• Proceedings of the Korean Society of Computer Information Conference
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• 2016.07a
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• pp.167-168
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• 2016

본 논문에서는 스마트폰을 이용하여 수학을 공부할 수 있는 지오지브라의 활용 방안을 제안하였다. 특히 원 및 원기둥 등 도형의 면적 계산 개념을 제안한 아르키메데스의 사고를 지오지브라를 활용하여 할 수 있는 구체적인 자료를 개발하였다. 이러한 자료를 통해 학생들은 도형의 면적을 구하는 공식을 암기하기 않고 스스로 이해하면서 아르키메데스가 제안한 불가불량의 개념을 통해 다양한 도형의 면적과 체적을 구하는 방법을 이해할 수 있을 것이다. 특히 수학을 어려워하는 학생들에게 머릿속으로 사고하기 어려운 내용을 컴퓨터라는 도구를 활용하여 이해할 수 있도록 하였다는 점에서 의미가 있다.

• Communications of Mathematical Education
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• v.17
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• pp.115-126
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• 2003

수학사는 수학적 사실이나 수학자에 대한 연대기적 나열만을 의미하는 것은 아니다. 수학사에서는 수학적 개념들, 정리들, 연구 방법의 발생, 축적, 그리고 발전에 대한 폭넓은 견해를 접할 수 있다. 특히, 수학사에서 접할 수 있는 수학 문제해결의 다양한 방법은 수학 교수-학습 과정에서 교사의 올바른 교수학적 선택을 위한 중요한 기초 자료가 될 수 있다. 본 연구에서는 그리스의 수학자 아르키메데스가 구의 부피를 구하기 위해 사용했던 공학적 문제해결 방법을 살펴보고, 공학적 방법의 활용에 관련된 수학적 기초를 살펴보고, 공학적 문제해결 방법을 중등학교 수학 영재교육에 활용할 수 있는 가능성을 모색할 것이다.

• Proceedings of the Korea Water Resources Association Conference
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• 2022.05a
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• pp.122-122
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• 2022

기후변화 대응 및 탄소 저감 노력의 일환으로 신재생에너지의 개발 및 활용이 전 세계적으로 활발하며, 우리나라에서도 2050년 탄소중립 달성을 위하여 친환경 에너지 시스템 구축에 많은 노력을 기울이고 있다. 전통적인 재생에너지인 수력은 발전의 효율성, 안정성과 발전 제어의 용이함 때문에 널리 사용되고 있으나, 경제성을 확보하기 위한 댐, 보의 설치 및 대규모 발전설비가 필요하여, 생태계, 환경 파괴 등의 문제점 등을 수반하여, 최근 들어 대규모 사업이 이루어지지 못하고 있다. 이러한 흐름에 따라 최근에는 유럽을 중심으로 친환경 소수력 발전으로 회전 나선형 아르키메데스 수차를 활용한 소수력 발전의 적용이 이루어지고 있으며, 특히 2000년대 이후 독일을 중심으로 활발히 개발되고 있다. 또한 휴대용 초소수력 발전은 새로운 산업분야로 민간용 초소수력 발전기의 개발 및 판매가 국내외에서 증가하고 있으며, 우리나라에서도 자연 하천 환경에 활용 가능한 초소수력 발전의 필요성이 꾸준히 제기되고 있다. 본 연구에서는 저유량 및 저낙차에 적용 가능한 '초소형 회전 나선형 아르키메데스 수차', 초소형 발전에 적합한 '발전기 및 발전시스템', 자연환경을 훼손하지 않는 친환경 '유도수로'로 구성되어, 원하는 하천이나 수로 등에 손쉽게 설치 가능한 초소형 소수력 발전시스템을 개발하였다. 회전 나선형 아르키메데스 수차는 3D프린터로 제작한 후, 강화 코팅제를 도포하여 내구성을 확보하였다. 상용 AC발전기, 소형 발전기용 '발전기 및 발전시스템'을 적용하고, 콘트롤 보드를 맞춤형으로 제작하여 경제성을 확보하였다. 이러한 발전 시스템은 개발 테스트 중에 있으며 향후 방류수로, 하수구 등 현장 적용을 준비 중에 있다.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.95-112
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• 2006

The purpose of this paper is to investigate a classic mathematician and inventor Archimedes' work ${\ll}$On the Sphere and Cylinder${\gg}$. The propositions of this book which deals with three dimensional geometry are reviewed. Through the review this study tries to find out how Archimedes mastered spherical figures and how classical mathematics ideas are related to the modern concept of integration. The results of this study seems to help people understand deeply modern mathematics and to be good resources to develop new mathematical ideas.

