• 한국수학교육학회지시리즈A:수학교육
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• 제46권4호
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• pp.493-502
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• 2007

What is a foundational element of plane geometry? Isn't it possible to constitute the contents of plane geometry from that element? In this paper, we suggest a view point that triangle is a foundational element of plane geometry. And take some examples of reconstruction of usually given contents and mathematical activity centered on the triangle in plane geometry.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.79-86
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• 2013

Taxicab plane geometry and Cinese-Checker plane geometry are non-Euclidean and more practical notion than Euclidean geometry in the real world. The ${\alpha}$-distance is a generalization of the Taxicab distance and Chinese-Checker distance. It was first introduced by Songlin Tian in 2005, and generalized to n-dimensional space by Ozcan Gelisgen in 2006. In this paper, we studied the isoperimetric inequality in ${\alpha}$-plane.

• 한국수학교육학회:학술대회논문집
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• 한국수학교육학회 2007년도 제38회 전국수학교육연구대회 프로시딩
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• pp.37-50
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• 2007

평면도형의 탐구에서 기본이 되는 것은 무엇이며, 그것으로부터 평면도형의 내용들을 일관성 있게 구성할 수는 없는가? 이 글에서는 평면도형 탐구의 기본 요소가 삼각형이라는 관점을 제시하고, 삼각형을 중심으로 한 평면도형 탐구 활동 설계 및 교과서 내용 재구성의 몇 가지 예를 제시한다. 그리고 이러한 관점 및 설계가 지니는 수학교육적 의의에 대하여 논의한다.

• East Asian mathematical journal
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• 제39권4호
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• pp.479-492
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• 2023

Although Euclidean plane geometry is implemented in the middle school course, there are three major problems in high school space geometry that can be intuitively taken for granted or misinterpreted as circular arguments. In order to solve this problem, this study proved three major problems using sets, Euclidean plane geometry, and parallel line postulates. This corresponds to a logical sequence and has mathematical and mathematical educational values. Furthermore, it will be possible to configure spatial geometry using sets, and by giving legitimacy to non-Euclidean spatial geometry, it will open the possibility of future research.

• 한국지능시스템학회논문지
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• 제12권2호
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• pp.171-176
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• 2002

This paper describes a new automated analysis system for model plane engine. An automatic finite element (FE) mesh generation technique, which is based on the fuzzy knowledge processing and computational geometry technique, is incorporated into the system, together with one of commercial FE analysis codes, ANSYS, and one of commercial solid modelers, Designbase, The system allows a geometry model of concern to be automatically converted to different FE models, depending on physical phenomena of plane engine to be analyzed, i.e. deformation analysis, thermal analysis and so on. The FE models are then automatically analyzed by the FE analysis code. Among a whole process of analysis, the definition of a geometry model, the designation of local node patterns, the assignment of material properties and boundary conditions onto the geometry model are only the interactive processes to be done by a user. The interactive operations can be processed in a few minutes. The other processes which are time consuming and labour-intensive in conventional CAE systems are fully automatically performed in a personal computer environment. The proposed analysis system is successfully applied to evaluate a model plane entwine.

• 대한기계학회논문집A
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• 제30권8호
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• pp.1008-1015
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• 2006

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit, collapse and instability load solutions for pipe bends under combined pressure and in-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide plastic collapse loads (using the twice-elastic-slope method) and instability loads. For the bending mode, both closing bending and opening bending are considered, and a wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and collapse load solutions for pipe bends under combined pressure and bending are proposed.

• 한국BIM학회 논문집
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• 제9권2호
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• pp.21-28
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• 2019

Recently, many scan projects are gradually increasing for maintenance, construction. The scan data contains useful data, which can be generated in the target application from the facility, space. However, modeling the scan data required for the application requires a lot of cost. In example, the converting 3D point cloud obtained from scan data into 3D object is a time-consuming task, and the modeling task is still very manual. This research proposes Scan-to-Geometry Mapping Rule Definition (S2G-MD) which maps point cloud data to geometry for irregular building plane objects. The S2G-MD considers user use case variability. The method to define rules for mapping scan to geometry is proposed. This research supports the reverse engineering semi-automatic process for the building planar geometry from the user perspective.

• 한국수학사학회지
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• 제29권3호
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• pp.191-216
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• 2016

Moulton plane is the plane where all the plane axioms of Hilbert except the side-angle-side axiom hold true, and enables us to understand the importance and significance of the side-angle-side axiom. In this article, we start with the definitions of the Moulton lines, distance, angle, and then introduce many theorems of the Moulton geometry, with many intuitive proofs or explanations of our own with appropriate examples. In particular, we provide our independent study of the tangent lines to the Moulton circles and the rigid motions of the Moulton plane.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권3호
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• pp.659-689
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• 2010

택시거리함수는 거리함수의 조건을 만족하면서 실제로 택시가 갈 수 있는 경로를 따라 이동할 때 거리 개념을 주는 실용적인 거리개념이라 할 수 있다. 비 유클리드 기하의 하나로서 실제로 평면상을 이동하는 우리 실생활을 반영할 수 있는 이 개념은 러시아 태생의 수학자 H. Minkowski에 의해 처음으로 제안되고, E. F. Krause(1986)에 의해 단행본으로 출판되어 기본개념과 그간의 결과들이 소개 되어졌다. 그 후 이 거리개념을 가지는 공간에서 많은 연구가 이루어지고 있다. 본 연구에서는 비 유클리드 기하인 택시기하의 문제를 유클리드 평면기하의 결과 및 택시기하에 대한 선행연구결과 등을 참조하여 유클리드 기하와의 차별점과 택시거리함수를 이용한 평면기하의 제정리를 고찰하였다.

• 대한수학회지
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• 제36권3호
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• pp.621-631
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• 1999

In this paper we briefly describe the geometry of the Cayley hyperbolic plane and we show that every uniform lattice in quaternionic space cannot be deformed in the Cayley hyperbolic 2-plane. We also describe the nongeometric bending deformation by developing the theory of the Cartan angular invariant for quaternionic hyperbolic space.