• School Mathematics
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• v.12 no.1
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• pp.45-60
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• 2010

In school mathematics, gakdo(korean, ie angular measure in english) lost effectiveness as a term, on the other hand, an expression gak-ui-kugi(korean, ie size of angle in english) is prevalent these days. So it is necessary to accept this expression. It is necessary to specify in textbook that the size of angle rely on the degree of gap between two edges regardless of the length of edges. The content of curriculum manual and the content of textbooks must be reconciled. Random units for measuring the size of angle are not contained in textbooks. It can be possible, but it is not carried out actually. So, it is necessary not to require it in curriculum manual considering this circumstance. In curriculum manual, it is necessary to specify the role of 1-right angle as a standard unit, and situations to use it must be presented in textbooks. In cut-paste method of finding the sum of the size of three angles in a triangle and the sum of the size of four angles in a quadrilateral, keeping a straight angle and one rotation in mind, an explanation is based upon a premise that students know how to express the $180{^{\circ}}$ and $360{^{\circ}}$ in figure as a result. It is a leap of logic.

• Education of Primary School Mathematics
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• v.27 no.2
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• pp.155-171
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• 2024

This study compared and analyzed students' reasoning processes and justification methods when introducing the concept of "the sum of angles in a triangle" in mathematics classes with a focus on both measurement and geometric aspects. To confirm this, the research was conducted in a 4th-grade class at H Elementary School in Suwon, Gyeonggi-do, South Korea. The conclusions drawn from this study are as follows. First, there is a significant difference when introducing "the sum of angles in a triangle" in mathematics classes from a measurement perspective compared to a geometric perspective. Second, justifying the statement "the sum of angles in a triangle is 180°" is more effective when explained through a measurement approach, such as "adding the sizes of the three angles gives 180°," rather than a geometric approach, such as "the sum of the angles forms a straight angle." Since elementary students understand mathematical knowledge through manipulative activities, the level of activity is connected to the quality of mathematics learning. Research on this reasoning process will serve as foundational material for approaching the concept of "the sum of angles in a triangle" within the "Geometry and Measurement" domain of the Revised 2022 curriculum.

• Proceedings of the Korean Society of Medical Physics Conference
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• 2003.09a
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• pp.42-42
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• 2003

목적 : 조사면 크기에 따른 금속쐐기와 가상쐐기에 의한 6 MV 와 15 MV 엑스선의 출력 및 상부와 하부 에 설치하는 금속쐐기의 출력을 비교하고자 한다. 대상 및 방법 : Varian Clinac21EX(미국)는 두부의 상부와 하부에 설치하는 각각의 금속쐐기와 제한기에 의한 가상쐐기 기능을 가지고 있다. 금속쐐기의 쐐기각은 네 가지 (15$^{\circ}$, 30$^{\circ}$, 45$^{\circ}$, 60$^{\circ}$)이며 투과력에 무관하게 한 쐐기각에 대한 쐐기는 사하부는 각 1 개이고, 가상쐐기는 일곱 가지 ($10^{\circ}$, 15$^{\circ}$, 20$^{\circ}$, 25$^{\circ}$, 30$^{\circ}$, 45$^{\circ}$, 60$^{\circ}$) 이다. 각 쐐기에 대하여 3$\times$3～20$\times$20 $\textrm{cm}^2$ 의 조사면 크기에서 6 및 15 MV 엑스선의 쐐기출력인수 (wedge field output factor)를 $d_{max}$와 10 $\textrm{cm}^2$ 깊이에서 측정하였다. 조사면크기와 측정깊이에 따른 쐐기출력인수의 변화추이를 관찰하였다. 쐐기출력인수 O $F_{Wdg}$는 다음과 같다. O $F_{Wdg}$(r)= $D_{Wdg}$(r)/ $D_{op}$ ( $r_{0}$) 여기서 $r_{0}$와 r은 각각 민조사면의 기준조사면크기, 쐐기조사면크기이다. 하부쐐기에 대한 상부쐐기의 출력인수의 상대적인 백분율 차이, %ROD=l00$\times$(O $F_{upWdg}$/O $F_{lowWdg}$ lowWdg/ - 1)를 구하였다. 조사면크기와 깊이에 따른 %ROD의 변화추이를 평가하였으며 쐐기 각각에 대하여 출력인수를 측정해야하는지 평가하였다. 결과 : 금속쐐기에 대한 쐐기출력인수는 방사선의 투과력과 깊이에 관계없이 조사면 크기가 커짐에 따라 증가하였으나 가상쐐기의 쐐기출력인수는 쐐기각이 작은 경우에는 조사면크기가 커짐에 따라 증가하다가 감소하였으며 최대값을 보이는 조사면크기는 쐐기각이 커짐에 반하여 감소하였으며 투과력에 관계없이 60。 쐐기에 대해서는 조사면 크기가 4 cm(A/P=1) 이상에서 조사면크기가 커짐에 따라 감소하였다. 6 MV 엑스선 에 대한 10 cm 깊이에서 15。 쐐기와 15 MV 엑스선에 대한 10 cm 깊이에서 45。 쐐기의 A/P 가 1.5보다 작은 조사면을 제외하고는 조사면의 크기가 커짐에 따라 %ROD는 감소하였다. $d_{max}$에서는 15。 쐐기와 30。 쐐기에 대해서는 %ROD가 음수였으며 절대값이 증가하였다. 이는 곧 조사면의 크기가 커짐에 따라 상부쐐기의 쐐기출력계수가 하부쐐기와 접근하고 드디어는 상부쐐기의 출력인수가 하부쐐기의 출력인수보다 작아질 수도 있다는 것을 의미하고 있다. 또한 %ROD 는 쐐기각이 클수록 변화가 컸으며, 조사면 크기가 커짐에 따라 10 cm 깊이에서보다 $d_{max}$에서 더 급하게 감소하였다. %ROD 는 6 MV 엑스선에 대해서는 -0.52～4.18 % 였고, 15 MV 엑스선에 대해서는 -0.44-4.18 % 였다. 결론 : 두 가지 투과력의 엑스선이 방출되는 선형가속기의 상하부 쐐기와 가상쐐기의 출력인수를 측정하여 비교하였다. 결과에서 얻어진 결론은 아래와 같다. 1. 조사면의 크기가 커짐에 따라 금속쐐기의 출력계수 는 증가하였으나 가상쐐기의 경우는 증가하다가 감소하거나 큰 쐐기각에 대해서는 감소만 하였다. 2. 상부쐐 기와 하부쐐기는 쐐기출력인수가 4% 이상 차이가 날 수 있으므로 독립적으로 측정하여 이용하여야 할 것이다.것이다.다.

