• Communications of Mathematical Education
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• v.13 no.2
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• pp.563-589
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• 2002

고학년으로 갈수록 지필 환경에만 머무르는 현실 속에서 생활 및 예술 작품 등에서 수학적 원리와 개념을 발견하도록 하는 테셀레이션 수업은 학생들의 흥미와 호기심을 유발하고 수학의 아름다움을 느끼게 하는 것 이상으로 기하학적 사고의 기초를 학습하는데 도움을 줄 수 있다. 이에 본 연구는 4학년까지 적용되고 있는 7차 교육과정을 중심으로 새롭게 등장하고 있는 테셀레이션에 대한 이해 및 교수 학습 자료가 체계적으로 정비되어 있지 못한 현실적인 문제의 해결 방안으로서 테셀레이션을 활용한 수학 학습의 내용을 분석하여 교사들에게는 테셀레이션의 이해 및 교수 학습 자료로서 , 학생들에게는 수학의 기하적 개념들을 쉽고 재미있게 학습할 수 있는 학습도구로서 활용할 수 있도록 하는 것을 목적으로 테셀레이션을 구현할 수 있는 컴퓨터 소프트웨어를 활용하여 테셀레이션 교수 학습 자료를 개발하였고 이를 위해 다음과 같은 연구 내용을 설정하였다. 가. 테셀레이션의 정의와 예 그리고 종류를 알아보고 테셀레이션 속의 수학적 개념을 활용방법과 함께 제시한다. 나. 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 테셀레이션을 적용할 수 있는 내용영역을 분석하고 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한다. 다. 제작된 테셀레이션 교수 학습 자료의 효과적 활용을 위한 활용 방안을 탐색한다. 라. 제작된 테셀레이션 교수 학습 자료의 활용 효과를 알아보기 위해 적용 실험을 하고 이에 대한 학생들의 반응을 분석하여 학습의 효과를 밝힌다. 제작된 테셀레이션 교수 학습 자료의 적용 실험을 위하여 광주대성초등학교 6학년 한 반을 선정하였고 약 4주에 걸쳐 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료를 투입하여 4번의 활동수업을 실시하였다. 수업 후 작성된 학습지와 소감문 및 연구자에 의해 관찰된 수업내용을 바탕으로 다음과 같은 연구 결과를 얻을 수 있었다. 첫째, 제7차 초등 수학 교육과정 중 도형 영역과 규칙성과 함수 영역을 중심으로 컴퓨터 소프트웨어를 활용한 테셀레이션 자료를 제시한 결과 지필적 환경에서 제한적이었던 탐구하고 조작해보는 활동을 할 수 있는 역동적인 수학 실험실 환경이 제공됨으로써 도구적 이해가 아닌 관계적 이해를 하는 것을 확인할 수 있었다. 수학적 개념을 암기하는 것에서 벗어나 자연스런 조작을 통해 학생들이 개념을 이해하고 탐구하는 과정 속에서 학생들은 수학을 공부한다기 보다는 수학 속에서 재미있게 놀이한다는 생각을 가지고 수업에 참여하였고 배우는 즐거움을 알고 자신감을 가지며 더 나아가 창의적인 생각을 하도록 하는 기회를 줄 수 있었다. 둘째, 테셀레이션은 우리 생활 속에서 쉽게 발견할 수 있는 것으로 수학이 단순히 책에서만 한정되지 않고 다양한 분야 즉 디자인, 생활 속에서의 벽지문양과 포장지, 예술작품 등에 활용되고 있음을 체험함으로써 수학이 실생활에 광범위하게 활용되고 있음을 알게 하였다. 역으로 생활 속에서의 테셀레이션을 통해 수학적 개념을 찾는 과정을 통해 수학이 아름다우면서도 실용적이라는 생각을 심어줄 수 있었다. 셋째, 테셀매니아, GSP, 캐브리, 거북기하 등 평소 수업에서는 활용도가 적은 컴퓨터 소프트웨어를 활용함으로써 컴퓨터 소프트웨어 자체에서 오는 호기심뿐만이 아니라 직접 조작하여 테셀레이션 작품과 개념을 익히고 새로운 작품과 학습을 해 내는 과정을 통해 자신감과 성취감 등에 있어 큰 변화가 있음을 발견할 수 있었다. 컴퓨터 기능이 미숙한 학생의 경우 처음에는 당황해 하고 어려워하는 부분도 있었으나 조작할 시간적 여유를 주고 교사와 우수한 학생들이 도우미로서 역할을 잘해내어 나중에는 큰 어려움 없이 마칠 수 있었다. 테셀레이션이라는 용어가 아직은 생소한 현장에서 교수 학습 자료가 부족하고 그에 따른 이해도 부족한 현실 속에서 컴퓨터 소프트웨어를 활용한 테셀레이션 교수 학습 자료가 교수 학습 현장에 투입되어 유용하게 사용될 수 있는지 그 가능성을 조사한 것을 목적으로 한 본 연구의 결과로서 테셀레이션이라는 주제는 도형 영역과 규칙성과 함수 영역에서 평면 도형의 각과 모양 등의 성질을 탐구하게 하고, 대칭변환의 개념을 효율적으로 학습하게 할 수 있고, 반복되는 모양에서 규칙성을 발견하고 부분과 전체를 파악하여 패턴을 인지할 수 있게 하며 제작하고 분석하는 과정을 통해 여러 가지 수학적 개념과 수학적 창의성, 수학적인 아름다움을 느끼게 할 수 있음을 발견할 수 있었다. 또한 테셀레이션은 수학적 개념은 물론 수학과 미술, 수학과 일상 생활과의 연결성을 논의하고 확인하는 데 흥미로운 주제가 될 수 있다. 초등학교 교육과정에서 새롭게 도입되고 있는 테셀레이션을 활용하여 지도하기 위한 교수 학습 자료로 유용하게 사용될 수 있고 앞으로는 테셀레이션과 관련된 내용이 직접적으로 교육과정 내에서 다루어지고, 또한 테셀레이션을 적용한 수업이 학생들의 기하학적 사고 및 수학적 태도에 미치는 영향과 관련한 연구가 뒤따라야 할 것으로 본다.

