• Title/Summary/Keyword: special angles

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Derivating the Ratios of Trigonometric Special Angles by Constructing Regular Polygon (정오각형 작도에 의한 특수각의 삼각비 유도)

  • Cho, Cheong-Soo
    • Journal for History of Mathematics
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    • v.19 no.1
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    • pp.79-90
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    • 2006
  • The purpose of this paper is to derive the ratios of trigonometric special angles from Euclid's by constructing regular pentagon and decagon. The intention of this paper is started from recognizing that teaching of the special angles in secondary math classroom excessively depends on algebraic approaches rather geometric approaches which are the origin of the trigonometric ratios. In this paper the method of constructing regular pentagon and decagon is reviewed and the geometric relationship between this construction and trigonometric special angles is derived. Through such geometric approach the meaning of trigonometric special angles is analyzed from a geometric perspective and pedagogical ideas of teaching these trigonometric ratios is suggested using history of mathematics.

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Study on seismic performance of SRC special-shaped columns with different loading angles

  • Qu, Pengfei;Liu, Zuqiang;Xue, Jianyang
    • Steel and Composite Structures
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    • v.44 no.6
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    • pp.789-801
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    • 2022
  • In order to study the influence of loading angles on seismic performance of steel reinforced concrete (SRC) special-shaped columns, cyclic loading tests and finite element analysis (FEA) were both carried out. Seven SRC special-shaped columns, including two L-shaped columns, three T-shaped columns and two cross-shaped columns, were tested, and the failure patterns of the columns with different loading angles were obtained. Based on the tests, the FEA models of SRC special-shaped columns with different loading angles were established. According to the simulation results, hysteretic curves and seismic performance indexes, including bearing capacity, ductility, stiffness and energy dissipation capacity, were analyzed in detail. The results showed that the failure patterns were different for the columns with the same section and different loading angles. With the increasing of loading angles, the hysteretic curves became fuller and the bearing capacity and initial stiffness appeared increasing tendency, but the energy dissipation capacity changed insignificantly. When the loading angle changed, the ductility got better with the larger area of steel at the failure side for the unsymmetrical section and near the neutral axis for the symmetrical section, respectively.

On Interpretation of Hyperbolic Angle

  • Aktas, Busra;Gundogan, Halit;Durmaz, Olgun
    • Kyungpook Mathematical Journal
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    • v.60 no.2
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    • pp.375-385
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    • 2020
  • Minkowski spaces have long been investigated with respect to certain properties and substructues such as hyperbolic curves, hyperbolic angles and hyperbolic arc length. In 2009, based on these properties, Chung et al. [3] defined the basic concepts of special relativity, and thus; they interpreted the geometry of the Minkowski spaces. Then, in 2017, E. Nesovic [6] showed the geometric meaning of pseudo angles by interpreting the angle among the unit timelike, spacelike and null vectors on the Minkowski plane. In this study, we show that hyperbolic angle depends on time, t. Moreover, using this fact, we investigate the angles between the unit timelike and spacelike vectors.

Variation of Specific Cutting Pressure with Different Tool Rake Angles in Face Milling (정면밀링에서 공구경사각에 따른 비절삭저항 변화)

  • 류시형
    • Proceedings of the Korean Society of Precision Engineering Conference
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    • 1996.04a
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    • pp.63-68
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    • 1996
  • In this study, the effect of tool rake angles and the change of cutting conditions on specific cutting pressure in face milling is investigated. The cutting force in face milling is predicted from the double cutting edge model in 3-dimensional cutting. Conventional specific cutting pressure model is modified by considering the variation of tool rake angles. Effectiveness of the modified cutting force model is verified by the experiments using special face milling cutters with different cutter pockets and various rake angles. From the comparison of the pressented model and the specific cutting pressure, it is shown that the axial force can be predicted by the tangential and redial forces without the knowledge of friction angle and shear angle. Also, the relation between specific cutting pressure and cutting cindition including feedrate, cutting velocity and depth of cut is studied.

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Prediction of Specific Cutting Pressure in Face Milling Considering Tool Rake Angles (정면밀리에서 공구경사각을 고려한 비절삭저항 예측)

  • Ryu, S.H.;Chu, C.N.
    • Journal of the Korean Society for Precision Engineering
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    • v.14 no.2
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    • pp.169-177
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    • 1997
  • In this study, investigated are the effects of tool rake angles and the change of cutting conditions on the specific cutting pressure in face milling. The cutting force in face milling is predicted from the double cutting edge model in3-dimensional cutting. Conventional specific cutting pressure model is modified by considering the variation of tool rake angles. Effectiveness of the modified cutting force model is verified by the experiments using special face milling cutters with different cutter pockets and various rake angles. From the comparison of the presented model and the specific cutting pressure, it is shown that the axial force can be predicted by the tangential force, radial force and geometric conditions. Also, the rela- tionship between specific cutting pressure and cutting conditions including feedrate, cutting velocity and depth of cut is studied.

