• 대한수학회지
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• 제49권3호
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• pp.475-491
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• 2012

In 1950 a class of generalized Petersen graphs was introduced by Coxeter and around 1970 popularized by Frucht, Graver and Watkins. The family of $I$-graphs mentioned in 1988 by Bouwer et al. represents a slight further albeit important generalization of the renowned Petersen graph. We show that each $I$-graph $I(n,j,k)$ admits a unit-distance representation in the Euclidean plane. This implies that each generalized Petersen graph admits a unit-distance representation in the Euclidean plane. In particular, we show that every $I$-graph $I(n,j,k)$ has an isomorphic $I$-graph that admits a unit-distance representation in the Euclidean plane with a $n$-fold rotational symmetry, with the exception of the families $I(n,j,j)$ and $I(12m,m,5m)$, $m{\geq}1$. We also provide unit-distance representations for these graphs.

• 대한수학회보
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• 제53권4호
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• pp.1197-1211
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• 2016

Let R be a finite commutative ring with nonzero identity. We define ${\Gamma}(R)$ to be the graph with vertex set R in which two distinct vertices x and y are adjacent if and only if there exists a unit element u of R such that x + uy is a unit of R. This graph provides a refinement of the unit and unitary Cayley graphs. In this paper, basic properties of ${\Gamma}(R)$ are obtained and the vertex connectivity and the edge connectivity of ${\Gamma}(R)$ are given. Finally, by a constructive way, we determine when the graph ${\Gamma}(R)$ is Hamiltonian. As a consequence, we show that ${\Gamma}(R)$ has a perfect matching if and only if ${\mid}R{\mid}$ is an even number.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.53-60
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• 2022

Let R be a finite commutative ring with non zero identity. The unit graph of R denoted by G(R) is the graph obtained by setting all the elements of R to be the vertices of a graph and two distinct vertices x and y are adjacent if and only if x + y ∈ U(R), where U(R) denotes the set of units of R. In this paper, we find the commutative rings R for which G(R) is a line graph. Also, we find the rings for which the complements of unit graphs are line graphs.

• 한국주거학회논문집
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• 제19권2호
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• pp.43-54
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• 2008

The aim of the research is to find out the direction of unit-plans in multi-dwellings for the future society. Shinonome Canal Court where residents actually live now are the objects in this study, and the residential floor plan of unit-plans were analyzed to find out the typical types. The analysis was focused on the unit-plans of 5 blocks of Shinonome Canal Court. Space Syntax Theory was used as the analysis method. As the first stage of the analysis, justified graphs were made to find out the characters of unit-plans through the classification of the graphs. Contents of the analysis are as follows: Relationship between classified justified graphs and dimension according to node number. Relationship between classified justified graph patterns and unit-plans. Characters of unit-plans in each blocks. Shinonome Canal Court consists of mainly small scale unit-plans and 30unit-plans are classified. 1LDK, 2LDK, 1LDK+S, 1LDK+f are typical unit-plans which are mainly supplied in the complex. It is noted that the results of the analysis by node, justified graph pattern and dimension are the same. It also presents diverse unit-plans which shows a change in nLDK pattern or add f (foyer), AN (annex), S (service room), Fs (free space) to basic nLDK type. In summary, it demonstrates the possibility of creating new residental floor plans in multi-dwellings.

• East Asian mathematical journal
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• 제40권2호
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• pp.209-229
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• 2024

In this study, we design a teaching unit that constructs Pascal graphs and extended Pascal triangles to explore number patterns inherent in them. This teaching unit is designed to consider the diachronic process of teaching-learning by combining Dörfler's theoretical generalization model with Wittmann's design science ideas, which are applied to the didactical practice of mathematization. In the teaching unit, considering the teaching-learning level of prospective teachers who studied discrete mathematics, we generalize the well-known Pascal triangle and its number patterns to extended Pascal triangles which have directed graphs(called Pascal graphs) as geometric models. In this process, the use of symbols and the introduction of variables are exhibited as important means of generalization. It provides practical experiences of mathematization to prospective teachers by going through various steps of the generalization process targeting symbols. This study reflects Wittmann's intention in that well-understood mathematics and the context of the first type of empirical research as structure-genetic didactical analysis are considered in the design of the learning environment.