• The Journal of the Korea Contents Association
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• v.14 no.6
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• pp.499-512
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• 2014

Architecture is usually seen as a product of art and technology. However, most historical buildings also exemplify various sophisticated principles of mathematics. Outstanding examples of architecture around the world such as Seokguram, Daewoongjun of Bulguksa, Muryangsujeon of Buseoksa, and the Parthenon provide students with a great opportunity to study their underlying mathematical properties and principles. The activity of identifying and investigating such mathematical principles in historical buildings enables students to realize that mathematics is a practical subject, and thus provides justification for the study and importance of mathematics. For the purpose of this study historical architecture was reviewed with this in mind in order to develop STEAM education materials focused on elementary school mathematics. The result of this study is as follows: first of all, appropriate examples of historical architecture were selected on the basis of the 2009 revised curriculum's content and teaching goals. These involved chapters on 'proportion', 'symmetry', 'movement of figures', 'building blocks', and 'triangles'. Secondly, a meta-analysis was performed on the historical buildings that clearly illustrate mathematical principles. Thirdly, STEAM education materials focused on elementary mathematics using architectural examples were developed which made actual application in classrooms possible. And lastly, surveys of professional groups were conducted to verify whether the produced materials were suitable teaching resources.

• Archives of design research
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• v.11
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• pp.22-29
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• 1995

I have to find standpoint of sight moulding of Chi I Sung Hwa(seven stars picture) analysis of graphic systems of a symbol sight native to our nation. And I will comprehend emotion of folkways by simple and graphic lines and colors in mathematical Grid of which ancestor had expressed in gauge moulding consciousness. This papers aim is to make a contribution to lead by on part of communication design. About structural analysis of pictorial graphic side. I) Mathematical thought of the Orient and space constitution are first basically the Orient expressed number notion of mathematics of unlimitedness and notion of zero so called space and empty second can analigize a diagonal expansion method by development of symmetry notion to basic the dual principle of the negative and positive by degrees development expressed space division method by direction notion. 2) About the proportion analysis it based the golden section globularity and in modern layout it takes vision center of position, after appointing the brow of sacred image of Chil Sung Hwa as center point of proportion and applied to the point proportion and so analigized the posibility of established. Rule in union of each elements and rule of forms about picture image. 3) Mathematical structure analysis to search a unified principle at the balanced arrangement and rule of forms it analigized the standard the rule of forms. it analigized the standard the rule of forms to body module of basic movement of protagonist and follower above basic forms of grid that is the basis of design system.

