• 한국수학사학회지
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• 제17권1호
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• pp.15-32
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• 2004

In this article we survey the sequences and the series in Mooksajipsanbup(默思集算法) which is the seventeenth century mathematics book of Chosun dynasty. First, we classify them into three categories: arithmetics, geometric, and general sequences (series). And then we explore the old methods to find the values of terms and the sum of terms.

• 대한수학교육학회지:학교수학
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• 제18권1호
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• pp.215-229
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• 2016

본 연구는 무한 등비급수의 합을 구하는 Archimedes의 상승적 아이디어를 소개하고 분배 상황을 이용하여 이를 은유적으로 확장하였다. Archimedes의 아이디어에 대한 은유적 확장 모델은 현행 고등학교 수준에서 강조되는 극한 개념의 동적 측면에 상보적으로 작동할 수 있는 정적인 특징을 갖고 있으며 중학교 수준에서 $0.999{\cdots}=1$임을 설명할 때 현행 교과서에서 대수적 무한 유추에 기반하여 유도하고 있는 식 $0.999{\cdots}=9/(10-1)$에 새로운 의미를 불어넣을 수 있는 장점이 있다. 실제로 중학교 2학년 영재학생들을 대상으로 한 본 연구자의 수업에서 은유적으로 확장된 모델은 구체적인 분배 상황을 통해 위의 식을 문맥화 함으로써 학생들의 흥미를 유발하였고 창의성과 오류를 이끌어 낼 수 있는 학습 환경을 제공하였다.

• 대한수학회보
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• 제44권3호
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• pp.461-473
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• 2007

For integral self-reciprocal polynomials P(z) and Q(z) with all zeros lying on the unit circle, does there exist integral self-reciprocal polynomial $G_r(z)$ depending on r such that for any r, $0{\leq}r{\leq}1$, all zeros of $G_r(z)$ lie on the unit circle and $G_0(z)$ = P(z), $G_1(z)$ = Q(z)? We study this question by providing examples. An example answers some interesting questions. Another example relates to the study of convex combination of two polynomials. From this example, we deduce the study of the sum of certain two products of finite geometric series.

• 대한산업공학회지
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• 제26권1호
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• pp.27-35
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• 2000

For a weighting method to be practically valid, it should produce weights which coincide with the relative importance of attributes perceived by the decision maker. In this paper, 'bootstrapping' is used to compare the practical validities of five weighting methods frequently used; the rank order centroid method, the rank reciprocal method, the rank sum method, the entropic method, and the geometric mean method. Bootstrapping refers to the procedure where the analysts allow the decision maker to make careful judgements on a series of similar cases, then infer statistically what weights he was implicitly using to arrive at the particular ranking. The weights produced by bootstrapping can therefore be regarded as well reflecting the decision maker's perceived relative importances. Bootstrapping and the five weighting methods were applied to a job selection problem. The results showed that both the rank order centroid method and the rank reciprocal method had higher level of practical validity than the other three methods, though a large difference could not be found either in the resulting weights or in the corresponding solutions.