• Transactions of Materials Processing
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• v.21 no.4
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• pp.252-257
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• 2012

Crystallographic texture evolution during forming processes has a significant effect on the anisotropic flow behavior of crystalline material. In this study, a crystal plasticity finite element method (CPFEM), which incorporates the crystal plasticity constitutive law into a three-dimensional finite element method, was used to investigate texture evolution of a face-centered-cubic material - an aluminum alloy. A rate-dependent polycrystalline theory was fully implemented within an in-house program, CAMPform3D. Each integration point in the element was considered to be a polycrystalline aggregate consisting of a large number of grains, and the deformation of each grain in the aggregate was assumed to be the same as the macroscopic deformation of the aggregate. The texture evolution during three different deformation modes - uniaxial tension, uniaxial compression, and plane strain compression - was investigated in terms of pole figures and compared to experimental data available in the literature.

• Steel and Composite Structures
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• v.10 no.2
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• pp.151-168
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• 2010

The subject of the paper is an isotropic metal foam rectangular plate. Mechanical properties of metal foam vary continuously through plate of the thickness. A nonlinear hypothesis of deformation of plane cross section is formulated. The system of partial differential equations of the plate motion is derived on the basis of the Hamilton's principle. The system of equations is analytically solved by the Bubnov-Galerkin method. Numerical investigations of dynamic stability for family rectangular plates with respect analytical solution are performed. Moreover, FEM analysis and theirs comparison with results of numerical-analytical calculations are presented in figures.

• Journal for History of Mathematics
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• v.36 no.1
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• pp.1-17
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• 2023

Paper folding is a versatile tool that can be used not only as a mathematical model for analyzing the geometric properties of plane and spatial figures but also as a visual method for finding the real roots of polynomial equations. The historical evolution of origami's geometric and algebraic techniques has led to the discovery of definitions and properties that can enhance one's cognitive understanding of mathematical concepts and generate mathematical interest and motivation on an emotional level. This paper aims to examine the history of origami geometry, the utilization of origami for solving polynomial equations, and the process of determining the real roots of quadratic, cubic, and quartic equations through origami techniques.

• East Asian mathematical journal
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• v.30 no.2
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• pp.173-195
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• 2014

This study, utilizing several features about plane figures covered in the current secondary curriculum of mathematics and reviewing two solutions to cube duplication problem presented by Menaechmus, proving the solution by Nicomedes and visualizing solutions based on Apollonius' 'Conics' by medieval Islam geometricians such as Ab$\bar{u}$ Bakr al-Haraw$\bar{i}$, AbAb$\bar{u}$ J$\acute{a}$far al-Kh$\bar{a}$zin, Nas$\bar{i}$r al-D$\bar{i}$n al-T$\bar{u}s\bar{i}$, Y$\bar{u}$suf al-Mu'taman ibn H$\bar{u}$d, introduce to teachers and students in the field where the question of cube duplication problem comes from and which solving method has developed it and suggests new methods for visualization using dynamic geometry program as well so that the contents reviewed can be used in the filed. The solving methods to cube duplication problem in this paper are very creative and increase the practicality, efficiency and value of Mathematics, and provide students and teachers with the opportunities to reconfirm the importance and beauty of basic knowledge in the secondary geometry in the process of visualization of drawing figures using dynamic geometry program.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.5
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• pp.89-100
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• 2001

The Ritz method Is applied In a three-dimensional (3-D) analysis to obtain accurate frequencies for thick. linearly tapered. annular plates. The method is formulated for annular plates haying any combination of free or fixed boundaries at both Inner and outer edges. Admissible functions for the three displacement components are chosen as trigonometric functions in the circumferential co-ordinate. and a1gebraic polynomials in the radial and thickness co-ordinates. Upper bound convergence of the non-dimensional frequencies to the exact values within at least four significant figures is demonstrated. Comparisons of results for annular plates with linearly varying thickness are made with ones obtained by others using 2-D classical thin place theory. Extensive and accurate ( four significant figures ) frequencies are presented 7or completely free. thick, linearly tapered annular plates haying ratios of average place thickness to difference between outer radius (a) and inner radius (b) radios (h$_{m}$/L) of 0.1 and 0.2 for b/L=0.2 and 0.5. All 3-D modes are included in the analyses : e.g., flexural, thickness-shear. In-plane stretching, and torsional. Because frequency data liven is exact 7o a\ulcorner least four digits. It is benchmark data against which the results from other methods (e.g.. 2-D 7hick plate theory, finite element methods. finite difference methods) and may be compared. Throughout this work, Poisson\`s ratio $\upsilon$ is fixed at 0.3 for numerical calculations.s.

