• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.61-78
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• 2023

In this paper, we introduce two new geometric constants related to the heights of triangles: ∆_H(X) and ∆_h(X, I). We also propose two new geometric constants, ∆_m(X) and ∆_M(X), related to the midlines of equilateral triangles, and discuss the relation between the heights and midlines in equilateral triangles. We give estimates for these geometric constants in terms of other geometric parameters, and the geometric constants are used to discuss geometric properties such as uniform non-squareness, uniform normal structure, and the fixed point property.

• 소성∙가공
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• 제32권5호
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• pp.255-267
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• 2023

Recently, 3D printing using a material extrusion method is used in various fields. Since plastic material has lower strength than steel, research to increase the strength is continuously being conducted. This study investigates the lattice structure for additive manufacturing of six 3D infill patterns (octet, quarter cubic, cubic, cubic subdivision, triangles and cross 3D) which consist of tetragons, hexagonal trusses, equilateral triangles and cross shapes. Consequently, in the tensile strength considering the weight and printing time, octet, quarter cubic, cubic and triangles patterns tended to increase linearly as the infill density increased, except for the infill density of 20%. However, the tensile strength/weight performed better than the infill density of 100% when the cubic subdivision pattern had the infill density of 20% and the cross 3D pattern had the infill density of 40%. Considering the weight and printing time, the infill patterns of high tensile strength were octet, quarter cubic, cubic, cubic subdivision, triangles and cross 3D order.

• East Asian mathematical journal
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• 제30권3호
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• 한국콘텐츠학회논문지
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• 제11권3호
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• pp.460-466
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• 2011

감은사는 첨성대가 건축되고 46년 후 서력 682년에 세워진 신라시대 사찰로 현재는 금당터와 석탑 및 각종 석조 유물로 전해지고 있다. 본 논문에서는 1959년 1차 발굴 때 감은사지 금당터의 동편에서 발견된 동편 태극 장대석과 2차 발굴 때 감은사지 남편 연못에서 발견되어 1993년 인위적으로 서편에 배치된 서편 태극 장대석에 대한 과학적 의미를 파악하기 위하여 유물에 각인된 도형의 기하학적 분석을 한다. 그리하여 감은사지 태극 장대석이 의미하는 수학적, 천문학적인 도형의 현대적 해석을 통하여 당시의 과학 수준을 가늠할 중요한 척도를 얻게 되었다. 또한 동편 및 서편 태극 장대석이 나타내는 이등변삼각형들의 배치가 각각 해와 달과 관련된 책력과 연관함을 추론하게 된다. 이러한 엄밀한 수학적 개념 조사를 통하여 역사적 사실이 빈약한 오래된 역사적 구조물을 이해하고 고증하는데 새로운 연구 방향을 제시해준다.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2000년도 추계종합학술대회
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• pp.568-572
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• 2000

This paper describes the experimental results of a transient impedance characteristics of grounding rods to a square pulse and standard lightning impulse current. The test were performed on single grounding rod($\phi$ 10mm, 1m) and triple-grounding rods( $\phi$ 10mm, 1m) of equilateral triangles with 5m spacing. For measurements of transient impedance, a pulse generator which can produce square wave of 30ns rise time and 20U Pulse duration was designed and fabricated. In the experiment, transient impedance of the grounding systems have been investigated from the recorded potential and current waveforms. The results showed that the value of the transient impedance is quite higher than the stationary resistance, and provide useful information for the value of a grounding system considered transient characteristics under a high frequency condition such as lightning stokes and ground-fault.

• 한국정밀공학회지
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• 제17권8호
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• pp.172-179
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• 2000

In this paper a technology for the fabrication of the oblique structure using the LIGA process will be presented. The fabricated microstructure is a tetrahedral 3- facet mirror. The mirror has an equilateral triangular base of hundreds ${\mu}m$ length mirror-like three side-facets inclined to the base at 45$^{\circ}$ and knife edges. Two regular triangles of 45$^{\circ}$ and tan-12. After development the shaded part of the PMMA the tetrahedral mirror remains, The completed mirror shows excellent aspects of mirror-like facets and knife-edges. By controlling the gap between the mask and the substrate the size of mirror easily can be changed. This mirror would be used as a laser beam splitter for the feedback control of the HDD slider.

