• 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.

• Communications of Mathematical Education
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• v.21 no.1 s.29
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• pp.51-64
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• 2007

In this study we generalize the law of cosine(in any triangle the square of one side is equal to the sum of the squares of the other sides minus twice their product times the cosine of their included angle), We find the following generalized law of cosine: in any polygon the square of one side is equal to the sum of the squares of the other sides minus twice their products times the cosines of their included angles, and prove it using vector.

• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.44 no.5
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• pp.719-731
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• 2024

For efficient construction management, linking BIM with schedule and cost is essential, but there are limits to the application of 5D BIM due to the difficulty in disassembling thousands of WBS and CBS. To solve this problem, a standardized WBS-CBS set is configured in advance, and when a new construction project occurs, the CBS in the BOQ is automatically linked to the WBS when a text most similar to it is found among the standard CBS (Public Procurement Service standard construction code) of the already linked set. A method was used to compare the text similarity of CBS more efficiently using artificial intelligence natural language processing techniques. Firstly, we created a civil term dictionary (CTD) that organized the words used in civil projects and assigned numerical values, tokenized the text of all CBS into words defined in the dictionary, converted them into TF-IDF vectors, and determined them by cosine similarity. Additionally, the search success rate increased to nearly 70 % by considering CBS' hierarchical structure and changing keywords. The threshold value for judging similarity was 0.62 (1: perfect match, 0: no match).