• Communications of Mathematical Education
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• v.22 no.4
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• pp.545-556
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• 2008

In this paper we study Gergonne's point and its adjoint points of triangle using the principle of the lever. We prove existence of Gergonne's point and its adjoint points, suggest new proof method of a equality related with Gergonne's point. We find new equalities related with adjoint points of Gergonne's points, and prove these using the principle of the lever.

• School Mathematics
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• v.13 no.1
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• pp.107-125
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• 2011

In this paper, we investigated how the GSP environments impact students' conjecturing of geometric properties. And we wanted to draw some implication in teaching and learning geometry in dynamic geometric environments. As results, we conclude that when students were given the problem situations which almost has no condition, they were not successful, and rather when the problem situations had appropriate conditions students were able to generate many conditions which were not given in the original problem situations, and consequently they were more successful in conjecturing geometric properties. And the geometric properties conjectured in GSP environments are more complex and difficult to prove than those in paper and pencil environments. Also the function of moving screen with 'Alt' key is frequently used in conjecturing geometric properties with functions of measurement and calculation of GSP. And students felt happier when they discovered geometric properties than when they could prove geometric properties.

• Communications of Mathematical Education
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• v.13 no.2
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• pp.515-525
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• 2002

중학교 기하영역 중 피타고라스의 정리를 논증적인 증명 대신에 역동적인 방법으로 이해할 수 있도록 GSP(Geometer's Skechpad)를 활용하여 구현했으며, 멀티미디어 환경에 익숙한 중학생들에게 시 ${\cdot}$ 공간을 초월하여 웹 상에서 개별학습, 반복학습을 할 수 있도록 JAVA 언어를 사용하여 웹으로 변환시켰다.

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

• The Mathematical Education
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• v.32 no.2
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• pp.137-149
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• 1993

• 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.

• The Mathematical Education
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• v.53 no.3
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• pp.383-397
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• 2014

This study aims to explore secondary students' thinking while doing proof in geometry. Two secondary students were interviewed and the interview data were analyzed. The results of the analysis suggest that the two students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles to solve a given problem, b) being confused about the rules of similar and congruent triangles, and c) being confused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the results revealed that a relatively low achieving student has tendency to rely on intuitive information such as visual representations.

• The KIPS Transactions:PartC
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• v.13C no.7 s.110
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• pp.865-872
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• 2006

Cooperative communications (CC) have received a great deal of attention recently as an efficient way to obtain the spatial diversity without physical arrays. Thus, space-time block codes (STBC) which are well-known for use in co-located multi-antenna systems can be still utilized for single-antenna users in a distributed fashion. In this paper, we propose a cooperative signaling structure using the $\frac{3}{4}$-rate STBC and derive closed-form BER expression which takes the effect of network geometry and transmit power constraint into account. A variety of simulated and numerical results demonstrated the cooperation considerably outperforms the direct transmission when partners are located in appropriate positions.

• Journal of KIISE:Computer Systems and Theory
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• v.34 no.4
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• pp.132-137
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• 2007

A point-wise car-like robot moving in the plane changes its direction with a constraint on turning curvature. In this paper, we consider the problem of computing a shortest path of bounded curvature between a prescribed initial configuration (position and orientation) and a polygonal goal, and propose a new geometric proof showing that the shortest path is either of type CC or CS (or their substring), where C specifies a non-degenerate circular arc and S specifies a non-degenerate straight line segment. Based on the geometric property of the shortest path, the shortest path from a configuration to a polygonal goal can be computed in linear time.