• Journal of Elementary Mathematics Education in Korea
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• v.17 no.2
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• pp.245-263
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• 2013

Mathematical learning via projects, which enables the reconstruction of curriculum through integration and emphasizes the process of solving problems by posing questions, has attracted the attention of the department of mathematics. This research is aimed at exploring the link between mathematics and project learning by analyzing an example of student-oriented project 'the secrets of pyramid' focused on understanding 'triangle' specifically designed for forth graders. From 115-hour process of subject-oriented project, this study reinterpreted the mathematical meaning of only 24 hours directly related to mathematics, especially to figure exploration. Consequently, this problem solving involved a variety of geometric activities as a process, such as measuring an angle, constructing a triangle, etc. Thus students attempt to actively participate in the process, thereby allowing them to learn how to measure things more accurately. Moreover, project learning improved students' understanding on not only plane figures but solid figures. This indicates that by project learning, learning from given problems or contents can be extended to other mathematical areas.

• Journal of Elementary Mathematics Education in Korea
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• v.13 no.1
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• pp.115-140
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• 2009

Freudenthal has advocated the mathematisation theory. Mathematisation is an activity which endow the reality with order, through organizing phenomena. According to mathematisation theory, the departure of children's learning of mathematics is not ready-made formal mathematics, but reality which contains mathematical germination. In the first place, children mathematise reality through informal method, secondly this resulting reality is mathematised by new tool. Through survey, it turns out that area unit of Korea's seventh elementary mathematics textbook is not correspond to mathematisation theory. In that textbook, the area formular is hastily presented without sufficient real context, and the relational understanding of area concept is overwhelmed by the practice of the area formular. In this thesis, first of all, I will reconstruct area unit of seventh elementary textbook according to Freudenthal's mathematisation theory. Next, I will perform teaching experiment which is ruled by new lesson design. Lastly, I analysed the effects of teaching experiment. Through this study, I obtained the following results and suggestions. First, the mathematisation was effective on the understanding of area concept. Secondly, in both experimental and comparative class, rich-insight children more successfully achieved than poor-insight ones in the task which asked testee comparison of area from a view of number of unit square. This result show the importance of insight in mathematics education. Thirdly, in the task which asked testee computing area of figures given on lattice, experimental class handled more diverse informal strategy than comparative class. Fourthly, both experimental and comparative class showed low achievement in the task which asked testee computing area of figures by the use of Cavalieri's principle. Fifthly, Experiment class successfully achieved in the area computing task which resulting value was fraction or decimal fraction. Presently, Korea's seventh elementary mathematics textbook is excluding the area computing task which resulting value is fraction or decimal fraction. By the aid of this research, I suggest that we might progressively consider the introduction that case. Sixthly, both experimental and comparative class easily understood the relation between area and perimeter of plane figures. This result show that area and perimeter concept are integratively lessoned.

