• 대한수학교육학회지:수학교육학연구
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• 제11권2호
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• pp.341-349
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• 2001

Infinity is one of the important concept in mathematics, science, philosophy etc. In history of mathematics, potential infinity concept conflicts with actual infinity concept. Reason that mathematicians refuse actual infinity concept during long period is because that actual infinity concept causes difficulty in our perceptions. This phenomenon is called epistemological obstacle by Brousseau. Potential infinity concept causes difficulty like history of development of infinity concept in mathematics learning. Even though students team about actual infinity concept, they use potential infinity concept in problem solving process. Therefore, we must make clear epistemological obstacles of infinity concept and must overcome them in learning of infinity concept. For this, it is useful to experience visualization about infinity concept. Also, it is to develop meta-cognition ability that students analyze and control their problem solving process. Conclusively, students must adjust potential infinity concept, and understand actual infinity concept that is defined in formal mathematics system.

• 대한수학교육학회지:수학교육학연구
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• 제18권4호
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• pp.469-482
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• 2008

본 연구에서는 무한 개념을 실무한적으로 파악하는 경우와 가무한적으로 파악하는 경우에 각각 부딪히게 되는 문제점들을 분석하였다. 또, 우리나라의 초등학교와 중학교 수학 교육과정에서 신중하지 못하게 실무한적 개념을 사용하고 있는 사례도 고찰하였다. 현대 수학에서 요구하는 실무한적 무한 개념의 학습을 위해서는 가무한적인 직관은 결국 단절해야 하는 인식론적 장애라고 할 수 있지만, 초기의 학교수학에서부터 그러한 단절을 요구하기에는 실무한 개념이 너무 비직관적이고 많은 패러독스를 유도하며 적절한 은유를 제공하지 못한다는 점이 문제가 된다.

• 한국수학사학회지
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• 제16권3호
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• pp.57-68
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• 2003

Infinity is very important concept in mathematics. In history of mathematics, potential infinity concept conflicts with actual infinity concept for a long time. It is reason that actual infinity concept causes difficulty in our perceptions. This phenomenon is called epistemological obstacle by Brousseau. So, in this paper, we examine the infinity in terms of mathematical didactics. First, we examine the history of development of infinity and reveal the similarity between the history of debate about infinity and episternological obstacle of students. Next, we investigate obstacle of students about infinity and the contents of curriculum which treat the infinity Finally, we suggest the methods for overcoming obstacle in learning of infinity concept.

• 대한수학교육학회지:수학교육학연구
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• 제20권3호
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• pp.293-303
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• 2010

이 연구의 목적은 인식론 분석을 통해 수학사의 세 가지 역할을 분류하는 것이다. 무한과 극한에 대한 수학사를 바탕으로 네 가지의 다른 인식론들을 통해 "잠재적 무한"과 "실제적 무한" 담화를 묘사한다. 무한과 극한 개념의 상호 의존성을 또한 제시한다. 이러한 분석들을 이용하여 무한과 극한에 대한 수학사의 세가지 다른 사용을 보이고자 한다 : 과거, 현재, 그리고 미래사용.

• 한국학교수학회논문집
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• 제10권1호
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• pp.91-111
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• 2007

본 연구는 컴퓨터를 활용하여 동적이며 직관적인 시각화 자료를 활용하여 실험에 참가한 고등학교 학생들의 수열 개념에 대해서 수열의 합 공식에 대해 귀납 추론으로 공식을 학생 스스로가 추론할 수 있는지를 알아보고자 했다. 학생들은 스스로가 수열의 합 공식을 사용하지 않고 귀납 추론으로 공식을 유도할 수 있음을 보았다. 또한 무한급수에서의 무한의 오개념인 잠재적 무한의 개념을 가진 학생들이 본 실험 자료로 학습을 하였을 때에 무한의 올바른 개념인 실 무한의 개념을 이해하는데 도움을 주는지에 대하여 연구를 하였는데 실험에 참가한 실험 학생들은 잠재적 무한 개념을 가지고 있었고 동적이고 직관적인 시각화 자료를 가지고 수업 후 실 무한의 개념으로의 변화가 있었다. 이들 학생들은 또한 컴퓨터를 활용하여 동적이고 직관적인 시각화 자료에 대해서 매우 흥미를 느꼈고, 수학에 대한 태도에도 영향을 주었다.

