengths and its direction of the sum of their directions. Also, the efforts to define the product of the two line segments having different direction in three dimensional space led to the introduction of quaternion. In addition, It is founded that the inner product and outer product of vectors was derived from the real part and vector part of multiplication of two quaternions. Based on these results, I claimed that we should review the current deployment method of making inner product and outer product as multiplications that are not related to each other, and suggested one approach for connecting the inner and outer product.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.9 no.3
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• pp.75-88
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• 1989

The state-of-art knowledge of highway performance analysis model was developed in this research and a computerized process named GUCAM(Geometric-specific User Cost Analysis Model) was established to facilitate the computational procedure. A comparison of GUCAM was made to HIAP program using a case study of widening two-lane rural highway into four-lane rural. The comparison indicated that GUCAM was more realistic and sensitive to the highway geometric features by virtue of the new methodology for the distribution of highway curves and grades. However, the model still remains insensitive to improvements at isolated locations such as specific grades or curves. Further research is required to straighten out this problem.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.22 no.4
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• pp.307-314
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• 2009

The present paper briefly describes the space frame element and the fundamental strategies in computational elastic bifurcation theory of geometrically nonlinear, single load parameter conservative elastic spatial structures. A method for large deformation(rotation) analysis of space frame is based on an eulerian formulation, which takes into consideration the effects of large joint translations and rotations with finite deformation(rotation). The local member force-deformation relationships are based on the beam-column approach, and the change in member chord lengths caused by axial strain and flexural bowing are taken into account. and the derived geometric stiffness matrix is unsymmetric because of the fact that finite rotations are not commutative under addition. To detect the singular point such as bifurcation point, an iterative pin-pointing algorithm is proposed. And the path switching mode for bifurcation path is based on the non-negative eigen-value and it's corresponding eigen-vector. Some numerical examples for bifurcation analysis are carried out for a plane frame, plane circular arch and space dome structures are described.

• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.4
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• pp.16-26
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• 1989

Diffraction patterns of electromagnetic fields for the incidence of E-polarized plane wave on both interfaces of an arbitrary-angle dielect wedge are obtained by sum of geometric optics term and the edge diffracted fields. The diffraction coefficients of the edge diffracted fields are evaluated by employing the physical optics approximation and then correcting its error with the multipole line source at the dielectric edge. For the wedge angle $120^{circ}$, the incident angle $60^{circ}$, the relative dielectric constant of the dielectric wedge, 2, 5, and 10, and the observation distance from the tip of the wedge, 5 and 10 wavelength, the diffraction coefficients and the diffraction patterns corresponding to geometric optics, physical optics, and the solution corrected by the multipole line source are plotted, respectively. While the corrected solutions presented in this paper are valid only in the far-field region, these asymptotic solutions show to satisfy the boundary condition on the dielectric interfaces.

• Journal of Elementary Mathematics Education in Korea
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• v.24 no.1
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• pp.129-149
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• 2020

This study reports the results of analyzing the learning opportunities about the plane figures provided by the first and second grade mathematics textbooks. The plane figures that students learn during this period are important in that it serves as the basis for the later geometric education. With assumptions that mathematics learning is related to the problem of meaning and that meaning-related activity can be viewed as a symbolic activity, it adopts and uses the perspectives and tools of semiotics to analyze the learning opportunities provided by the mathematics textbook. The analysis of the semiotic process of the textbook activities revealed the significance of learning opportunities and helped to distinguish the seemingly similar learning opportunities. Based on the results of the analysis, I discussed the link between learning opportunities provided by grade 1 and grade 2 mathematics textbooks. Finally, the paper concludes with suggestions and conclusions and suggestions for further research.

• Journal of Korean Society of Transportation
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• v.18 no.1
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• pp.35-43
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• 2000

The Purpose of this Paper was to study the relationship between the change of operating speeds and the accidents on horizontal curves. For this purpose, we divided a horizontal curve section into two parts, a tangent section and a curve section, to estimate the operating speed for each vehicle. For studying relationship between the change of speed and geometric effect, the free-flow speed was used. The location and speed for the lowest speed were studied. Also, we analyzed the relationship between the change of operating speeds and the accidents. The followings are resulted in this study. First, drivers tend to reduce speeds significantly before they reach a curve. And the lowest speed was recorded at the downstream of the Point of curve (PC) due to the limited sight-distance of drivers on curve. Second, the larger the change of operating speeds become, the greater frequency of accident was recorded. These results can be used for developing the safety index on highways to check the design consistency.