• Communications of Mathematical Education
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• v.18 no.2 s.19
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• pp.251-263
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• 2004

피타고라스 정리와 코사인 제 2법칙 사이에는 어떤 관계가 있을까. 현재 우리의 교육과정에서는 피타고라스 정리는 중학교 3학년에서 코사인 제 2법칙은 고등학교 1학년에서 배운다. 그런데, 이 두 가지 수학적 사실 사이에는 밀접한 관계가 있다. 피타고라스 정리의 확장으로서 코사인 제 2법칙을 유도할 수 있다는 것이다. 코사인 제2법칙이 소개되어진 최초의 문헌은 Euclid의 <원론>으로 거슬러 올라간다. <원론>에 소개되어진 코사인 제 2법칙의 증명방법으로 시작하여 수 천년 동안 증명되어온 다양한 증명방법을 소개하고자 한다. 특히, 직각삼각형과 원이라는 큰 틀을 바탕으로 코사인 제 2법칙의 증명 방법에 대해 고찰하고, 그 외 다양한 증명방법을 분석하고자 한다.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.147-166
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• 2007

This study is about the law of cosines. It dealt with its historical origin and the developmental process of the age of Greece, Islam and Modern age. Especially, we tried to find out how the extension of the law of cosines for spherical triangles and tetrahedron from the law of cosines for plane was done. On the basis of this analysis, we investigated how the law of cosines was generated and proved it through the logical demonstration and mathematical induction. This made us find out the mathematical meaning of mathematical concepts.

• Journal of the Korean School Mathematics Society
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• v.16 no.4
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• pp.927-941
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• 2013

In this paper, we investigate and analysis high school students' generalization of cosine rule using analogy, and we study teaching and learning methods improving students' analogical thinking ability to improve mathematical thinking process. When students can reproduce what they have learned through inductive reasoning process or analogical thinking process and when they can justify their own mathematical knowledge through logical inference or deductive reasoning process, they can truly internalize what they learn and have an ability to use it in various situations.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.37 no.3
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• pp.189-198
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• 2019

In photogrammetry, single photo resection is a method of determining exterior orientation parameters corresponding to a position and an attitude of a camera at the time of taking a photograph using known interior orientation parameters, ground coordinates, and image coordinates. In this study, we proposed a single photo resection algorithm that determines the exterior orientation parameters of the camera using cosine law and linear equation-based three-dimensional coordinate transformation. The proposed algorithm first calculated the scale between the ground coordinates and the corresponding normalized coordinates using the cosine law. Then, the exterior orientation parameters were determined by applying linear equation-based three-dimensional coordinate transformation using normalized coordinates and ground coordinates considering the calculated scale. The proposed algorithm was not sensitive to the initial values by using the method of dividing the longest distance among the combinations of the ground coordinates and dividing each ground coordinates, although the partial derivative was required for the nonlinear equation. In addition, since the exterior orientation parameters can be determined by using three points, there was a stable advantage in the geometrical arrangement of the control points.

• Communications of Mathematical Education
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• v.35 no.2
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• pp.193-212
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• 2021

This study is to support the school's mathematics exploration activities. Mathematics exploration is a very important mathematical activity not only for mathematics teachers, but also for students. Looking at the development of mathematics, it has been extended from one mathematical fact to a new mathematical fact. Mathematics exploration activities are not unique to mathematicians, and opportunities are equally given to all ordinary people who are learning mathematics and teaching mathematics. Therefore, the purpose of this study is to develop a method of mathematics exploration activities that teachers and students can perform in schools, based on mathematics exploration activities based on one mathematical fact. Specifically, the cosine law was selected as one mathematical fact, and mathematical exploration activities were performed based on the cosine law. By analyzing the results of these mathematics exploration activities, we developed a method to explore school mathematics. Through the results of this study, it is expected that mathematics exploration activities will be conducted equally by students and teachers in the mathematics classroom.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.34 no.12B
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• pp.1387-1398
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• 2009

In the latest we will make a demand for the precision position estimation for the Mobile-station(MS)'s position. But, we have a lot of problems the position estimation method using the existing method. The Base-station(BS) measure a distance according to time delay waves to receive propagate from the MS and estimate the position using the existing circle equation with method to be selected BSs in close proximity the MS. It knows that happens a lot of error the estimated position and the true position. This paper propose that the method is selected round BSs to estimate for MS's position and estimated the angle using the second law of cosine. This paper demonstrate that using simulation the proposal method is a predominant method to compare with the existing method.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• Proceedings of the Korea Information Processing Society Conference
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• 2013.11a
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• pp.1378-1381
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• 2013

가상현실 체험형 콘텐츠는 컴퓨터를 이용하여 만들어낸 가공의 상황이나 환경을 사람의 감각 기관을 통해 느끼게 하여 사용자가 몰입감을 느끼고 상호작용하게 하는 기술이다. 본 연구에서는 스마트폰에서 LBS, Push 기술을 활용하여 증강현실 및 실감체험 기능이 있는 앱 실행 시 사용자 의도에 따른 콘텐츠 제공이 매치되기 위한 방안을 제안하였다. 그 예로 임의의 관광지에서 실제 피사체와 피사체를 비추는 스마트폰 카메라 화면속의 이미지가 일치되었을 때 카메라와 피사체간의 거리를 정확히 계산하는 방법으로 코사인 법칙 및 카메라 초점거리를 이용한 거리계산 방법을 제시하였다.

• Proceedings of the Korean Society of Computer Information Conference
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• 2023.07a
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• pp.87-88
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• 2023

본 논문에서는 COVID-19 팬데믹으로 인해 사회적 거리두기 및 규제조치가 시행되면서 다양한 분야에서 큰 영향을 가져왔다. 변화된 홈트레이닝 분야는 운동기구를 구비하여 개인운동을 통해 건강을 유지하고 있으나 전문적인 교육을 받지 않은 홈트레닝으로 부상 위험에 노출 되고 있다. 요가는 호흡운동과 명상을 지향하는 운동으로 요가의 효과를 얻기 위해 올바른 움직임과 자세가 중요 하다. 본 논문에서는 실시간으로 입력된 영상 프레임을 OpenCV와 MediaPipe를 통해 추출된 주요좌표 값을 벡터 내적공식을 대입, 코사인2법칙을 통해 요가의 올바른 자세를 분석하여 종합적인 정보를 제공하는 요가교정 모델이다.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.121-126
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• 2003

소득분배의 가장 대표적인 불평등척도는 Gini index이며, 이것은 통계학자인 Gini가 제안한 지표로서 소득분배에 관한 분석에서 가장 널리 이용되고 있다. 본 논문에서는 두 원의 호에 의해 Lorenz 곡선을 추정하고 코사인법칙을 이용하여 Gini index를 추정하기 위한 새로운 간편한 방법을 제시하여, 소득분포를 따르는 파레토분포에서 모의실험을 통해 Ogwang and Rao (1996)의 추정방법과 평균제곱오차 면에서 비교 분석한다.