• Journal of Elementary Mathematics Education in Korea
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• v.17 no.1
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• pp.165-184
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• 2013

In order to utilize Sphinx Puzzle in shape education or deductive reasoning, a lesson employing Dienes' six-stage theory of learning mathematics was structured to be applied to students of 6th grade of elementary school. 4 students of 6th grade of elementary school, the researcher's current workplace, were selected as subjects. The academic achievement level of 4 subjects range across top to medium, who are generally enthusiastic and hardworking in learning activities. During the 3 lessons, the researcher played role as the guide and observer, recorded observation, collected activity sheet written by subjects, presentation materials, essays on the experience, interview data, and analyzed them to the detail. A task of finding every possible triangle out of pieces of Sphinx Puzzle was given, and until 6 steps of formalization was set, students' attitude to find a better way of mathematical deduction, especially that of operational thinking and deductive thinking, was carefully observed and analyzed.

• School Mathematics
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• v.5 no.4
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• pp.401-420
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• 2003

We have many problems in the teaching and learning of proof, especially in the demonstrative geometry of middle school mathematics introducing the proof for the first time. Above all, it is the serious problem that many students do not understand the meaning of proof. In this paper we intend to show that teaching the meaning of proof in terms of historic-genetic approach will be a method to improve the way of teaching proof. We investigate the development of proof which goes through three stages such as experimental, intuitional, and scientific stage as well as the development of geometry up to the completion of Euclid's Elements as Bran-ford set out, and analyze the teaching process for the purpose of looking for the way of improving the way of teaching proof through the historic-genetic approach. We conducted lessons about the angle-sum property of triangle in accordance with these three stages to the students of seventh grade. We show that the students will understand the meaning of proof meaningfully and properly through the historic-genetic approach.

• 한국HCI학회:학술대회논문집
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• 2006.02a
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• pp.1044-1049
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• 2006

얼굴 추적은 Vision base HCI의 핵심인 얼굴인식, 표정인식 그리고 Gesture recognition등의 다른 여러 기술을 지원하는 중요한 기술이다. 이런 얼굴 추적기술에는 영상(Image)의 Color또는 Contour등의 불변하는 특징들을 사용 하거나 템플릿(template)또는 형태(appearance)를 사용하는 방법 등이 있는데 이런 방법들은 조명환경이나 주위 배경등의 외부 환경에 민감하게 반응함으로 해서 다양한 환경에 사용할 수 없을 뿐더러 얼굴영상만을 정확하게 추출하기도 쉽지 않은 실정이다. 이에 본 논문에서는 deformable한 model을 사용하여 model과 유사한 shape과 appearance를 찾아 내는 AAM(Active Appearance Model)을 사용하는 얼굴 추적 시스템을 제안하고자 한다. 제안된 시스템에는 기존의 Combined AAM이 아닌 Independent AAM을 사용하였고 또한 Fitting Algorithm에 Inverse Compositional Image Alignment를 사용하여 Fitting 속도를 향상 시켰다. AAM Model을 만들기 위한 Train set은 150장의 4가지 형태에 얼굴을 담고 있는 Gray-scale 영상을 사용 하였다. Shape Model은 각 영상마다 직접 표기한 47개의 Vertex를 Trianglize함으로서 생성되는 71개의 Triangles을 하나의 Mesh로 구성하여 생성 하였고, Appearance Model은 Shape 안쪽의 모든 픽셀을 사용해서 생성하였다. 시스템의 성능 평가는 Fitting후 Shape 좌표의 정확도를 측정 함으로서 평가 하였다.

• The Mathematical Education
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• v.37 no.1
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• pp.115-138
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• 1998

We seek the possibility of introduction of Fractals to the high school math. curriculum through identifying Fractals teaching programs appropriate for the scopes and sequences in math. education for the high school students. We presented the contents of Fractal theory suitable for the high school students. The following subjects were chosen to be introduced; self-similarity, Fractal dimension, Cantor set, Sierpinsky triangle, Sierpinsky carpel Koch curve, Koch island, perimeter estimate of rugged profiles drawn on paper, and chaos game. We developed the working papers and the criteria for appraisal. Each working paper focuses on the activities in which students can solve the given problems, understanding the characteristics and ideas of Fractals. The working papers were given to the second year students who take science course, and the degree of achievements were analyzed based on the appraisal criteria. The results show that it is possible to introduce Fractals to the high school students.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.284-287
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• 1998

