• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.833-855
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• 2017

This study aims to reinvestigate the reason for introducing radian as a new unit to express the size of angles, what is the meaning of radian measures to use arc lengths as angle measures, and why is the domain of trigonometric functions expanded to real numbers for expressing general angles. For this purpose, it was conducted historical, mathematical and applied mathematical analyzes in order to research at multidisciplinary analysis of the radian concept. As a result, the following were revealed. First, radian measure is intrinsic essence in angle measure. The radian is itself, and theoretical absolute unit. The radian makes trigonometric functions as real functions. Second, radians should be aware of invariance through covariance of ratios and proportions in concentric circles. The orthogonality between cosine and sine gives a crucial inevitability to the radian. It should be aware that radian is the simplest standards for measuring the length of arcs by the length of radius. It can find the connection with sexadecimal method using the division strategy. Third, I revealed the necessity by distinction between angle and angle measure. It needs justification for omission of radians and multiplication relationship strategy between arc and radius. The didactical suggestions derived by these can reveal the usefulness and value of the radian concept and can contribute to the substantive teaching of radian measure.

• Journal of Educational Research in Mathematics
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• v.19 no.3
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• pp.443-459
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• 2009

Despite the many discussions of mathematics education, there are a lot of controversy of the Radian. Generally, Radian is taken to have two properties. One property is an angular property and other is a property of fore numbers. For this reason, both Students and teachers are hard to understand the radian. This study is to provide a base of the radian understand. In essence, radian has only angular property, and other property is a derived property. So radian is to be understood in an angle.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.6
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• pp.40-45
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• 2000

교정은 모든 측정분야에서 어렵고 까다로운 주제인데, 특히 정전센서, 레이저간섭계, AFM, STM 등을 포함하는 나노메트롤로지(nanometrology : 나노측정) 분야에서는 그러하다. 나노측정에서는 전체 측정범위가 센서들의 한계분해능 값과 비슷한데, 이러한 측정에서 높은 소급성을 유지하기는 매우 어렵기 때문이다.(중략)

• School Mathematics
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• v.17 no.2
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• pp.309-329
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• 2015

This study is to provide didactical implications for teaching and learning of radian through a analysis of investigation result about pre-service teachers' understanding of radian. The results of this study are as follows. First, pre-service teachers understood the radian as ${\frac{180^{\circ}}{\pi}}$, rather than as the definition. Secondly, the definition style of radian affected the problem solving strategy for the measurement of the angle. Thirdly, pre-service teachers had insufficient content knowledge about properties of measurement as a pure number of radian. Lastly, They failed to describe the usefulness of circular measure. We suggested the definition of radian in textbooks should be changed from ${\frac{180^{\circ}}{\pi}}$ to mathematical definition of radian. And the general angle should be stated as the reason why the domain of trigonometric function is real numbers.

• School Mathematics
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• v.17 no.3
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• pp.447-467
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• 2015

The purpose of this study is to examine how the learning experience understanding degree and radian as the measurement of arc affects the conceptual understanding of radian and measuring angle. For this purpose, we investigated pre-service teachers' understanding about measurement of angle using a length of arc, and then conducted a teaching experiment with two middle school students. The results of analyzing pre-service teachers' and students' response are as follows. Students' experience interpreting the concept of degree into measurement of arc had a positive effect on understanding of radian and students' learning process in which they got measurement of angle as measurement of arc enabled conceptual understanding of 'linear measuring'. Also a circle context and a strategy dividing by arc operated as effective strategies for solving various problems about an angle. Finally, we confirmed that providing direct manipulative activities as a chance to explore relationships between an angle and arc measure can help students' conceptual understanding of measuring angle.

• Journal of Educational Research in Mathematics
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• v.18 no.2
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• pp.263-281
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• 2008

This study is to provide a base for discussions on teaching and teaming of radian through a theoretical analysis of it. Radian possesses two-fold comprehensive properties of measurement as a magnitude and a pure number. As a magnitude of an angle, it has some theoretical advantages in mathematics and in physics, in spite of its non-superiority to other angular measures in practical sense. As a pure number, it has some advantages in that it simplifies theoretical developments of trigonometric functions and justifies omitting the unit in the calculations and final expressions in physics. Radian should be taught and learnt with an appreciation of the advantages of the two-fold properties. Activities to measure angles from various viewpoints may be helpful for this. Students' awareness of the advantages of radian needs to be stimulated and deepened repeatedly as related content appears.

