• The Mathematical Education
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• v.6 no.2
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• pp.1-9
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• 1968

In mathematics, a definition must have authentic reasons to be defined so. On defining geometric figures, there must be adequencies in sequel and consistency in the concepts of figures, though the dimensions of them are different. So we can avoid complicated thoughts from the study of geometric property. From the texts of SMSG, UICSM and others, we can find easily that the same concepts are not kept up on defining some figures such as ray and segment on a line, angle and polygon on a plane, and polyhedral angle and polyhedron on a 3-dimensionl space. And the measure of angle is not well-defined on basis of measure theory. Moreover, the concepts for interior, exterior, and frontier of each figure used in these texts are different from those of general topology and algebraic topology. To avoid such absurdness, I myself made new terms and their definitions, such as 'gan' instead of angle, 'polygonal region' instead of polygon, and 'polyhedral solid' instead of polyhedron, where each new figure contains its interior. The scope of this work is hmited to the fundamental idea, and it merely has dealt with on the concepts of measure, dimension, and topological property. In this case, the measure of a figure is a set function of it, so the concepts of measure is coincided with that of measure theory, and we can deduce the topological property for it from abstract stage. It also presents appropriate concepts required in much clearer fashion than traditional method.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.209-221
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• 2018

Angle concepts have a multifaceted nature such as quantitative aspects as the amount of rotation, qualitative aspects as geometric shapes, and relationship aspects made with planes or lines. This study analysed angle concepts and introduction methods of angles in elementary mathematics textbooks which have been used from the Syllabus Period to the 2015 Revised Mathematics Curriculum. First, the concepts of angles in mathematics textbooks focus through the definitions, representations, and components of angles presented in mathematics textbooks are analyzed. Secondly, how various aspects of each angle are sequenced through the tasks or activties in the introduction of lesson is looked. As a result of analysis, the methods of introducing angles in the changes of mathematics textbooks have mainly focused on learning about geometric shapes and relations of components. In the mathematics classroom, students should experience various aspects of geometric shapes, rotations, relational aspects of points, lines and surfaces, and support and link them to form a wide range of concepts.

• Journal of ILASS-Korea
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• v.11 no.4
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• pp.244-250
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• 2006

Of the macroscopic spray characteristics of non-reacting diesel fuel sprays, the spray angle reflects directly the atomization and air entrainment processes downstream the nozzle. In addition, spray angle is important because it will be closely related to the spray penetration. The existing definitions for the measurement of spray angle as well as the correlations for the prediction of spray angle are, therefore, summarized and reviewed. The existing definition of spray angle can be classified into four groups: distance based on orifice diameter, distance based on spray tip penetration, definition based on surface wave, and definition based on atomization. It is strongly required to specify the definition and measurement method when the data for spray angle is reported. The existing correlations for spray angle can be classified into two groups: theoretical and empirical correlations. The study on the evaluation of the existing correlations fer spray angle is required.

• Journal for History of Mathematics
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• v.29 no.3
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• pp.191-216
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• 2016

Moulton plane is the plane where all the plane axioms of Hilbert except the side-angle-side axiom hold true, and enables us to understand the importance and significance of the side-angle-side axiom. In this article, we start with the definitions of the Moulton lines, distance, angle, and then introduce many theorems of the Moulton geometry, with many intuitive proofs or explanations of our own with appropriate examples. In particular, we provide our independent study of the tangent lines to the Moulton circles and the rigid motions of the Moulton plane.

• Journal of ILASS-Korea
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• v.16 no.1
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• pp.15-26
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• 2011

In this article, spray characteristics in CI engines fuelled with vegetable oils and its derivatives will be reviewed. Of edible vegetable oils, soybean oil and rapeseed oil were mainly investigated. Of inedible vegetable oils, jatropha oil and used frying oil were main concern on the research on the spray characteristics in CI engine. Spray angle and spray penetration were mainly examined among the macroscopic spray characteristics and Sauter mean diameter was only investigated among the microscopic spray characteristics. There exist six different definitions of spray angle which should be examined. Neat vegetable oil and biodiesel fuels show smaller spray angle than diesel fuel. Biodiesel fuel and vegetable oils and its blend have a longer spray penetration than diesel fuel. However, biodiesel blends with diesel shows the similar spray penetration with diesel fuel. SMDs in the biodiesel spray, vegetable oils and its blends spray are higher than that in the diesel spray.

