• 한국실내디자인학회논문집
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• 제38호
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• pp.75-82
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• 2003

The symmetry is general geometric design principal in contemporary architecture shape. But, Symmetry sometimes easily causes unreasonable design. In some reason, two of symmetric units in the apartment, one side of unit have very reasonable plan and arrangement but opposite side unit nay not. For example, if the kitchen on right unit had right-handed arrangement, the symmetrical other would have left-handed kitchen arrangement. In addition to this, if each house unit has the same plan but different direction, each unit has different usage or affects the residents' life pattern. Nevertheless, Architects use only one unit plan to design public housing development by using symmetric operator (mirror, proper rotation, inversion center) at their option. This study suggests that using group theory and mathematical matrix rather than designer's discretion can solve this symmetry problem clearly. And, this study analysis the merits and demerits between each symmetrical pair of unit plan shapes by using mathematical point group theory and matrix.

• 한국수학교육학회지시리즈A:수학교육
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• 제56권3호
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• pp.235-255
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• 2017

This study compared and contrasted the topics related to congruence and symmetry in the elementary mathematics textbooks series of Korea, Japan, Hong Kong, Finland, and Singapore in three aspects: (a) when to teach, (b) what to teach, and (c) how to teach. Firstly, the results of when to teach showed differences across the countries with a variation of teaching the topics among grades from 3 to 6. Secondly, the results of what to teach revealed subtle but significant differences. Regarding congruence, Korea and Japan deal with congruence in a systematic manner, while Finland tends to address the brief definition of congruence, and Hong Kong and Singapore focus on teaching tessellation which implies congruence. Regarding symmetry, Korea and Japan deal only with a symmetric figure for a line and that for a point, while Hong Kong includes a rotational symmetry and Finland extends further to cover the figures positioned in a symmetry both for a line and for a point. Lastly, the results of how to teach demonstrated that Korea tends to focus on the procedure of drawing both triangles to be congruent and symmetric figures. This implies that we need to consider alternative methods such as using various instructional materials and making an explicit connection among mathematical concepts in teaching congruence and symmetry.

• 대한수학교육학회지:수학교육학연구
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• 제12권4호
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• pp.509-521
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• 2002

The purpose of this paper is as follows: $^{\circleda}$ to disclose the essence of symmetry $^{\circledb}$ to propose the desirable strategy of problem-solving as to symmetry $^{\circledc}$ to clarify the relationship between symmetry and group $^{\circledd}$ to propose a way of introduction of 'group' in school mathematics according to its fundamental characteristic, symmetry. This study shows that the nature of symmetry is 'invariance under a transformation' and symmetry is the main idea of 'group'. In mathematics textbooks and mathematics education literature, we find out that the logic of symmetry is widespread. We illustrate two paradigmatic problem related to symmetrical logic and exemplify a desirable instruction of Pascal's triangle. This study also suggests a possibility of developing students' unformal and unconscious conception of group with sym metry idea from elementary to secondary school mathematics.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2002년도 춘계학술대회
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• pp.51-73
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• 2002

Empirical likelihood ratio method is a new technique in nonparametric inference developed by A. Owen (1988, 2001). Sometimes empirical likelihood has difficulties to define itself. As such a case in point, we discuss the way to define a modified empirical likelihood for the location of symmetry using well-known points of symmetry as a side conditions. The side condition of symmetry is defined through a finite subset of the infinite set of constraints. The modified empirical likelihood under symmetry studied in this paper is to construct a constrained parameter space $\theta+$ of distributions imposing known symmetry as side information. We show that the usual asymptotic theory (Wilks theorem) still hold for the empirical likelihood ratio on the constrained parameter space and the asymptotic distribution of the empirical NPMLE of difference of two symmetric points is obtained.

• East Asian mathematical journal
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• 제37권4호
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• pp.355-379
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• 2021

In this article, we investigated plane figures introduced in elementary school mathematics in the perspective of traditional classification, and also analyzed plane figures focused on the invariance of plane figures out of traditional classification. In the view of traditional classification, how to treat trapezoids was a key argument. In the current mathematics curriculum of the elementary school mathematics, the concept of sliding, flipping, and turning are introduced as part of development activities of spatial sense, but it is rare to apply them directly to figures. For example, how are squares and rectangles different in terms of symmetry? One of the main purposes of geometry learning is the classification of figures. Thus, the activity of classifying plane figures from a symmetrical point of view has sufficiently educational significance from Klein's point of view.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권3호
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• pp.273-292
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• 2007

The purpose of this study was to find out how second, fourth and sixth graders understood the main contents related to spatial sense in the Seventh National Mathematics Curriculum. For this purpose, this study examined students' understanding of the main contents of congruence transformation (slide, flip, turn), mirror symmetry, cubes, congruence and symmetry. An investigation was conducted and the subjects included 483 students. The main results are as follows. First, with regards to congruence transformation, whereas students had high percentages of correct answers on questions concerning slide, they had lower percentages on questions concerning turn. Percentages of correct answers on flip questions had significant differences among the three grades. In addition, most students experienced difficulties in describing the changes of shapes. Second, students understood the fact that the right and the left of an image in a mirror are exchanged, but they had poor overall understanding of mirror symmetry. The more complicated the cubes, the lower percentages of correct answers. Third, students had a good understanding of congruences, but they had difficulties in finding out congruent figures. Lastly, they had a poor understanding of symmetry and, in particular, didn't distinguish a symmetric figure of a line from a symmetric figure of a point.