• Proceedings of the Korean Society of Computer Information Conference
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• 2011.06a
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• pp.315-316
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• 2011

수학 함수 중에서 삼각함수는 그 활용도가 매우 높아서 아주 많이 사용되는 함수 중 하나이다. 직각 삼각형의 직각이 아닌 한 각의 크기를 a라 하면, 이 삼각형의 임의의 두 변의 길이의 비는 이 각 a의 크기에 의하여 결정되므로 이 비를 이각의 삼각 함수라 하였다. 즉, 삼각함수는 직각삼각형에서 한 각의 크기가 일정하면, 이들 변의 비의 값은 삼각형의 크기에는 관계없이 일정하다는 가장 단순하고 독특한 성질에 기초를 둔 학문이다. 어떠한 대상체의 높이는 직삼각형의 밑변의 길이와 건물을 올려다본 각이 있다면 삼각함수를 이용하여 쉽게 구할 수 있다.

• Communications of Mathematical Education
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• v.33 no.3
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• pp.295-317
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• 2019

Angle concept is widely used in all mathematics curriculums and is a basic concept in geometric domain. Since angle have a multifaceted and affect subsequent learning, it is necessary for students to understand various angle concepts. In this study, Singapore, U.K., Australia, and U.S. are selected as comparable countries to examine the angle-related contents and learning process that appear in the curriculum as a whole, and then look at the perspectives and the size aspects of angle in detail and give implications to the Korean curriculum based on them. According to the analysis, the four countries except Korea, supplement angle, complement angle, angles on a straight line, angles at a point, and finding angle were explicitly covered in the curriculum. And most countries gradually covered angle-related contents over several years, compared to Korea which intensively studied in a particular school year. In common, definition of angle was described as static, measurement of angle was described as dynamic. But in Korean curriculum, dynamic views on angles are described later and less compared to other countries, and range of angle size was narrower than in other countries'. From this comparison, this study suggest to discuss how to place and develop various contents of characteristics of angle in curriculum, address the angle using both static and dynamic perspectives, and introduce the angle size as the amount of rotation to learn the reflex angle, $180^{\circ}$, $360^{\circ}$ angle.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2000.04a
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• pp.76-80
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• 2000

본 논문은 입체 음상 정위 시스템에 있어서 청취자의 머리 크기와 음상 정위를 원하는 위치와의 거리에 따른 머리전달함수 (HRTF; Head Related Transfer Function)의 보정 방법에 관한 것이다. 제안된 방법은 먼저 표준 반경에서 표준 머리 크기의 더미 헤드를 이용해 측정된 표준 머리전달함수 데이터베이스로부터 실제의 왼쪽 또는 오른쪽 귀를 기준으로 한 방위각과 고도각을 산출한다. 이렇게 산출된 방위각과 고도각을 기준으로 머리전달함수 데이터베이스의 인덱스를 보정한다. 음상 정위하고자 하는 3차원 공간상의 위치를 입력받게 되면, 입력받은 위치로부터 청취자의 왼쪽 또는 오른쪽 귀를 기준으로 한 방위각과 고도각을 산출한 후에 보정된 머리전달함수 데이터베이스로부터 머리전달함수를 가져와서 입력 모노 신호를 보정된 머리전달함수와 콘볼루션하여 입체음향을 생성하게 된다.제안된 방법에 의해 청취자의 머리 크기 및 거리에 따라 보정된 머리전달함수를 사용함으로써 청취자에게 보다 실감나는 3차원 음상 정위 효과를 제공할 수 있다.

