• 한국수학사학회지
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• 제15권1호
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• pp.115-134
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• 2002

The increasing use of computers in mathematics and in mathematics education is strongly reflected in the teaching on Euclid geometry, in particular in the use of dynamic graphics software. This development has raised questions about the role of analytic proof in school geometry. One can sometimes find a proof which is rather more explanatory than the one commonly used. Because we, math educators are concerned with tile explanatory power of the proofs, as opposed to mere verification, we should devise ways to use dynamic software in the use of explanatory proofs.

• 한국학교수학회논문집
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• 제13권2호
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• pp.225-241
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• 2010

기하는 수학의 기초를 이루는 중요한 영역이다. 그러나 수학영재를 위한 기하 학습프로그램과 영재를 지도하기 위한 교수전략 연구가 부족한 실정이다. 이에 본 연구는 해석기하학과 사영기하학을 중심으로 영재들의 특성을 고려한 학생중심의 학습 프로그램 설계에 대한 모델을 제시하고 새로운 교수전략으로 기초전략단계(문제제시, 문제해결), 지지전략단계(수학적 개념추출, 수학화, 확장), 전이전략단계 등을 소개한다. 이를 통해 수학영재들에게 필요한 기하교육의 방향성을 제시하고자 한다.

• 한국수학사학회지
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• 제21권2호
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• pp.39-54
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• 2008

이 논문에서는 문제해결의 입장에 서서 수학사에서 중요한 의미를 지닌 데카르트의 <기하학>을 고찰한다. 문제해결의 일반적 원리를 천명한 것만이 아니라 실제로 당면한 문제를 해결하기 위하여 새로운 방법을 찾아내는 것이야말로 데카르트가 문제해결에 관하여 후세에 영향을 크게 남긴 업적이라 할 수 있다. 따라서 본고에서는 그의 방법에 초점을 맞추어 분석하도록 한다.

• East Asian mathematical journal
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• 제37권4호
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• pp.499-521
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• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1996년도 춘계학술발표회논문집(1)
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• pp.131-136
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• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• 제어로봇시스템학회논문지
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• 제5권8호
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• pp.955-960
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• 1999

This paper describes the effect of impact configurations on a single robot manipulator. The effect of different configurations of kinematically redundant arms on impact forces at their end effectors during contact with the environment is investigated. Instead of the well-known impact ellipsoid, I propose an analytic method on the geometric configuration of the impact directly from the mathematical definition. By calculating the length along the specified motion direction and volume of the geometry, we can determine the characteristics of robot configurations in terms of both the impact along the specified direction and the ability of the robot withstanding the impact. Simulations of various impact configurations are discussed at the end of this paper.

• East Asian mathematical journal
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• 제28권4호
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• pp.453-474
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• 2012

The conic sections is an important topic in the current high school geometry. It has been recognized by many researchers that high school students often have difficulty or misconception in the learning of the conic sections because they are taught the conic sections only with algebraic perspective or analytic geometry perspective. In this research, we suggest a way of teaching the conic sections using a dynamic geometry software based on some mathematics teaching and learning theories such as Freudenthal's and Dienes'. Students have various experience of constructing and manipulating the conic sections for themselves and the experience of deriving the equations of the quadratic curves under the teacher's careful guidance. We identified this approach was a feasible way to improve the teaching and learning methods of the conic sections.

• 한국지구물리탐사학회:학술대회논문집
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• 한국지구물리탐사학회 2003년도 Proceedings of the international symposium on the fusion technology
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• pp.238-243
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• 2003

As there are many advantages on underground caverns, such as safety and operation, they can also be used for gas storage purpose. When liquefied gas is stored underground, the cryogenic temperature of the gas will affect the stability of the storage cavern. In order to store the liquefied gas successfully, it is essential to estimate the exact temperature distribution of the rock mass around the cavern. In this study, an analytic solution and a conceptual model that can estimate three-dimensional temperature distribution around the storage cavern are suggested. When calculating the heat transfer within a solid, it is likely to consider the solid as the intersection of two or more infinite or semi-infinite geometries. Therefore heat transfer solution for the solid is expressed by the product of the dimensionless temperatures of the geometries, which are used to form the combined solid. Based on the multi-dimensional transient heat transfer theory, the analytic solution is successfully derived by assuming the cavern shape to be of simplified geometry. Also, a conceptual model is developed by using the analytic solution of this study. By performing numerical experiments of this multi-dimensional model, the temperature distribution of the analytic solution is compared with that of numerical analysis and theoretical solutions.

• 한국해안해양공학회지
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• 제18권4호
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• pp.308-320
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• 2006

축대칭 함몰지형 위를 진행하는 파에 관한 완경사 방정식의 해석 해를 유도하였다. 함몰지형 내부에서의 수심은 함몰지형 중심으로부터의 거리의 덕에 비례하여 변한다. 변수 분리법을 사용하여 지배 방정식을 상미분 방정식으로 전환하였으며, Hunt(1979)의 근사식을 사용하여 방정식의 계수들을 양함수의 형태로 변환하였다. 마지막으로 Frobenius 급수를 사용하여 해석 해를 유도하였다. Hunt 근사식의 특성 상 본 연구에서 유도된 해석 해는 천해와 심해에서는 정확하고 중간수심에서는 덜 정확하다. 해석 해의 타당성을 검토하기 위하여 수치 모델 결과와 비교하였다. 또한 해석 해를 이용하여 함몰지형의 형상과 상대수심 등을 변화시키면서 다양한 조건에 대한 파랑 변형을 검토하였다.

• Biomedical Engineering Letters
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• 제8권4호
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• pp.383-392
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• 2018

For prompt gamma ray imaging for biomedical applications and environmental radiation monitoring, we propose herein a multiple-scattering Compton camera (MSCC). MSCC consists of three or more semiconductor layers with good energy resolution, and has potential for simultaneous detection and differentiation of multiple radio-isotopes based on the measured energies, as well as three-dimensional (3D) imaging of the radio-isotope distribution. In this study, we developed an analytic simulator and a 3D image generator for a MSCC, including the physical models of the radiation source emission and detection processes that can be utilized for geometry and performance prediction prior to the construction of a real system. The analytic simulator for a MSCC records coincidence detections of successive interactions in multiple detector layers. In the successive interaction processes, the emission direction of the incident gamma ray, the scattering angle, and the changed traveling path after the Compton scattering interaction in each detector, were determined by a conical surface uniform random number generator (RNG), and by a Klein-Nishina RNG. The 3D image generator has two functions: the recovery of the initial source energy spectrum and the 3D spatial distribution of the source. We evaluated the analytic simulator and image generator with two different energetic point radiation sources (Cs-137 and Co-60) and with an MSCC comprising three detector layers. The recovered initial energies of the incident radiations were well differentiated from the generated MSCC events. Correspondingly, we could obtain a multi-tracer image that combined the two differentiated images. The developed analytic simulator in this study emulated the randomness of the detection process of a multiple-scattering Compton camera, including the inherent degradation factors of the detectors, such as the limited spatial and energy resolutions. The Doppler-broadening effect owing to the momentum distribution of electrons in Compton scattering was not considered in the detection process because most interested isotopes for biomedical and environmental applications have high energies that are less sensitive to Doppler broadening. The analytic simulator and image generator for MSCC can be utilized to determine the optimal geometrical parameters, such as the distances between detectors and detector size, thus affecting the imaging performance of the Compton camera prior to the development of a real system.