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MIXED-MODE CRACK PROPAGATION BY MOVABLE CELLULAR AUTOMATA METHOD

  • Pak, Mik-Hail;Lee, Choon-Yeol;Chai, Young-Suck
    • Proceedings of the KSME Conference
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    • 2007.05a
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    • pp.1754-1759
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    • 2007
  • Propagation of a mixed-mode crack in Soda-Lime silica glass using Movable Cellular Automata (MCA) method is demonstrated in this study. In MCA method, special fracture criterion is used to describe the process of crack initiation and propagation. Comparison between MCA and other crack initiation criteria results are made. The crack resistance curves and bifurcation angles under different loading angles are found. In comparisons with results of maximum circumferential tensile stress criterion, MCA result showed the sufficient agreement.

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A Plan to Establish Agriculture and Fisheries Special Channel - Marketing Expert, Farmer and Fisher, Broadcasting Expert FGI Result - (농수산식품 전문채널 설립방안 - 농수산 마케팅 전문가, 농수산업인, 방송전문가 FGI 결과 -)

  • Park, Ji Seob;Moon, Junghoon;Kim, Jin Gi
    • Agribusiness and Information Management
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    • v.2 no.1
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    • pp.15-29
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    • 2010
  • Recently, IPTV population is growing by leaps and bounds. and We performed FGI(Focus Group Interview) with various experts related to agriculture field to establish Agriculture and Fisheries special channel. this growth has social background that is change of paradigm caused by the convergence of broadcasting, demand for Agriculture and Fisheries special channel using new media thanks to interests in Wellbeing, Green food. so we think that we need to consider the way to establish Agriculture and Fisheries special channel and its validity from all angles. that is why we are having a heated discussion with Agriculture and Fisheries marketing experts, farmer, fisher(Korean Cyber Farmer Association), broadcasting experts. Concretely, government budget is needed to establish Agriculture and Fisheries special channel, so we are just about to examine its validity and find business model. to make this discussion detailed, we made 4 subjects. First, Do we need agro-fishery products distribution channel using media? Second, After establishing of Agriculture and Fisheries special channel, how many demands will occur? Third, Should we make Agriculture and Fisheries special channel public channel? Fourth, What would be profit model of Agriculture and Fisheries special channel?

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Analysis of Cutting Edge Geometry Effect on Surface Roughness in Ball-end Milling Using the Taguchi Method (다구찌 방법을 통한 볼 엔드밀 절삭날 형상이 가공면 거칠기에 미치는 영향 분석)

  • Cho, Chul Yong;Ryu, Shi Hyoung
    • Journal of the Korean Society of Manufacturing Technology Engineers
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    • v.23 no.6
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    • pp.569-575
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    • 2014
  • In this study, the effect of cutting edge geometry, such as helix and rake angles, on surface roughness in ball-end milling is investigated by using the Taguchi method. A set of experiments adopting the $L_{27}(3^{13})$ design with an orthogonal array are conducted with special WC ball-end mills having different helix and rake angles. Analysis of variance (ANOVA) is performed to analyze the effects of tool geometry and machining parameters, such as cutting speed, feed per tooth, and depth of cut, on surface roughness. The ANOVA results reveal that helix and rake angles are critical factors affecting surface roughness; the interaction of helix angle and cutting speed is also important. This research can contribute to novel cutting edge designs of ball-end mills and optimization of cutting parameters.

Fatigue Strength Evaluation of Self-Piercing Riveted Al 5052-H32 Joints under Mixed Mode Loading Conditions (혼합모드상태에서의 Al 5052-H32 셀프 피어싱 리벳 접합부의 피로강도 평가)

  • Kwak, Jin Gu;Kang, Se Hyung;Kim, Ho Kyung
    • Journal of the Korean Society of Safety
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    • v.31 no.3
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    • pp.1-7
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    • 2016
  • In this study, static and fatigue tests on the self-piercing riveted (SPR) joint were conducted using cross-shaped specimens with aluminum alloy (Al-5052) sheets. Mixed mode loading was achieved by changing the loading angles of 0, 45, and 90 degrees using a special fixture to evaluate the static and fatigue strengths of the SPR joints under mixed mode loading conditions. Simulations of the specimens at three loading angles were carried out using the finite element code ABAQUS. The fatigue specimens failed in an interfacial mode where a crack initiated at the upper sheet and propagated along the longitudinal direction and finally fractured Maximum principal stress, von-Mises effective stress failed to correlate the fatigue lifetimes at three loading angles. However, the equivalent stress intensity factor was found to be appropriate to correlate the fatigue lifetimes at three loading angles.

A Study on the Problems and Development Plan of Statistics in Special Library (전문도서관 통계의 문제점과 발전방안에 관한 연구)

  • Noh, Younghee
    • Journal of the Korean BIBLIA Society for library and Information Science
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    • v.32 no.2
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    • pp.25-47
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    • 2021
  • Using the data shown in the national library statistics system, we tried to identify the current situation from various angles and derive problems, and based on this, we tried to find a development plan. First, it is necessary to conduct a thorough survey to know the statistics of Special library. Second, some degree of unification of the names used in Special libraries should be achieved. Third, it is necessary to present the subject classification for Special libraries. Fourth, it is necessary to actively promote and incentive Special libraries to participate in statistical surveys. Fifth, it is necessary to solve the problem that Special libraries are classified into other statistics. Sixth, statistics of national and large Special libraries such as the Court Library, Constitutional Court Library, and Korea Institute of Science and Technology Information cannot be found anywhere. Unless these problems are solved, the overall evaluation of Special libraries and policy proposals at the national level will be meaningless.