It is important to develop a method of assembling a set of sub pictures automatically into a mosaic picture , because a view through fiberscopes or microscopes with higher magnifying power is much larger than the field of view taken by a camera. This paper presents a method of assembling sub pictures, where roughly estimated junctions called approximate junctions are employed for matching triangles formed by selected junctions in sub pictures. To over come the difficulties in processing speed and noise corruption, fuzzy rules is applied to get fuzzy values for existence of approximate junctions and fuzzy similarity for congruent triangle matching. Some demonstration, exemplified by assembling microscopic metal matrix photographs, are given to show feasibility of this method.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.533-544
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• 2013

The multiplicative version of Wiener index (${\pi}$-index), proposed by Gutman et al. in 2000, is equal to the product of the distances between all pairs of vertices of a (molecular) graph G. In this paper, we first present some sharp bounds in terms of the order and other graph parameters including the diameter, degree sequence, Zagreb indices, Zagreb coindices, eccentric connectivity index and Merrifield-Simmons index for ${\pi}$-index of general connected graphs and trees, as well as a Nordhaus-Gaddum-type bound for ${\pi}$-index of connected triangle-free graphs. Then we study the behavior of ${\pi}$-index upon the case when removing a vertex or an edge from the underlying graph. Finally, we investigate the extremal properties of ${\pi}$-index within the set of trees and unicyclic graphs.

• Proceedings of the KIEE Conference
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• 2003.10a
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• pp.266-269
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• 2003

In this work, a new formulation is presented for analyzing the transient electromagnetic response from wire antennas using the time-domain integral equation. The solution method is based on the Galerkin's method that involves separate spatial and temporal testing procedures. Piecewise triangle basis functions have been used for spatial expansion functions for arbitrarily shaped wire structures. The time-domain variation is approximated by a set of orthonormal basis functions that are derived from the Laguerre polynomials. The method presented in this paper results in very stable transient responses from wire antennas.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.63.2-63
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• 2001

It is necessary to distance measurement to detect about obstacles and front vehicles to autonomously navigate. In this paper, we propose an algorithm using stereo vision. It is as follows this algorithm´s procedure. First, It has detected a front vehicle´s common edges from left and right images by image processing. We select number plate of a front vehicle as edges. Then, we estimate distance by triangle measurement method after stereomatching using corner points of the plate´s edges as feature-based points. Experimental results show errors and values compand with experimental ones after set up distance between vehicles in advance.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.39-48
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• 2006

Let ${\gamma}$(G) be the domination number of a graph G. It is shown that for any $k {\ge} 0$ there exists a Cartesian graph bundle $B{\Box}_{\varphi}F$ such that ${\gamma}(B{\Box}_{\varphi}F) ={\gamma}(B){\gamma}(F)-2k$. The domination numbers of Cartesian bundles of two cycles are determined exactly when the fibre graph is a triangle or a square. A statement similar to Vizing's conjecture on strong graph bundles is shown not to be true by proving the inequality ${\gamma}(B{\bigotimes}_{\varphi}F){\le}{\gamma}(B){\gamma}(F)$ for strong graph bundles. Examples of graphs Band F with ${\gamma}(B{\bigotimes}_{\varphi}F) < {\gamma}(B){\gamma}(F)$ are given.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.343-357
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• 2014

In many non-life insurance applications past data are given in a form known as the run-off triangle. Smoothing such data using parametric crisp regression models has long served as the basis of estimating future claim amounts and the reserves set aside to protect the insurer from future losses. In this article a fuzzy counterpart of the Hoerl curve, a well-known claim reserving regression model, is proposed to analyze the past claim data and to determine the reserves. The fuzzy Hoerl curve is more flexible and general than the one considered in the previous fuzzy literature in that it includes a categorical variable with multiple explanatory variables, which requires the development of the fuzzy analysis of covariance, or fuzzy ANCOVA. Using an actual insurance run-off claim data we show that the suggested fuzzy Hoerl curve based on the fuzzy ANCOVA gives reasonable claim reserves without stringent assumptions needed for the traditional regression approach in claim reserving.