• Research in Mathematical Education
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• v.14 no.3
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• pp.263-279
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• 2010

Teachers' personal knowledge (PK) is an element in their pedagogic-practical knowledge. This study exposes the PK of primary school mathematics teachers regarding solid geometry through reflection. Students are exposed to solid geometry on various levels, from kindergarten age and above. Previous studies attested to the fact that students encounter difficulties-strong dislike and fear engendered by geometry. A good number of teachers have strong dislike to solid geometry, as well. Therefore, those engaged in teaching the subject must address the problem and try to overcome these difficulties. In this paper we have introduced the reflective process among teachers in primary school, including application of Van-Hiele's theory to solid geometry.

• Journal of The Korean Digital Architecture Interior Association
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• v.9 no.3
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• pp.15-23
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• 2009

Chaos theory, qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems, is dominant paradigm in the twenty first century. Fractal geometry, as an expressed form of chaos, now influences many areas such as architecture, art, music, economics, literature, etc. The purpose of this study is to analyze fractal geometry and fractal formative elements in architectural design. There are scaling, superimposition, distortion, deformation and repetition in the fractal form generator that can be applied to design concept and process in architecture. This study shows fractal geometry can be the architectural form creation method. Fractal geometry similar to nature's patterned order can be provided endless possibilities for design analysis and methodology in architecture. Therefore the further study of fractal geometry should progress synthetically through the basis of the study.

• Journal of Welding and Joining
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• v.17 no.4
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• pp.39-45
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• 1999

The procedure of robotic Gas metal Arc (GMA) welding in order to achieve the optimized bead geometry needs the selection of suitable process parameters such as arc current, welding voltage, welding speed. It is required the relationships between process parameters and bead geometry. The objective of this paper is to develop the algorithm that enables the determination of process parameters from the optimized bead geometry for robotic GMA welding. It depends on the inversion of empirical equations derived from multiple regression analysis of the relationships between the process parameters and the bead dimensions using the least square method. The method not only directly determines those parameters which will give the desired set of bead geometry, but also avoids the need to iterate with a succession of guesses employed Finite Element Method(FEM). These results suggest that process parameter from experimental equation for robotic GMA welding may be employed to monitor and control the bead geometry in real time.

• Research in Mathematical Education
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• v.11 no.3
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• pp.209-218
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• 2007

The purpose of this study is to create an interactive tool Geometry Player for geometric explorations. In designing this software, we referred to van Hiele's geometric learning theory of and Duval's cognitive comprehension theory of geometric figures. With Geometry Player, it is easy to construct and manipulate dynamic geometric figures. Teachers can easily present the dynamic process of geometric figures in class, and students can use it as a leaning tool to construct geometric concepts by themselves. It is hoped that Geometry Player can be a useful assistant for teachers and a nice partner for students. A brief introduction to Geometry Player and some application examples are included in this paper.

• The Mathematical Education
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• v.43 no.2
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• pp.177-186
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• 2004

In this paper, we introduce new functional definitions for school geometry based on DGS (dynamic geometry system) teaching-learning environment. For the vertices forming a geometric figure, we first consider the relationship between the independent vertices and dependent vertices, and using this relationship and educational considerations in DGS, we introduce functional definitions for the geometric figures in terms of its independent vertices. For this purpose, we design a new DGS called JavaMAL MicroWorld. Based on the needs of new definitions in DGS environment for the student's construction activities in learning geometry, we also design a new DGS based geometry curriculum in which the definitions of the school geometry are newly defined and reconnected in a new way. Using these funct onal definitions, we have taught the new geometry contents emphasizing the sequential expressions for the student's geometric activities.

• School Mathematics
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• v.2 no.1
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• pp.111-144
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• 2000

The purpose of this study is to develop instruction sequence and teaching units for secondary school geometry using dynamic computer software like CabriII, GSP, Wingeom, Poly. For this purpose, literature was reviewed on various issues of geometry education and geometry curriculum using dynamic software. By the literature review, instructional sequence for teaching geometry in middle schools was designed. And, based on the newly developed instructional sequence, one sample teaching unit was developed. The basic principles for the development were to connect intuition geometry and formal geometry, and to emphasize students' investigative experience. Finally, experiment to check out teachers' response to the newly developed material was conducted by using questionnaire.

• 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.31 no.6
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• pp.291-313
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• 2018

This study aims to analyze Pardies' ${\ll}$Elements of geometry${\gg}$. This book is very interesting from the perspectives of mathematical history as well as of mathematical education. Because it was used for teaching Kangxi emperor geometry in the Qing Dynasty in China instead of Euclid's which was considered as too difficult to study geometry. It is expected that this book suggests historical and educational implications because it appeared in the context of instruction of geometry in the seventeenth century of mathematical history. This study includes the analyses on the contents of Pardies' ${\ll}$Elements of geometry${\gg}$, the author's advice for geometry learning, several geometrical features, and some features from the view of elementary school mathematics, of which the latter two contain the comparisons with other authors' as well as school mathematics. Moreover, some didactical implications were induced based on the results of the study.

• Journal for History of Mathematics
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• v.34 no.3
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• pp.89-111
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• 2021

This paper is a continuation of the study on the history of the Japanese school of Finsler geometry. We had studied on the birth of Japanese school of Finsler geometry. In this paper, we find out what motivated Japanese to embrace Finsler geometry and we collect the history and analyze trends of Japanese school of Finsler geometry since its founding by M. Matsumoto.

• Journal of Educational Research in Mathematics
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• v.10 no.2
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• pp.215-227
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• 2000

This study is on the differences of the functions of definitions between in proof geometry and in intuitional geometry. There are the functions of definitions in intuitional geometry which may connect to those in proof geometry. We assert that when we teach them, we should be careful, for the teaching of the functions of definitions in proof.