• 한국전기전자재료학회논문지
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• 제26권6호
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• pp.472-477
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• 2013

This paper carried out the comparative analysis on ground impedance of a carbon block and a copper rod. Two types of grounding electrode were compared ; a carbon block (L : 1 m, ${\Phi}$ : 245 mm) buried at a depth of 0.8 m and a three-linked copper rod (L : 1 m, ${\Phi}$ : 10 mm) of equilateral triangles with 1 m spacing. Ground impedance depending on applied current source was evaluated by the application of a sine wave current with 60 Hz ~ 3.5 MHz, a fast-rise pulse with rising time of 200 ns, a standard lightning impulse of $8/20{\mu}s$ and a 600 Hz square wave. Ground impedance for both electrodes were almost the same value below 100 kHz, and increased rapidly afterwards. The maximum ground impedance appeared $400{\Omega}$ at around 1.5 MHz. Ground impedance of the carbon block was lower at the square wave and was higher at fast-rise pulse than that of the copper rod. Also, ground impedance as ages showed no difference for the last 8 months. From the results, it is likely that ground performance for both electrodes shows no difference against commercial frequency and lightning impulse current, while the copper rod shows better performance against a fast-rise pulse with rise-time of a few hundred ns.

• 한국정보통신학회논문지
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• 제5권1호
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• pp.133-143
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• 2001

본 논문은 직각파 및 뇌충격진류에 대한 봉상접지각의 과도임피던스 특성을 정상접지지항과 비교.분석하였다. 접지계는 단일$(\Psi10[mm], 1[m])$과 5[m]의 간격을 두고 서로 연접한 3연접 봉상접지극으로 구성하였으며, 과도 임피던스 특성을 분석하기 위하여 상승시간 30[ns], 펄스폭 $20[\mus]$의 직각파전류 발생장치를 설계 제작하였다. 실제 낙뢰에 의한 접지임피던스의 변화를 관찰하기 위하여, 국제규격 ANSI/IEEE, IEC에 규정되어 있는 뇌충격전류를 인가하여 이에 따른 특성변화를 측정.분석하였다. 접지계로 유입된 과도전류는 접지계의 전위를 상승시키며, 이 때의 전위상승과 유입전류의 비로써 접지임피던스를 산출하며, 뇌격전류에 대한 경제적인 보호 수준을 평가.예측하기 위하여 임피던스 파라미터를 측정결과로부터 산출하였다. 또한 연접에 따른 접지임피던스의 감소와 접지리드선이 미치는 영향도 분석하였다.

• 한국수학교육학회지시리즈C:초등수학교육
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• 제20권2호
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• pp.163-175
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• 2017

본 연구는 평면 도형의 도형 분류하기 과제를 제시할 때 길이와 각의 표기 여부가 도형의 개념 이해에 어떤 영향을 주는지 알아보는데 목적이 있다. 이를 위해, 초등학교 4학년 학생 33명을 대상으로 분류하기 과제 해결 과정을 Eye-tracker를 통해 녹화하고 정답률과 Gaze Duration을 중심으로 분석하였다. 그 결과, 이등변삼각형과 정삼각형의 분류하기에서는 길이를 제시하였을 때 정답률이 증가하고 Gaze Duration은 감소하였다. 예각삼각형과 둔각삼각형 과제에서도 직각을 표기했을 때 정답률이 증가하고 Gaze Duration이 감소하였다. 이러한 결과로 볼 때, 평면도형을 분류하는 과제를 제시할 때는 길이와 각을 표기하여 학생들이 어림하여 도형을 분류하기 보다는 도형의 개념 이해를 바탕으로 분류하는 것을 측정하는 데 초점을 두어야 할 것이다.

• 한국실내디자인학회논문집
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• 제21권3호
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• pp.128-135
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• 2012

The purpose of this study is to investigate and analyze the compositional elements of plan of art museums by selecting architectural works, which have strong symbolic meaning when evaluating value, from architectural works by Louis Kahn. First, the centrality of artworks, which are being displayed at the Yale Art Gallery, is complex. It includes three patterns of Void (spatial) Centrality+Symbolic Centrality+Functional Centrality among the five patterns suggested in this study. Second, the ratio system of interior space, which is expressed in the extension of the Yale Art Gallery, can be classified into the floor and walls. The floor used the square 1:1 ratio system. The ceiling used the grid patterns of equilateral triangles (regular tetrahedrons). It was applying a geometric ratio system when creating forms by using one side as a beam and the other sides as decorations of the ceiling. Third, the contours of interior space, which were expressed in Kahn's works, used the method of forming separate space according to the contouring rule (structural unit) defined by columns, and they were used in constructing the entire space through the integration of separate spaces. Fourth, according to the characteristics that were expressed by artworks displayed within the Yale Art Gallery Extension, the concept of accessibility was not as clear as that of residential buildings, because an approach of respecting existing architecture and context was used, rather than the starting point of interior space, or differentiated circulation, which has the function of a determined position.