• School Mathematics
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• v.8 no.3
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• pp.291-300
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• 2006

Proofs in school mathematics are regarded as the procedures to examine a proposition's truth or falsehood. However, they are not based on an axiomatic system in general. This implies the possible existence of vicious circles in proofs in school mathematics. The concept of proof can be more completely acquired when accompanied with concept of circular reasoning and necessity of axiomatic system. Therefore, it is necessary to discuss on the axiomatic system in school mathematics curriculum. The vicious circle can be found in computing an area of a circle by using definite integral in differentiation/integration part of high school textbooks. This paper will first illustrate this in detail and then offer several comments on the axiomatic methods related to the dissolution of that circular reasoning. To further the discussion, Archimedes' derivation for the area of a circle will be considered next. Finally, several arguments on circular reasoning, local organization, and axiomatic system in school curriculum will be presented at the end of the paper.

• School Mathematics
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• v.9 no.4
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• pp.487-506
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• 2007

The aims of this study is figure out the characteristics of justification patterns and mathematical representation which are derived from 14 mathematically gifted middle school students in the process of solving the spatial tasks on Archimedean solid. This study shows that mathematically gifted students apply different types of justification such as empirical, or deductive justification and partial or whole justification. It would be necessary to pay attention to the value of informal justification, by comparing the response of student who understood the entire transformation process and provided a reasonable explanation considering all component factors although presenting informal justification and that of student who showed formalization process based on partial analysis. Visual representation plays an valuable role in finding out the Idea of solving the problem and grasping the entire structure of the problem. We found that gifted students tried to create elaborated symbols by consolidating mathematical concepts into symbolic re-presentations and modifying them while gradually developing symbolic representations. This study on justification patterns and mathematical representation of mathematically gifted students dealing with spatial geometry tasks provided an opportunity for understanding their the characteristics of spacial geometrical thinking and expending their thinking.

• Journal of Korean Society of Water and Wastewater
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• v.23 no.6
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• pp.865-870
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• 2009

In this study, the adequacy of Reynolds numbers and Froude numbers derived from about sixty domestic water treatment plants (WTPs) were analyzed in order to estimate the characteristics of hydraulic behavior within the rectangular shaped sedimentation basins used widely. From the results of analysis, most of domestic WTPs have satisfied the criteria regulated as that Reynolds number should less than 1,000(dimensionless). On the other hand, they have not been able to satisfy the Froude number criteria, which should be higher than $1.0{\times}10^{-6}$. The reasons why most of domestic WTPs could not satisfy the criteria are that its criteria basis has been not only inadequate, but also the concept of external flow occurred around a settling particle has been ignored. Accordingly, this study proved the feasibility of Archimedes number, which indicates the ratio between particle Reynolds number and Froude number, to evaluate the hydraulic efficiency and its function of scale factor.

• Journal of the Korean Society for Nondestructive Testing
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• v.14 no.2
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• pp.90-100
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• 1994

Ultrasonic velocities are widely used in the investigation of material properties. In this paper, a micromechanics model and the ultrasonic velocity were used to develop a nondestructive method to determine the density variation due to porosity in structural SiC. The micromechanics model developed can consider the pore shape and orientation. The model also takes into account the interaction between pores so that it can be applied to the material with high porosity content. A contact pulse overlap method was used to measure the ultrasonic velocities of porous SiC samples, and there was a linear correlation between the velocity and density (or porosity). Using the model and the measured velocity, the bulk density can be easily calculated. The calculated density was in good agreement with that obtained by Archimedes' method.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.19-30
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• 2008

Cavalieri is chiefly remembered for his work on the problem "indivisibles." Building on the work of Archimedes, he investigated the method of construction by which areas and volumes of curved figures could be found. Cavalieri regarded an area as made up of an indefinite number of parallel line segments and a volume of an indefinite number of parallel plane areas. He called these elements the indivisibles of area and volume. Cavalieri developed a method of the indivisibles which he used to determine areas and volumes. We call this Cavalieri's principle which states that there exists a plane such that any plane parallel to it intersects equal areas In both objects, then the volumes of the two objects are equal. Cavalieri's principle and method of the indivisibles are very important to understand of volume of a pyramid for gifted students.

• Solar Energy
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• v.11 no.1
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• pp.50-60
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• 1991

A centrifugal pump was selected as a basic study, for it was utilized widely at the industry among various types of pumps. The purpose of this study was to develop the software for design of centrifugal pump. The step of this design was divided into two stages. First, the impeller was designed by the experiences and theory of A.J.Stepanoff, and the head was checked whether the design of impeller was acceptable. Second, the volute chamber was designed by the Archimedes spiral. Then, These procedures of impeller and volute chamber were developed into the software in C-language. Checked the validity of the developed software, the results were consistent with the actual pump produced domestically.