• The Mathematical Education
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• v.46 no.4
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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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• v.31 no.1_2
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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.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2007.06a
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• pp.37-50
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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.

• East Asian mathematical journal
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• v.39 no.4
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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.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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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.

• Journal of KIBIM
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• v.9 no.2
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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.

• Journal for History of Mathematics
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• v.29 no.3
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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.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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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.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.659-689
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• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.