• The Mathematical Education
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• v.50 no.3
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• pp.355-365
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• 2011

The purpose of this study is to provide mathematical knowledge for supporting the didactical knowledge on circular measure and radian in the high school curriculum. We show that circular measure related to arcs can be mathematically justified as an angular measure and radian is a well defined concept to be able to reconcile the values of trigonometric functions and ones of circular functions, which are real variable functions. Radian has two-fold intrinsic attributes of angular measure and arc measure on the unit circle, in particular, the latter property plays a very important role in simplifying the trigonometric derivatives. To improve students's low academic achievement in trigonometry section, the useful advantage and the background over the introduction of radian should be preferentially taught and recognized to students. We suggest some teaching plans to practice in the class of elementary and middle school for enhancing teachers' and students' understanding of radian.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.4
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• pp.121-127
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• 1985

This paper deals with simultaneous geodetic networks adjustment by geographical coordinates(${\varphi}$, ${\lambda}$). The adjustment computation is performed by variation of coordinates, and the classical method with fixed points and free networks are also compared. Provisional values for observation equations are computed by extended Gauss-mid lattitude formula using existing official coordinates. Bessel ellipsoid and unit weight are adopted. The processing of a test-network by distances yields the average root mean square error of position 6.2 cm for classical method and 2.4cm for free networks. The standard error of unit weight in a test-network is $1.66{\times}10^{-6}$ radian (0.3"), and the analysis of error ellipses shows that free networks are more normally distributed errors.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.38 no.12
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• pp.1387-1394
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• 2014

In a photoelastic experiment, it is necessary to know the material stress fringe constant of the photoelastic specimen to determine the stresses from the measured isochromatic fringe orders. The material stress fringe constant can be obtained using a simple tension specimen and/or a circular disk under diametric compression. In these methods, there is generally a need to apply numerous loads to the specimen in response to the relationship of the fringe order. Then, the least squares method is used to obtain the material constant. In this paper, the fringe orders that appear on a four-point bending specimen are used to determine the fringe constant. This method requires four photoelastic fringes obtained from a circular polariscope by rotating the analyzer to 0, ${\pi}/4$, ${\pi}/2$, and $3{\pi}/4$ radians. Using the four-point bending specimen to determine the material stress fringe constant has an advantage because measurements can be made at different locations by applying a constant load. The stress fringe constant measured with this method is within the range suggested by the manufacturer of the photoelastic material.

• Journal of Korean Society of Steel Construction
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• v.23 no.4
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• pp.503-514
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• 2011

In this research, the seismic connection details for two concrete-filled U-shape steel beam-to-H columns were proposed and cyclically tested under a full-scale cruciform configuration. The key connecting components included the U-shape steel section (450 and 550 mm deep for specimens A and B, respectively), a concrete floor slab with a ribbed deck (165 mm deep for both specimens), welded couplers and rebars for negative moment transfer, and shear studs for full composite action and strengthening plates. Considering the unique constructional nature of the proposed connection, the critical limit states, such as the weld fracture, anchorage failure of the welded coupler, local buckling, concrete crushing, and rebar buckling, were carefully addressed in the specimen design. The test results showed that the connection details and design methods proposed in this study can well control the critical limit states mentioned above. Especially, the proposed connection according to the strengthening strategy successfully pushed the plastic hinge to the tip of the strengthened zone, as intended in the design, and was very effective in protecting the more vulnerable beam-to-column welded joint. The maximum story drift capacities of 6.0 and 6.8% radians were achieved in specimens A and B, respectively, thus far exceeding the minimumlimit of 4% radians required of special moment frames. Low-cycle fatigue fracture across the beam bottom flange at a 6% drift level was the final failure mode of specimen A. Specimen B failed through the fracture of the top splice plate of the bolted splice at a very high drift ratio of 8.0% radian.