• Kyungpook Mathematical Journal
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• v.63 no.1
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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.

• Transactions of Materials Processing
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• v.32 no.5
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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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• v.30 no.3
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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.

• The Journal of the Korea Contents Association
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• v.11 no.3
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• pp.460-466
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• 2011

Kameun temple was constructed in A.D. 682 after 46 year after Chumsungdae was constructed. This paper discusses the scientific implication of Taegeuk stone rods of Kameun temple site through the geometric analysis of their engraved figures. So we can estimate that the west Taegeuk of Kameun temple site has 2 circles comparing the path of the moon with that of the sun leading to the asymmetry in its emblem(Taegeuk) and the east Taegeuk of Kameun temple site has 1 circle representing the path of the sun. The Taegeuks along with around 30 equilateral triangles representing the north latitude $35.8^{\circ}$ give the explicit information of period of the orbit of the moon and the sun. These mathematical methods can explain some relics structure of antiquity with a few historical expounds.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2000.10a
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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.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.8
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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.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.26 no.6
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.5 no.1
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• pp.133-143
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• 2001

This paper describes the correlation of the transient impedance and its parameters with the stationary resistance of a grounding system to a square pulse current and a lightning impulse current. In the experiment, the grounding system consists of a single grounding rod$(\Psi10[mm], 1[m])$and/or a triple-grounding rods of equilateral triangles with 5[m] spacing for operation. To analyze the transient impedance characteristics of the grounding system, a pulse generator which can produce square wave of a 30[ns] rise-time and a $20[\mus] $pulse duration is designed and fabricated. The injected content in the grounding system and the developed potential were recorded, and the time variation of the transient impedance were calculated as the ratio of the potential rising to the injected current at each time. The transient impedance and the effective surge impedance Z3 which defines economic protection level in power system were quite higher than the stationary resistance. The grounding impedance is decreased by the application of the triple-rods grounding system, and its effect is decreased as the frequency of the current is increased due to the inductance of the grounding leads.

• Education of Primary School Mathematics
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• v.20 no.2
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• pp.163-175
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• 2017

The purpose of the study is to identify the effect of length and right angle indication on the understanding of the concept of the figure when presenting the task of classifying the plane figures. we recorded thirty three 4th grade students' performance with eye-tracking technologies and analyzed the correct answer rate and gaze duration. The findings from the study were as follows. First, correctness rate increased and Gaze duration decreased by marking length in isosceles triangle and equilateral triangle. Second, correctness rate increased and Gaze duration decreased by marking right angle in acute angle triangle and obtuse triangle. Based on these results, it is necessary to focus on measuring the understanding of the concept of the figure rather than measuring the students' ability to measure by expressing the length and angle when presenting the task of classifying the plane figures.

• Korean Institute of Interior Design Journal
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• v.21 no.3
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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.