• 한국실내디자인학회논문집
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• 제24권5호
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• pp.31-41
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• 2015

The objective of this research is to investigate the artistic meaning of "infinity," manifested by the fourth dimensional value in the genres of photography and architecture, by analyzing how Sugimoto Hiroshi's photographic spatio-temporal infinity transfers to his architectural approaches. The research is initiated by scrutinizing the themes, characteristics, techniques, and artistic meaning of Sugimoto's famous photographic series, including "Seascapes," "Theatres," and "Architecture"; the concept of infinity can be defined as infinite divergence and infinitesimal convergence between antithetical concepts in time, space, and being. Sugimoto's photographic works display "temporal infinity" by connecting ancient times, the present, and the future; "spatial infinity" by offering the potential for transformation from flat photographs into infinite three-dimensional space and fourth-dimensional concepts through time; and "existential infinity" of life and death by making us think about being and essence, being and time, and origin and religion. These perspectives are also used to analyze Sugimoto's architectural works, such as "Appropriate Proportion" and "Glass Tea House Mondrian." As a result, the research finds that in Sugimoto's architectural approaches, spatio-temporal infinity between antithetical values is manifested through the concept of origin, geometric form, extended axis, immaterial threshold, transparent materiality, and connectivity of light and shadow, provoking our existence to transcend into infinity itself.

• 한국수학사학회지
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• 제27권2호
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• pp.139-152
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• 2014

This paper aims to compare and contrast Kierkegaard and Turing, whose birth dates were one hundred years apart, analyzing them from the perspective of the limit. The model of analysis is two concentric circles and movement in them and on the boundary of outer circle. In the model, Kierkegaard's existential stages have 1:1 correspondences: aesthetic stage, ethical stage, religious stage A and religious stage B correspond to inside of the inner circle, outside of the inner circle, the boundary of the outer circle and the outside of the outer circle, respectively. This paper claims that Turing belongs to inside of the outer circle and moves to the center while Kierkegaard belongs to outside of the outer circle and moves to the infinity. Both of them have movement of potential infinity but their directions are opposite.

• 한국수학교육학회지시리즈A:수학교육
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• 제47권4호
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• pp.447-465
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• 2008

The purpose of this study is to suggest effective teaching methods on the concept of infinity for students to obtain the right concept in the middle school curriculum. Many people have thought that infinity is something vouge and unapproachable. But, nowadays it is rather something with a precise definition that lies at the core of modern mathematics. To understand mathematics and science very well, it is necessary to comprehend the concept of infinity. But students tend to figure out the properties of infinite objects and limit concepts only through their experience closely related to finite process, and so they are apt to have their spontaneous intuition and misconception about it. Since most of them have cognitive obstacles in studying the infinite concepts and misconception, mathematics teachers need to help them overcome the obstacles and establish the right secondary intuition for the concepts through good examples and appropriate explanation. In this study, we consider the developing process of the concept of infinity in human history and give some comments and suggestions in teaching methods relative to that concept with new suitable examples.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1609-1612
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• 1997

Kinematically redundantant manipulators have a nimber of potential advantages over nonredundant ones. Questions associated with manipulability measures for (non)redundant manipulators derived by minimum 2-norm solution and minimum infinity-norm solution in unit joint velocity are examined in detail.

• 대한수학회보
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• 제51권2호
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• pp.423-435
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• 2014

In this paper, the fractional Hardy-type operator of variable order ${\beta}(x)$ is shown to be bounded from the Herz-Morrey spaces $M\dot{K}^{{\alpha},{\lambda}}_{p_1,q_1({\cdot})}(\mathbb{R}^n)$ with variable exponent $q_1(x)$ into the weighted space $M\dot{K}^{{\alpha},{\lambda}}_{p_2,q_2({\cdot})}(\mathbb{R}^n,{\omega})$, where ${\omega}=(1+|x|)^{-{\gamma}(x)}$ with some ${\gamma}(x)$ > 0 and $1/q_1(x)-1/q_2(x)={\beta}(x)/n$ when $q_1(x)$ is not necessarily constant at infinity. It is assumed that the exponent $q_1(x)$ satisfies the logarithmic continuity condition both locally and at infinity that 1 < $q_1({\infty}){\leq}q_1(x){\leq}(q_1)+$ < ${\infty}(x{\in}\mathbb{R}^n)$.