• 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 the Mineralogical Society of Korea
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• v.15 no.1
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• pp.44-58
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• 2002

A new polymorph of tridymite, an incommensurately modulated phase (IC phase), has been identified. While the symmetry of the IC lattice is same as that of the Ll phase, the geometry of the IC lattice structure is same as the basis of the L3 structure with a different modulation (modulation vector q=0.22 $c*_{H}$;$\lambda$ 37 ). On the other hand, the characteristic curved diffuse diffration observed from the Ll atoms could occur even at room phase suggests that the dynamic disordering of atoms, especially oxygen atoms could occur even at room temperature. The phase transition of Ll to L3 by grinding is gradual but very conspicuous: LllongrightarrowL1+IClongrightarrowIC+L3longrightarrowL3. However, it is revealed that real transition processes of individual grains are directly related to the local stress fields and preexisting microstructures.

• Journal of the Microelectronics and Packaging Society
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• v.13 no.4
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• pp.17-25
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• 2006

Thermo-mechanical behavior of flip-chip plastic ball grid array (FC-PBGA) packages are characterized by high sensitive $moir\'{e}$ interferometry. $Moir\'{e}$ fringe patterns are recorded and analyzed for several temperatures. Deformation analysis of bending displacements of the packages and average strains in the solder balls for both single and double-sided package assemblies are presented. The bending displacement of the double-sided package assembly is smaller than that of the single-sided one because of its symmetric structure. The largest effective strain occurred at the solder ball located on the edge of the chip and its magnitude of the double-sided package assembly is greater than that of single-sided one by 50%.

• Science of Emotion and Sensibility
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• v.25 no.4
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• pp.21-32
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• 2022

Minimalism is an increasingly popular lifestyle in which people deliberately seek to live with fewer possessions. However, little scientific research has been done to examine the relationships between minimalism, social value, and happiness. Two recent studies have investigated whether critical components of minimalism, such as subtraction and decluttering could lead to changes in social values and happiness. In Study 1, the participants were presented with pictures of unstable Lego structures for which they were asked to create ideas to resolve problems, either through adding new supports or removing the existing ones. Participants with a stronger tendency to use subtractive transformations reported higher happiness scores. In addition, higher scores in intrinsic value preferences were correlated with higher levels of happiness. In Study 2, cuing minimalism or consumerism using pictures led to changes in materialistic values, motivation for social engagement, and reported happiness scores. These results imply that minimalism as an alternative lifestyle can contribute to social wellbeing and increased happiness. Limitations and implications for future studies are discussed.

• Archives of design research
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• v.19 no.2 s.64
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• pp.121-128
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• 2006

The elements to enhance preference in symbol design are mainly related to consumers' response and aesthetic elements. Because certain aesthetic elements in design affect consumers' response and it is actually presented through (the different level of) preference. This study through surveying case studies examines whether a certain aesthetic element in symbol design gives rise to much preference. According to the result of study, high preference in symbolic design depends on high level of Rhythm, Balance, Harmony, Elaboration, Round, Gestalt, Organic, and Artificial/Natural among aesthetic elements. In comparison, it is founded that Simplicity/complexity, Objective/Abstract, depth, and symmetry should be designed at the moderate level, and proportion, repetition of elements be at the low level. Additionally(or Besides) this study makes out that symbol design cases with high preference have shapes from natural material or patterns of traditional culture, while cases with low preference have shapes from geometric figures. On the basis of these results, a guideline of symbol design could De offered(or suggested) to fit preference of consumers. But, this study is mostly concerned with only affect among emotional reactions of consumer in a scope of study, and is considered only in the aspect of form excluding color and texture.