• Radiation Oncology Journal
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• v.21 no.2
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• pp.135-142
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• 2003

Purpose: The purpose of this study was to investigate the positional change of the uterus during radiotherapy. Materials and Methods: Between 1997 and 2001, 47 patients received definitive radiotherapy for cervical cancer at the Samsung Medical Center. For each patient, two MRI scans were taken; one before and the other 3$\~$4 weeks after the radiotherapy treatment. In T2 weighted MRI images, the positional change of the uterine was quantified by measuring six quantities; the distance from the cervix os to the isthmus of the uterus (Dcx), the maximum length from the isthmus of the uterus to the uterine fundus (Dco), the maximum vertical distance of the uterine body (Dco-per), the angle between the vertical line and the cervical canal in the sagittal images (Acx), the angle of the uterine corpus from the vertical line in the sagittal plan (Aco-ap), and the relative angle of the uterine corpus from a fixed anatomical landmark in the axial images (Aco-axi). Results: The mean Dcx values, before and during the treatment, were 36.7 and 27.8 mm, respectively. The Dco deviated by more than 10 mm in 14 cases (29.8$\%$). The change in the Acx ranged from 0.1 to 67.8$^{\circ}$ (mean 13.2$^{\circ}$). The Aco-ap changed by a maximum of 84.8$^{\circ}$ (mean 16.9$^{\circ}$). The differences in the Dcx plus the Dco in the smaller (<4 cm) and larger ($geq$4 cm) tumors were 5.3 and 19.4 mm, respectively. With patients less than 60 years old, or with a tumor size larger than 4 cm, the difference in the Acx was statistically significant. Conclusion: The positional changes of the uterus, during radiation treatment, should be considered in the 3DCRT or IMRT treatment planning, particularly in patients under 60 years of age or in those with a tumor size greater than 4 cm in maximum diameter.

• Journal of the Korean Data and Information Science Society
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• v.27 no.5
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• pp.1241-1251
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• 2016

We consider a correlated discrete-time random walk in which the current jump size depends on the previous jump size and a noncorrelated discrete-time random walk where the jump size is determined independently. By using the strong law of large numbers of Markov chains we derive the formula for the asymptotic means of the random mixture and the periodic pattern of these two random walks and then we show that there exists Parrondo's paradox where each random walk has mean 0 but their random mixture and periodic pattern have negative or positive means. We describe the parameter sets at which Parrondo's paradox holds in each case.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.431-449
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• 2017

Acute triangles and obtuse triangles are defined according to the classification of triangles by angles. The definitions of acute triangles and obtuse triangles are difficult for students because they are related to different logical elements. The purpose of this study is to seek desirable methods for teaching the classification of triangles by angles related to logic. To do this, based on the theoretical consideration and the longitudinal analysis of the elementary mathematics textbooks, some implications are found for teaching. And then the lesson was planned and applied to $4^{th}$ graders. After the lesson, we reviewed and analyzed their worksheets and test results for examining the effects by teaching methods. Based on the result, we discussed and made some didactical suggestions for teaching the classification of triangles by angles.

• School Mathematics
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• v.17 no.1
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• pp.35-46
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• 2015

In this paper, the teaching contents for angle and measure of an angle in elementary mathematics textbook between Korea and Japan were compared. From this comparison, the following five suggestions were presented as implications to improve the teaching contents for angle and measure of an angle in elementary mathematics textbook in Korea. First, it is necessary to reconsider the way of the definition of angle. There is no use of half line in elementary mathematics, except when to define angle, and the way to define angle and the way to define right angle are not consistent. Second, considering to associate the turning of plane geometrical figures to the $90^{\circ}$, $180^{\circ}$, $270^{\circ}$, $360^{\circ}$ is necessary, and associating them is connected to dealing with point-symmetrical shapes in the fifth grade. Third, there is a need to deal with "the measures of angles are same." in comparing angles. This is possible by superimposing two angles in comparing the measures of them. Fourthly, it is necessary to consider the introduction of the rotational angle. Dealing with the $360^{\circ}$ as the rotational angle is related to explaining that the sum of measures of interior angles in quadrangle is $360^{\circ}$. Fifth, it is necessary to be connected with middle school mathematics curriculum. The term 'straight angle' is used in middle school, and to obtain the sum of the measures of the interior angles of a regular polygon is the contents to be dealt with in middle school.