• The Research Journal of the Costume Culture
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• v.1 no.2
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• pp.131-144
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• 1993

Even though it has been to research on the variance of clothing pressure and on its effect of human body, it has not been available to evaluate the clothing pressure as an objective standard ta for the determination of an extra quantity of bodice' basic pattern. In this paper the basic pattern(the close adherence original shape) is determined by a drawing of plane figure after detaching an unweaving clothing from the inside of the gypsum, and the extra quantity is figured by a extension quantity when is formatted with 0.5, 1.0, 1.5 cm extra quantity longitudinal-cross section figures. With our experimental method, review the variance of clothing pressure according to difference of the extra quantity which was figured with subjects wearing experimental clothing including the extra quantity. The difference of the extra quantity was able to calculate with data form the subjects when anatomical position and five movements, then compare with subjects wearing non-extra quantity experimental clothing. The results of experiment as the follows : 1. There is only few body portions with the significant variance according to the increasing of he extra quantity at he body portion and the sleeve portion. 2. The clothing pressure of the sleeve portion was higher than the clothing pressure of the body portion. The difference of clothing pressure according to the variance of the extra quantity at the sleeve portion is more significant than the body portion. 3. Consider several important pressure points which wil be the No. 1 at the front of body portion. No. 17, 18 at the back of body portion and No. 21 at the sleeve portion. 4. It is important to have plane figure of gypsum when format an basis pattern.

• Korean Journal of Human Ecology
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• v.9 no.1
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• pp.51-61
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• 2006

The purpose of this study is to examine the relation between the trend of art and fashion which predominate a certain time. In order to achieve this goal, this study intends to analyze how plasticity found in Mondrian's pictures are applied to modern fashion with its focus on formative elements. Mondrian was ahead of abstractionism, a major trend of contemporary art, and defined the theory of neo-plasticism. The theory of neo-plasticism defined by Mondrian is characterized by the limited expression of lines and shapes by using only vertical and horizontal straight lines, and right angles and four-sided figures weaved by the lines, and the use of achromatic color(black, white, and gray) in three primary colors(red, blue, and yellow). Based on his theory, he fully displayed the world of geometric abstraction. Mondrian's formative elements which have been applied in modern fashion can be divided into shape and color, For the element of shape, first, horizontal and vertical lines have been applied to patterns, trimmings, detail, and plane of textiles through simplification of design, representing proportion, balance, and stress in a silhouette, Second, plane and diamond shapes made of horizontal and vertical lines have been applied to textiles or patterns with uniqueness. For the element of color, first, three primary colors and achromatic colors are used to seek the aesthetics of balance and harmony that are produced in the strain of conflict through brightness, chroma, and complementary colors, Second, primary colors of high chroma and brightness which are much stronger than pictures are used to express a modern sense. Formative elements of neo-plasticism, which have been applied to modern fashion suggested by this study, are connected with the trend of art contemporary designers have borrowed, Accordingly, this study will become a very helpful material which provides designers with original ideas in developing materials and patterns which connect design with art.

• The Research Journal of the Costume Culture
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• v.11 no.3
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• pp.367-374
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• 2003

When analyzing forms in the human body and clothes, we conceptualize each part into a cone, sphere, and cylinder, and the esthetic characteristics of our fashion culture and esthetic fashion characteristics of Koreans are composed by expressing with universal images such as circle, square, and triangle when forms are expressed in a plane. To determine how the structural principle of shapes that are the shapes of all things and basic to geometry, i.e., circle, square, and triangle, applies to clothes that cloth our body called the small cosmos, we discussed the symbolic meaning hidden inside the structure of Korean clothes based on the basic pattern drafting method of Korean men’s traditional trousers. We drew the conclusion that Korean men's trousers composed of circles, triangles, and squares express the five elements diagram through their plane structure, are designed in circles with cones and pyramids, and are made to well express the principle of the small cosmos of our body. Moreover, when the basic pattern of Korean men’s trousers explained with the antipathy diagram is viewed to create all things while maintaining opposite and complementary relationship with Sangsang (mutually benefitting factor), it would be correct to say that the principle of the top verse the bottom is viewed as conflicting. From the structural point of view, since the philosophy of the Samsu principle (the principle of 1, 2 and 3 in which 1 represents the heaven, 2 represents the earth, and 3 represents the people) is hidden in Korean men's trousers in which Hurimalgi (the part of trousers corresponding to the waist band of Western pants) is the circle representing the heaven, Marupok is the square representing the earth, and Sapok is the triangle representing the people, we could look at deep meaning of our ancestors expressed in our clothes.