• 한국멀티미디어학회논문지
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• 제17권2호
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• pp.208-217
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• 2014

본 논문은 효과적인 물체 검출이 가능하도록 명도값의 변화방향에 따라 수렴하는 경우와 발산하는 경우의 대칭기여도를 적응적으로 제어할 수 있도록 가우시안 함수형태의 위상가중함수를 이용한 적응적 대칭기여도 제어 기반 일반화 대칭변환을 제안하였다. 제안한 방법에서는 먼저 수렴영역과 발산 영역을 정의한 후 정의된 수렴/발산 영역에서 대칭극점과 거리 함수로 표현된 대칭정도에 따라 대칭기여도의 반영 비율을 달리 할 수 있도록 가우시안함수 형태의 위상가중 함수를 사용하였으며, 가우시안함수 형태의 위상 가중함수에서 차단주파수 조절을 통한 대칭기여도의 적응적인 제어를 통해 효과적인 물체 검출이 가능하도록 하였다. 제안한 방안의 성능을 평가하기 위해 IR영상을 포함한 다양한 영상에서 대해 차단주파수 조절을 통한 대칭기여도의 적응적 제어가 물체검출에 미치는 영향을 기존의 GST와 비교, 분석하여 제안한 방법의 우수한 성능을 증명하였다.

• Archives of Plastic Surgery
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• 제41권1호
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• pp.57-62
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• 2014

Background Achieving symmetry is a key goal in breast reconstruction. Anatomically shaped tabbed expanders are a new tool in the armamentarium of the breast reconstruction surgeon. Suture tabs allow for full control over the expander position and thus inframammary fold position, and, in theory, tabbed expanders mitigate many factors responsible for poor symmetry. The impact of a tabbed expander on breast symmetry, however, has not been formally reported. This study aims to evaluate breast symmetry following expander-implant reconstruction using tabbed and non-tabbed tissue expanders. Methods A chart review was performed of 188 consecutive expander-implant reconstructions that met the inclusion criteria of adequate follow-up data and postoperative photographs. Demographic, oncologic, postoperative complication, and photographic data was obtained for each patient. The photographic data was scored using a 4-point scale assessing breast symmetry by three blinded, independent reviewers. Results Of the 188 patients, 74 underwent reconstruction with tabbed expanders and 114 with non-tabbed expanders. The tabbed cohort had significantly higher symmetry scores than the non-tabbed cohort ($2.82/4{\pm}0.86$ vs. $2.55/4{\pm}0.92$, P=0.034). Conclusions The use of tabbed tissue expanders improves breast symmetry in tissue expander-implant-based breast reconstruction. Fixation of the expander to the chest wall allows for more precise control over its location and counteracts the day-to-day translational forces that may influence the shape and location of the expander pocket, mitigating many factors responsible for breast asymmetry.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제38권2호
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• pp.215-230
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• 2024

합동과 대칭은 일상생활에서 접할 수 있는 친숙한 개념으로, 이러한 개념을 효과적으로 이해하고 습득하기 위하여 적절한 시각적 예시의 역할이 중요하다. 본 연구에서는 초등 수학 교과서에서 합동과 대칭 개념을 학습하는 과정에서 제시되는 시각적 예시를 살펴보았으며 오목다각형의 활용에 초점을 맞추어 분석하였다. 분석 결과, 교과서에서 다양한 형태의 다각형이 합동과 대칭의 교수학습을 위한 시각적 예시로 활용되고 있었고 합동, 선대칭도형, 점대칭도형의 순서로 오목다각형의 활용 빈도가 높게 나타났다. 또한, 개념의 도입보다 성질 탐구에서 오목다각형이 더 자주 활용되는 것을 확인하였다. 이러한 분석 결과를 바탕으로 합동과 대칭의 교수학적 시사점을 모색하였다.

• 한국전기전자재료학회논문지
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• 제23권1호
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• pp.70-75
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• 2010

We have designed the backward wave oscillator operating at 24 GHz. From the research which sees researches in the goal which will design and will produce K-band BWO where is a backward wave oscillator which departs from cycle prisoner 24 GHz until now is higher. To design Chrencov instibility and branch of family used a slow cyclotron instibility. Calculation used a dispersion relation and in order for as the box over-flow not to happen, a asymtotic expansion. Used a beam mode and a waveguide mode and axial symmetry and expense used in compliance with sattle point interpreted the relationship of axial symmetry.