• Journal of Astronomy and Space Sciences
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• v.41 no.2
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• pp.87-106
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• 2024

The objective of this research is to address the issue of frozen orbits in charged satellites by incorporating geopotential zonal harmonics up to J6 and the initial tesseral harmonics. The employed model starts from the first normalized Hamiltonian to calculate specific sets of long-term frozen orbits for charged satellites. To explore the frozen orbits acquired, a MATHEMATICA CODE is developed. The investigation encompasses extensive variations in orbit altitudes by employing the orbital inclination and argument of periapsis as freezing parameters. The determined ranges ensuring frozen orbits are derived from the generated figures. Three-dimensional presentations illustrating the freezing inclination in relation to eccentricity, argument of periapsis, and semi-major axis parameters are presented. Additional three-dimensional representations of the phase space for the eccentricity vector and its projection onto the nonsingular plane are examined. In all investigated scenarios, the impacts of electromagnetic (EM) field perturbations on the freezing parameters of a charged satellite are demonstrated.

• Journal of Educational Research in Mathematics
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• v.21 no.2
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• pp.181-199
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• 2011

The area formula for a plane figure represents the relations between the area and the lengths which determine the area of the figure. Students are supposed to understand the relations in it as well as to be able to find the area of a figure using the formula. This study investigates how 5th grade students understand the formulas for the area of triangle, rectangle and parallelogram, focusing on their understanding of functional relations in the formulas. The results show that students have insufficient understanding of the relations in the area formula, especially in the formula for the area of a triangle. Solving the problems assigned to them, students developed three types of strategies: Substituting numbers in the area formula, drawing and transforming figures, reasoning based on the relations between the variables in the formula. Substituting numbers in the formula and drawing and transforming figures were the preferred strategies of students. Only a few students tried to solve the problems by reasoning based on the relations between the variables in the formula. Only a few students were able to aware of the proportional relations between the area and the base, or the area and the height and no one was aware of the inverse relation between the base and the height.

• Journal of Educational Research in Mathematics
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• v.23 no.2
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• pp.135-152
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• 2013

The purpose of this study is to navigate to the desired direction for the figure of number line through the extensive analysis of number line in middle school textbooks and literatures. For the efficient achievement of this purpose, three research questions were posed as follows: First, we compare the figures of number line in textbooks of Korea and other countries. Korean math textbooks mark the arrow on both sides of number line. But, however, coordinate plane was marked with arrow on only positive direction of number line. In contrast, the majority of secondary school textbooks in several foreign countries has the arrow only on positive direction. Second, the change in the figure of number line has been analyzed historically from two perspectives. From the first to 2007-revised curriculum, math textbooks of Korea were analyzed. Since the 6th curriculum, the number of textbooks with arrows on both sides has increased sharply. That is, textbooks with one arrow almost have disappeared. It is strange that any explanation for this abrupt change can't be found. The following analysis was also performed on published foreign literatures since Descartes. There was no arrow in the early figures of number line. But after 19th century, number lines with one arrow have begun to appear. Third, based on the previous study, we propose a reasonable way for the figure of number line. In fact, we claim that, in terms of linguistic symbols, the number line should be with only one arrow on positive side.

• The Journal of the Korea Contents Association
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• v.19 no.11
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• pp.527-548
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• 2019

For Deleuze, the frame is a closed system with numerous subsets of information. the frame can be defined by mathematics and physics. it is a geometric system of equilibrium and harmony with variables or coordinates. like paintings, Linear perspective represents a three-dimensional depth in a two-dimensional plane through vanishing points, horizontal lines in the frame. Linear perspective makes it possible to assume the infinity towards the vanishing point and the infinity towards the outside of the frame, the opposite of the vanishing point. Not only figures and lines in the drawing paper, but also the space between the figures and lines in the drawing paper was recognized. that is space, the 3rd dimension. with the centripetal force and centrifugal force of the frame, frame follow the physical rules of power and movement. de framing is against the dominant linear perspective and central tendency of the frame. The film contains four-dimensional time while reproducing three-dimensional space in two dimensions. It may be that the outside of the frame, or outside the field of view, contains thought, the fifth dimension.

• Journal of Fashion Business
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• v.10 no.5
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• pp.159-179
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• 2006

This research checked about the necessity for the development of men's dress forms in the first investigation for the educational circle and the men's wear industry. Somatotype characteristics were analyzed in the second investigation of body measurement with the subjects of 200 male adults in their twenties residing in Busan. The following are the results of the present research to develop male dress forms for patternmaking: 1. In the group analysis for the characterization of front body types, three somatotypes were found and named H, Semi X, and Y. In the cluster analysis of side body types, four types were identified: D, I, d, and q. In the combination of front and lateral body types, four kinds were chosen: semi X-I, semi X-q, semi Y-I, and Y-q. 2. Through the comparison of plane figures by the plaster method as well as horizontal and vertical cross sections by the sliding gauge method, semi X-I was finally chosen as the standard somatotype for male dress form development. 3. Compared with the sliding gauge method of the present dress forms, the research dress form reflected better the shapes of the parts of the back and hips and the position of the waist, especially for males in their 20's. In addition, the dress form in the current research had superior points in all the items of clothing evaluation. Based on the above results, the sizes and models of the men's dress forms for patternmaking were developed.