• 한국실내디자인학회논문집
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• 제13권1호
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• pp.81-88
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• 2004

The purpose of this study is to analyze spatial configuration of the unit floor plan characteristics of the apartments built in Seoul Metropolitan area by using the Space Syntax methodology and finally to test the relationship between space in the unit floor plans. So the unit floor plans are analyzed using sector graphs from justified graph and computer programs based on the Space Syntax model and compared by size. The results are as follows; The sector graphs are summarized in 14 types. The total depth of spaces is not in proportion to the plan area. And the global and local integration and intelligibility are inversely proportional to the area. But in the case of largest areas(265$m^2$ and above), the integration and intelligibility increase.

• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.555-569
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• 1999

The graph unit(chapter) is a good example of a topic in elementary school mathematics for which computer use can be incorporated as part of the instruction. Teaching graph can be facilitated by using the graphing utilities of computers, which make it possible to observe the property of many types of graphs. This study was concerned with utilizing an educational software Graphers as an instructional tool in teaching to help young students gain a better understanding of graph concepts. For this purpose, three types of instructional activities using Graphers were shown in the paper. Graphers is a data-gathering tool for creating pictorial data chosen from several data sets. They can represent their data on a table or with six types of graphs such as Pictograph, Bar Graph, Line Graph, Circle Graph, Grid Plot and Loops. They help students to select the graph(s) which are the most appropriate for the purpose of analyzing data while comparing various types of graphs. They also let them modify or change graphs, such as adding grid lines, changing the axis scale, or adding title and labels. Eventually, students have a chance to interpret graphs meaningfully and in their own way.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제22권3호
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• pp.289-310
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• 2008

본 연구는 고등학교 <10-나>의 삼각함수의 성질을 단위원이 아니라 삼각함수 sin(x), cos(x), tan(x)의 그래프 성질을 이용하여 구할 수 있는 방법을 제시하여 삼각함수의 값을 구하는 학습활동과 삼각함수의 그래프에 대한 학습활동과의 연계성을 높이고, 이를 통하여 삼각함수의 성질에 대한 학생들의 이해를 향상시킬 수 있는지를 논의하고자 한다. 본 연구의 결론은 삼각함수 그래프 이용에 의한 삼각 함수값 구하기의 효율성 증대, 일반각에 대한 삼각 함수값 구하기의 정확한 용어 사용, 삼각 함수값 구하기와 삼각함수의 그래프 지도내용 사이의 연계성, 삼각함수의 그래프의 선행 지도 등이며 이에 대한 논의가 제시되어 있다.

• 한국공작기계학회:학술대회논문집
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• 한국공작기계학회 1999년도 춘계학술대회 논문집
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• pp.153-158
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• 1999

In the multi-purpose lathe, the design of tilting turret slide system has an important and critical role to enhance the accuracy of the machining process. Tilting turret unit is traveled by 3-axis slide systems. There is a need to design this part very carefully. In this research, the 3-axis slide system with tilting turret unit is modeled and simulated using ADAMS software. The dynamic behavior of this system is visualized by data graphs and dynamic animations. The first step of virtual prototype which makes it possible to design economically and effectively is developed.

• 대한수학교육학회지:학교수학
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• 제19권3호
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• pp.593-615
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• 2017

본 연구에서는 학교 수학의 내용을 담아낸 모바일 기반 수학 학습 어플리케이션을 개발하고, 이를 수학 교수 학습 상황에서 활용할 수 있는 방안을 모색하였다. 먼저, 중학교 수학의 '이차함수와 그래프', '대푯값과 산포도' 단원에서 조작을 통한 개념 탐구와 토론 학습이 가능하도록 어플리케이션 <중3수학교실>을 안드로이드 버전으로 수학교육 전문가, 수학 교사, 컴퓨터공학 전문가, 디지털 애니메이션 감독과 협업하여 개발하였다. 이때, 예비교사의 도움을 받아 중학교 3학년 남녀 학생 4명을 대상으로 개발한 어플리케이션을 적용하여 그 활용가능성을 검증하였다. 또한, 수학 수업에 어플리케이션을 활용하는 교수 학습 지도안과 어플리케이션 활용 매뉴얼을 개발하고 중학교 3학년 1개 학급을 대상으로 사례 연구를 실시하여 그 현장 적용 가능성을 모색하였다.