• 대한수학회지
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• 제48권2호
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• pp.421-430
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• 2011

By evaluating the containment measure of one domain to contain another, we will derive some new Bonnesen-type inequalities (Theorem 2) via the method of integral geometry. We obtain Ren's sufficient condition for one domain to contain another domain (Theorem 4). We also obtain some new geometric inequalities. Finally we give a simplified proof of the Bottema's result.

• 대한수학회지
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• 제34권2호
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• pp.371-381
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• 1997

Our basic concern in this paper is to investigate some geometric properties of the graph of a maximal monotone operator in the one dimensional case. Using a well-known theorem of Minty, we answer S. Simon's questions affirmatively in the one dimensional case. Further developments of these results are also treated. In addition, we provide a new proof of Rockafellar's characterization of maximal monotone operators on R: every maximal monotne operator from R to $2^R$ is the subdifferential of a proper convex lower semicontinuous function.

• 호남수학학술지
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• 제42권4호
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• pp.747-755
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• 2020

The mathematical proof for establishing some new inequalities involving arithmetic, geometric, harmonic means for the arguments lying on the paths of triangular wave function (linear) and new parabolic function (curved) over the interval (0, 1) are discussed. The results representing an extension as well as strengthening of Ky Fan Type inequalities.

• 대한수학회지
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• 제58권1호
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• pp.173-205
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• 2021

The spherical buildings associated with absolutely simple algebraic groups of relative rank 2 are all Moufang polygons. Tits polygons are a more general class of geometric structures that includes Moufang polygons as a special case. Dagger-sharp Tits n-gons exist only for n = 3, 4, 6 and 8. Moufang octagons were classified by Tits. We show here that there are no dagger-sharp Tits octagons that are not Moufang. As part of the proof it is shown that the same conclusion holds for a certain class of dagger-sharp Tits quadrangles.

• 대한수학회지
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• 제58권2호
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• pp.501-523
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• 2021

We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two different ways to desingularize this space. One is Vakil-Zinger's desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger's desingularization.

• 대한수학교육학회지:학교수학
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• 제9권4호
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• pp.523-533
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• 2007

이 논문에서는 피타고라스 정리에 대한 피타고라스와 유클리드의 증명의 의미를 역사적, 수학적 관점에서 고찰하였다. 피타고라스의 닮음비에 의한 증명 방법은 통약성이라는 수에 대한 가정에 근거한 것이라고 볼 수 있다. 반면 유클리드는 통약성이 필요 없는 분해 합동이라는 순수한 기하학적 방법으로 다시 증명하였다. 피타고라스 정리의 증명에서 엿볼 수 있는 피타고라스와 유클리드의 기하에 대한 다른 접근 방식을 현 학교 기하의 바탕이 되는 Birkhoff와 Hither 공리계와 연관하여 논의하였다. Birkhoff는 엄밀하게 정의된 실수 개념을 상식으로 수용하여 현대수학적인 평면 기하 공리계를 제안하였으며, Hilbert는 실수 개념에 의존하지 않는 순수한 기하학을 추구했던 유클리드적 정신을 계승하였다. 따라서 피타고라스 정리에 대한 닮음비와 분해합동을 이용한 증명, 또 넓이에 의한 증명과 넓이가 같음에 의한 증명의 차이는 전통적인 유클리드의 종합기하적 전개와 현대수학적 전개사이의 갈등이라는 기하 교육에서 아직도 완전히 해결되지 않은 논점과 관련이 있다.

• 한국수학교육학회지시리즈A:수학교육
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• 제46권3호
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• pp.331-349
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• 2007

This study aims to improve the teaching and learning method on the conic sections. To do that the researcher analyzed the impact of dynamic geometry software on students' problem solving of the conic sections. Students often say, "I have solved this kind of problem and remember hearing the problem solving process of it before." But they often are not able to resolve the question. Previous studies suggest that one of the reasons can be students' tendency to approach the conic sections only using algebra or analytic geometry without the geometric principle. So the researcher conducted instructions based on the geometric and historico-genetic principle on the conic sections using dynamic geometry software. The instructions were intended to find out if the experimental, intuitional, mathematic problem solving is necessary for the deductive process of solving geometric problems. To achieve the purpose of this study, the researcher video taped the instruction process and converted it to digital using the computer. What students' had said and discussed with the teacher during the classes was checked and their behavior was analyzed. That analysis was based on Branford's perspective, which included three different stage of proof; experimental, intuitive, and mathematical. The researcher got the following conclusions from this study. Firstly, students preferred their own manipulation or reconstruction to deductive mathematical explanation or proving of the problem. And they showed tendency to consider it as the mathematical truth when the problem is dealt with by their own manipulation. Secondly, the manipulation environment of dynamic geometry software help students correct their mathematical misconception, which result from their cognitive obstacles, and get correct ones. Thirdly, by using dynamic geometry software the teacher could help reduce the 'zone of proximal development' of Vigotsky.

• 대한수학회지
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• 제47권3호
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• pp.445-454
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• 2010

The braid group $B_n$ maps homomorphically into the Temperley-Lieb algebra $TL_n$. It was shown by Zinno that the homomorphic images of simple elements arising from the dual presentation of the braid group $B_n$ form a basis for the vector space underlying the Temperley-Lieb algebra $TL_n$. In this paper, we establish that there is a dual presentation of Temperley-Lieb algebras that corresponds to the dual presentation of braid groups, and then give a simple geometric proof for Zinno's theorem, using the interpretation of simple elements as non-crossing partitions.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제19권4호
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• pp.699-713
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• 2005

In this paper, we attempted to find out the meaning of several means and inequalities, their relationships and proposed the effective ways to teach them in college mathematics classes. That is, we introduced 8 proofs of arithmetic-geometric mean equality to explain the fact that there exist diverse ways of proof. The students learned the diverseproof-methods and applied them to other theorems and projects. From this, we found out that the attempt to develop the students' logical thinking ability by encouraging them to find out diverse solutions of a problem could be a very effective education method in college mathematics classes.

• 열병합발전
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• 통권30호
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• pp.21-25
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• 2002

According to recent Korea Electric Power Company report, yearly distribution line brass cramp bolts failure summed up to 4,400 cases emerging as one of main local break-down causes. Naturally, the need for the investigation was proposed To determine the root cause of the cramp bolt failures, mechanical and metallurgical investigation were performed for 90 samples which collected from various sites. For the understanding of the geometric characteristics, stress distribution was evaluated by CAE program and proof load of each bolts was tested. The SEM&EDS was used for metallurgical investigation. Through the investigation, the root causes of failures were confirmed. All damaged bolts showed intergrannular fracture mode and the all fractured bolt showed ß phase morphology contrast to the a&ß mixture morphology of the non-damaged samples. Additionally, EDS analysis confirmed the existence of lead rich layer on grain boundaries.