• Journal of Educational Research in Mathematics
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• v.16 no.1
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• pp.1-23
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• 2006

It is regarded as critical to analyse and re-appreciate Euclidean geometry for the sake of improving school geometry This study, a critical analysis of demonstrative plane geometry in current secondary school mathematics with an eye to the viewpoints of 'Elements of Geometry', is conducted with this purpose in mind. Firstly, the 'Elements' is analysed in terms of its educational purpose, concrete contents and approaching method, with a review of the history of its teaching. Secondly, the 'Elemens de Geometrie' by Clairaut and the 'histo-genetic approach' in teaching geometry, mainly the one proposed by Branford, are analysed. Thirdly, the basic assumption, contents and structure of the current textbooks taught in secondary schools are analysed according to the hypothetical construction, ordering and grouping of theorems, presentations of proofs, statements of definitions and exercises. The change of the development of contents over time is also reviewed, with a focus on the proportional relations of geometric figures. Lastly, tile complementary way of integrating the two 'Elements' is explored.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.499-524
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• 2015

In the present study, we propose four participating $8^{th}$ grade students' genetic decomposition of congruent transformation and investigate the role of their dragging activities while understanding the concept of congruent transformation in GSP(Geometer's Sketchpad). The students began to use two major schema, 'single-point movement' and 'identification of transformation' simultaneously in their transformation activities, but they were inclined to rely on the single-point movement schema when dealing with relatively difficult tasks. Through dragging activities, they could expand the domain and range of transformation to every point on a plane, not confined to relevant geometric figures. Dragging activities also helped the students recognize the role of a vector, a center of rotation, and an axis of symmetry.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.425-441
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• 2009

The cube-accumulation is a new theme included in the 7th elementary mathematics curriculum for improving children's spatial ability. One activity of the cube-accumulation is to recognize the configuration of accumulated cube given three plane figures in the directions of the above, the front and the side, respectively. The approach to this activity presented in the mathematics textbook is more or less intuitive and constructive, and difficult to some children. So we suggest an alternative, more analytic method, 'elimination method', that is eliminating unnecessary parts from $n{\times}n{\times}n$ whole cubes. This method was adopted to the 32 sixth graders, in special five applicants among them. Their responses and activities were analyzed. We confirm that we can teach the cube-accumulation by the elimination method, and some children prefer this method. 13u1 this method requires more exercises to be executed skillfully.

• Communications of Mathematical Education
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• v.32 no.3
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• pp.297-314
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• 2018

This article aims at providing implication for teacher preparation program through interpreting pre-service teachers' knowledge by using Shulman-Fischbein framework. Shulman-Fischbein framework combines two dimensions (SMK and PCK) from Shulman with three components of mathematical knowledge (algorithmic, formal, and intuitive) from Fischbein, which results in six cells about teachers' knowledge (mathematical algorithmic-, formal-, intuitive- SMK and mathematical algorithmic-, formal-, intuitive- PCK). To accomplish the purpose, five pre-service teachers participated in this research and they performed a series of tasks that were designed to investigate their SMK and PCK with regard to students' misconception in the area of geometry. The analysis revealed that pre-service teachers had fairly strong SMK in that they could solve the problems of tasks and suggest prerequisite knowledge to solve the problems. They tended to emphasize formal aspect of mathematics, especially logic, mathematical rigor, rather than algorithmic and intuitive knowledge. When they analyzed students' misconception, pre-service teachers did not deeply consider the levels of students' thinking in that they asked 4-6 grade students to show abstract and formal thinking. When they suggested instructional strategies to correct students' misconception, pre-service teachers provided superficial answers. In order to enhance their knowledge of students, these findings imply that pre-service teachers need to be provided with opportunity to investigate students' conception and misconception.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.10
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• pp.4903-4929
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• 2018

In this study, a fully automatic pose and expression invariant 3D face alignment algorithm is proposed to handle frontal and profile face images which is based on a two pass course to fine alignment strategy. The first pass of the algorithm coarsely aligns the face images to an intrinsic coordinate system (ICS) through a single 3D rotation and the second pass aligns them at fine level using a minimum nose tip-scanner distance (MNSD) approach. For facial recognition, multi-view faces are synthesized to exploit real 3D information and test the efficacy of the proposed system. Due to optimal separating hyper plane (OSH), Support Vector Machine (SVM) is employed in multi-view face verification (FV) task. In addition, a multi stage unified classifier based face identification (FI) algorithm is employed which combines results from seven base classifiers, two parallel face recognition algorithms and an exponential rank combiner, all in a hierarchical manner. The performance figures of the proposed methodology are corroborated by extensive experiments performed on four benchmark datasets: GavabDB, Bosphorus, UMB-DB and FRGC v2.0. Results show mark improvement in alignment accuracy and recognition rates. Moreover, a computational complexity analysis has been carried out for the proposed algorithm which reveals its superiority in terms of computational efficiency as well.