• Journal for History of Mathematics
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• v.17 no.3
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• pp.93-108
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• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• Communications of Mathematical Education
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• v.10
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• pp.143-154
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• 2000

현재, 중학교에서 사용 가능한 수학 교과서는 8종류인데, 이처럼 다양한 종류의 교과서가 필요한 이유들 중의 하나는 수학적 개념이나 정리 등에 대한 다각적인 접근 방법들을 모색할 수 있는 가능성을 보장한다는 것이다 그러나, 현재의 교과서들은, 예를 들어, 정리의 증명에 있어 비슷한 증명 방법을 제시하고 있기 때문에, 학습자들에게 수학에 대한 폭넓은 시각과 다양한 수학적 아이디어를 제공할 수 있는 기회를 효과적으로 살리지 못하고 있다. 본 연구에서는 평면 기하학의 중요한 정리들 중의 하나인 ‘삼각형의 세 중선은 한 점에서 만나고, 각각의 중선은 교점에 의해 2:1로 나뉜다.’에 대한 다양한 증명들을 살펴보고, 각각의 증명들이 가지는 수학 교육적 의의를 고찰할 것이다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.45 no.1
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• pp.9-14
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• 2008

This paper presents an observer design methodology for a special class of multi input multi output(MIMO) nonlinear systems. First, we characterize the class of MIMO nonlinear systems with a triangular structure. Also, the observability matrices that plays an important role in proving the convergence of the proposed observer are generalized to MIMO systems. By using the generalized observability matrices, it is shown that under the boundedness conditions of system state and input, the proposed observer guarantees the local exponential convergence to zero of the estimation error.

• Communications of Mathematical Education
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• v.13 no.1
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• pp.305-316
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• 2002

벡터는 수학 문제해결을 위한 중요한 도구로써, 벡터를 이용한 문제해결 과정에서 학생들은 수학적 탐구 활동에 관련된 풍부한 경험을 가질 수 있다. 본 연구에서는 벡터를 이용하여 삼각형의 무게중심에 관한 정리를 증명하기 위한 수학적 탐구 능력이나 아이디어를 학생들이 준비할 수 있도록 정리 증명과 관련된 몇몇 문제들을 체계화하여 제시하였다. 이 문제들을 해결하는 과정에 관련된 탐구 능력을 추출하였으며, 체계화된 문제에 바탕을 둔 무게중심에 관한 정리 증명을 제시하였고, 증명 과정과 관련된 수학적 탐구 능력을 제시하였다.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.13-26
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• 2011

The purpose of this research is to analyze geometrical level and the justification process in the proofs of construction by mathematically gifted elementary students. Justification is one of crucial aspect in geometry learning. However, justification is considered as a difficult domain in geometry due to overemphasizing deductive justification. Therefore, researchers used construction with which the students could reveal their justification processes. We also investigated geometrical thought of the mathematically gifted students based on van Hieles's Theory. We analyzed intellectual of the justification process in geometric construction by the mathematically gifted students. 18 mathematically gifted students showed their justification processes when they were explaining their mathematical reasoning in construction. Also, students used the GSP program in some lessons and at home and tested students' geometric levels using the van Hieles's theory. However, we used pencil and paper worksheets for the analyses. The findings show that the levels of van Hieles's geometric thinking of the most gifted students were on from 2 to 3. In the process of justification, they used cut and paste strategies and also used concrete numbers and recalled the previous learning experience. Most of them did not show original ideas of justification during their proofs. We need to use a more sophisticative tasks and approaches so that we can lead gifted students to produce a more creative thinking.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 2001.11a
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• pp.117-120
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• 2001

본 논문에서는 약한 키를 가지는 대화식 영지식 증명을 이용한 인증 프로토콜의 안전성을 강화하는 방법을 제시한다. 일반적으로 대화식 영지식 증명을 이용한 인증 프로토콜은 충분히 길고 랜덤한 비밀키를 가정하고 그 비밀키에 대한 영지식 증명을 수행하게 된다. 하지만 때에 따라서 충분히 길지 않거나 랜덤하지 않은 비밀키가 선택될 수 있다. 즉, 좋지 않은 난수 발생기를 써야 하는 경우, 또는 패스워드처럼 의도적으로 약한 키를 사용하는 경우가 생기며, 대화식 영지식 증명은 이에 적합하지 않다고 알려져 있다. 본 논문에서는 비밀 동전 던지기(Secret Coin Tossing)라는 개념을 제시해서, 일반적인 영지식 증명을 이용한 인증 프로토콜을 약한 키를 가지는 영지식 증명 기반 인증 프로토콜로 쉽게 변환할 수 있는 프레임웍을 제안한다. 또한, 이 프레임웍을 이용해서 설계된 인증 프로토콜이 ideal cipher model에서 안전함을 보인다.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.47 no.2
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• pp.16-24
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• 2010

This paper is proposed a novel fuzzy disturbance observer based on backstepping method for nonlinear systems with unknown disturbance. Using fuzzy logic systems, a fuzzy disturbance observer with the disturbance observation input is introduced for unknown disturbance. To guarantee that the proposed disturbance observer estimates the unknown disturbance, the disturbance observation error dynamic system is employed. Under the framework of the backstepping design, the fuzzy disturbance observer is constructed recursively and an adaptive laws and the disturbance observation input are derived. Numerical examples are given to demonstrate the validity of our proposed disturbance observer for nonlinear systems.

• Journal of KIISE:Software and Applications
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• v.37 no.1
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• pp.54-59
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• 2010

Special-purpose microcontrollers PLCs have been widely used in the area of industrial automation. For the research of analysis and verification for PLC programs, first of all we have to specify formal sematics of PLC programming languages. This paper defines formally the operational semantics of LD language. After we transform the graphical language LD into its textual representation Symbolic LD, we give semantics of Symbolic LD since LD language is a graphical language. This paper defines the natural sematics of Symbolic LD and formalizes it in Coq proof assistant.

• Communications of Mathematical Education
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• v.5
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• pp.288-299
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• 1997