• Journal of the Korean Institute of Traditional Landscape Architecture
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• v.28 no.3
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• pp.72-84
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• 2010

This study was attempted in order to offer basic data for implementing and applying Samjonseokjo(三尊石造), which is one of traditional stone construction method, by confirming how the constructive principle is expressed such as proportional beauty, which is contained in the modeling of Triad of Buddha Carved on Rock that was formed in the period of the Three States, centering on Triad of Buddha Carved on Rock in Susan. The summarized findings are as follows. 1. As a result of analyzing size and proportion of totally 17 of Triad of Buddha Carved on Rock, the average total height in Bonjonbul(本尊佛) was 2.96m. Right Hyeopsi(右挾侍) was 2.19m. Left Hyeopsi(左挾侍) was 2.16m. The height ratio according to this was 100:75:75, thereby having shown the relationship of left-right symmetrical balance. The area ratio in left-right Hyeopsi was 13.4:13.7, thereby the two area having been evenly matched. 2. The Triad of Buddha Carved on Rock in Seosan is carved on Inam(印岩) rock after crossing over Sambulgyo bridge of the Yonghyeon valley. Left direction was measured with $S47^{\circ}E$ in an angle of direction. This is judged to target an image change and an aesthetic sense in a Buddhist statue according to direction of sunlight while blocking worshipers' dazzling. 3. As for iconic characteristics of Buddha Carved on Rock in Seosan, there is even Hyeopsi in Bangasang(半跏像) and Bongjiboju(捧持寶珠) type Bosangipsang. In the face of Samjon composition in left-right asymmetry, the unification is indicated while the same line and shape are repeated. Thus, the stably visual balance is being shown. 4. In case of Triad of Buddha Carved on Rock in Seosan, total height in Bonjonbul, left Hyeopsi, and right Hyeopsi was 2.80m, 1.66m, and 1.70m, respectively. Height ratio in left-right Hyeopsibul was 0.60:0.62, thereby having been almost equal. On the other hand, the area ratio was 28.8:25.2, thereby having shown bigger difference. The area ratio on a plane was grasped to come closer to Samjae aesthetic proportion. 5. The axial angle of centering on Gwangbae was 84:46:50, thereby having been close to right angle. On the other hand, the axial angle ratio of centering on Yeonhwajwa(蓮華坐: lotus position) was measured to be 135:25:20, thereby having shown the form of inequilateral triangle close to obtuse angle. Accordingly, the upper part and the lower part of Triad of Buddha Carved on Rock in Susan are taking the stably proportional sense in the middle of maintaining the corresponding relationship through angular proportion of inequilateral triangle in right angle and obtuse angle. 6. The distance ratio in the upper half was 0.51:0.36:0.38. On the other hand, the distance ratio in the lower half was 0.53 : 0.33 : 0.27. Thus, the up-down and left-right symmetrical balance is being formed while showing the image closer to inequilateral triangle. 7. As a result of examining relationship of Samjae-mi(三才美) targeting Triad of Buddha Carved on Rock in Susan, the angular ratio was shown to be more notable that forms the area ratio or triangular form rather than length ratio. The inequilateral triangle, which is formed centering on Gwangbae(光背) in the upper part and Yeonhwajwa(lotus position) in the lower part, is becoming very importantly internal motive of doubling the constructive beauty among Samjae, no less than the mutually height and area ratio in Samjonbul.

• Journal of the Korea institute for structural maintenance and inspection
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• v.27 no.6
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• pp.120-129
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• 2023

To evaluate the vertical loads on railway bridges, conventional load tests are typically conducted. However, these tests often entail significant costs and procedural challenges. Railway conditions involve nearly identical load profiles due to standardized rail systems, which may appear straightforward in terms of load conditions. Nevertheless, this study aims to validate load tests conducted under operational train conditions by comparing the results with those obtained from conventional load tests. Additionally, static and dynamic structural behaviors are extracted from the measurement data for evaluation. To ensure the reliability of load testing, this research demonstrates feasibility through comparisons of existing measurement data with sensor attachment locations, train speeds, responses between different rail lines, tendency analysis, selection of impact coefficients, and analysis of natural frequencies. This study applies to the Dongho Railway Bridge and verifies the applicability of the proposed method. Ten operational trains and 44 sensors were deployed on the bridge to measure deformations and deflections during load test intervals, which were then compared with theoretical values. The analysis results indicate good symmetry and overlap of loads, as well as a favorable comparison between static and dynamic load test results. The maximum measured impact coefficient (0.092) was found to be lower than the theoretical impact coefficient (0.327), and the impact influence from live loads was deemed acceptable. The measured natural frequencies approximated the theoretical values, with an average of 2.393Hz compared to the calculated value of 2.415Hz. Based on these results, this paper demonstrates that for evaluating vertical loads, it is possible to measure deformations and deflections of truss railway bridges through load tests under operational train conditions without traffic control, enabling the calculation of response factors for stress adjustments.