• (The) Research of the performance art and culture
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• no.32
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• pp.243-267
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• 2016

Deonum preexisted prior to it being named. Of course, the object designated as deonum at that time is not the same as the object designated as deonum at this time. There have been historical transitions in the definitions of the term deonum. This paper traced the term deonum to its origin from another angle. On closer inspection about the possible use as the everyday language and the technical language in the field of arts except for pansori, the term deonum was essentially a word for a tune. Deonum was in the same category as deureum, a great word in the Korean traditional music. But the definition of deonum as a tune used in the early part of the former period of eight master singers or before that gradually disappeared for a long time. When the term deonum as an everyday language first entered the field of pansori, it meaned characteristic tune singed by master singers. As pansori develop artistically, the term deonum changed into the word refers to the sori part, and this example become common in the former period of eight master singers. Most sori part acknowledged as a deonum in the former period of eight master singers was a deonum as a creative repertories, the master singer's creative work, but a deonum as a popular repertories, the master singer's specialty, began to be acknowledged as a deonum after the latter period of eight master singers. The differentiation between the definitions of deonum as a sori part occured. And most sori part acknowledged as a deonum after the modern era of five master singers have belonged to a deonum as a specialty. In this context, it was confirmed that Cheong Nosik wrote Joseonchanggeuksa, with carefully considering the historical change of definitions of deonum. This book includes three definitions of deonum, a deonum as a tune, a deonum as a creative work, and deonum as a specialty.

• School Mathematics
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• v.18 no.2
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• pp.425-440
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• 2016

Concept images play an important role in the acquisition of mathematical concept. However, sometimes concept images are derivatives of student's misconceptions. In addition, students always learn concept images despite teachers' efforts to teach concept definitions. Therefore, teachers need to know about all the concept images of a particular concept. This study aimed to analyze the concept image that students have about the triangle when they have already learned about the triangle in school. It was found that some students have different concept images about the triangle between Semo. Moreover, many students have misconceptions about vertices, sides, and angles. In particular, students think Gak denotes a side, although it means angle. Based on these results, I suggest that the curriculum and textbook require improvement.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2000.04b
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• pp.51-58
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• 2000

Lateral buckling behavior of laminated composite thin-walled I-section beams subjected to bending moment is investigated by applying the nonlinear anisotropic thin-walled beam theory. The constituent laminated thin-walled elements of I-section are assumed to be symmetrically laminated. The bending, twisting, and warping stiffnesses of the cross section are obtained based on the definitions of these stiffnesses In the thin-walled anisotropic beam theory In numerical examples, singly-symmetric I-beams with specially orthotropic, quasi-isotropic, angle-plys and various boundary conditions are considered. To validate the proposed theoretical approach, present analytical solutions are compared with three dimensional finite element solutions.

• Steel and Composite Structures
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• v.16 no.4
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• pp.375-387
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• 2014

The purpose of this paper is to propose a method for evaluation of varying stiffness coefficients of tailored conical shells (TCS). Furthermore, a comparison between buckling loads of these shells under axial load with the different fiber path is performed. A circular truncated conical shell subjected to axial compression is taken into account. Three different theoretical path containing geodesic path, constant curvature path and constant angle path has been considered to describe the angle variation along the cone length, along cone generator of a conical shell are offered. In the TCS with the arbitrary fiber path, the thickness and the ply orientation are assumed to be functions of the shell coordinates and influencing stiffness coefficients of the structure. The stiffness coefficients and the buckling loads of shells are calculated basing on classical shells theory (CST) and using finite-element analysis (FEA) software. The obtained results for TCS with arbitrary fiber path, thickness and ply orientation are derived as functions of shell longitudinal coordinate and influencing stiffness coefficients of structures. Furthermore, the buckling loads based on fiber path and ply orientation at the start of tailored fiber get to be different. The extent of difference for tailored fiber with start angle lower than 20 degrees is not significant. The results in this paper show that using tailored fiber placement could be applied for producing conical shells in order to have greater buckling strengths and lower weight. This work demonstrates the use of fiber path definitions for calculated stiffness coefficients and buckling loads of conical shells.

• Journal of Multimedia Information System
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• v.4 no.3
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• pp.107-114
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• 2017

As to talk about computer aided 3D modeling, it can be conformed to the popular aesthetics based theory of heightening the organizing useful visual information. This thesis heightens the formativeness of the 3D modeling from the angle of the Gestalt psychology and attempts a finding of a method as also explains among the grouping laws of Gestalt. They are the definitions and the special features of 'The Law of Proximity', 'The Law of Similarity', 'The Law of Closure', 'The Law of Continuity', etc. And, through a logical, theoretical analysis, the relationships between such laws are found out. And the case examples of the uses of such laws in the 3D animation character designs and the situation in which such laws are applied to the things in the actual lives are analyzed. If it is intended to improve the formativeness of the 3D model forms, the rules of the simplicity, the safety, and the symmetry must be pursued according to the visual recognitions of the human beings. Because the actual objects are seen and touched, other than the visual pursuits by the human beings, the functionalities and the practicalities of the objects must be considered.