• East Asian mathematical journal
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• v.31 no.4
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• pp.483-503
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• 2015

While some studies have examined the concave and convex regular polygons respectively, very little work has been done to integrate and restructure polygon shapes. Therefore, this study aims to systematically reclassify the regular polygons on the through a comprehensive analysis of previous studies on the convex and concave regular polygons. For this study, the polygon's consistency with respect to the number of sides and angles was examined. Second, the consistency on the number of diagonals was also examined. Third, the size of the interior and exterior angels of regular polygons was investigated in order to discover the consistent properties. Fourth, the consistency concerning the area in regular polygons was inspected. Last, the consistency of the central figure number in the "k-th" regular polygons was examined. Given these examinations, this study suggests a way to create a concave regular polygon from a convex regular polygon.

• East Asian mathematical journal
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• v.30 no.3
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• pp.303-310
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• 2014

We study the existence of regular polygons and regular solids whose vertices have integer coordinates in the three dimensional space and study side lengths of such squares, cubes and tetrahedra. We show that except for equilateral triangles, squares and regular hexagons there is no regular polygon whose vertices have integer coordinates. By using this, we show that there is no regular icosahedron and no regular dodecahedron whose vertices have integer coordinates. We characterize side lengths of such squares and cubes. In addition to these results, we prove Ionascu's result [4, Theorem2.2] that every equilateral triangle of side length $\sqrt{2}m$ for a positive integer m whose vertices have integer coordinate can be a face of a regular tetrahedron with vertices having integer coordinates in a different way.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.99-116
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• 2009

In this paper we study errors related with constructing regular polygons in the book 'Method of Ruler and Compass' written three hundreds years ago. It is well known that regular heptagon and regular nonagon are not constructible using compass and ruler. But in this book construction methods of these regular polygons is suggested. We show that the construction methods are incorrect, it include some errors.

• Journal for History of Mathematics
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• v.14 no.1
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• pp.17-26
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• 2001

Ri, Sang-Hyeok(1810-\ulcorner) explained in detail and repeatedly solution of problems which find the area and diameter of inscribed and circumscribed circles of regular polygons from a side and find a side of regular polygons from the area of the book Su-Ri-Jeong-On in the chapter ‘Gak-Deung-Byeon-Hyeong-Seup-Yu’ of his book San-Sul-Gwan-Kyeun. The explanation of each question describes the procedure to make the equation in detail, but only presents the solution with few step to solve.

• East Asian mathematical journal
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• v.26 no.4
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• pp.487-507
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• 2010

We study mathematization of natural thinking and some materials developed in geometric construction of regular n-polygons. This mathematization provides a nice model for illustrating interesting approaches to trigonometric functions and trigonometric ratios as well as their inter-connections. Thereby, results of this paper will provide the procedure of the development for these concepts in natural way, which will be helpful for understanding background knowledges.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.119-134
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• 2008

In this paper we study a book 'Method of Ruler and Compass' written in Russia three hundreds years ago. In this book many construction problems related with plane figures and solid figures are solved. In this study we analyze construction method of some regular polygon(square, regular pentagon, regular octagon, regular decagon) suggested in 'Method of Ruler and Compass', give mathematical proofs of these construction.

• Journal for History of Mathematics
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• v.14 no.2
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• pp.115-124
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• 2001

In this paper, we developed a Web application program that could show the shape, the number of the vertices, the edges, the faces and development figures of polygons(regular tetrahedron, regular hexahedron, etc). The program was implemented using GSP(Geometer's SketchPad) and then converted to JAVA to display the results of GSP on the Web. The results of this paper are applicable to geometry of a junior high school course.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.581-598
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• 2017

The early Renaissance artist Albrecht $D{\ddot{u}}rer$ is an amateur mathematician. He published a book on geometry. In the second part of that book, $D{\ddot{u}}rer$ gave compass and straight edge constructions for the regular polygons from the triangle to the 16-gon. For mathematics education, I extracted base constructions of polygon constructions. And I also showed how to use $D{\ddot{u}}rer^{\prime}s$ idea in constructing divergent forms with compass and ruler. The contents of this paper can be expected to be the baseline data for mathematics education.

• Journal of the Korean Society of Clothing and Textiles
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• v.30 no.6 s.154
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• pp.948-960
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• 2006

Chogakpos are highly artistic works created by Korean women as a part of the Kyubang culture in the Chosun Dynasty from the late 19th century to the early 20th. Tessellation is a plaid pattern composed of squares that covers a surface or a space with figures completely without any gap or overlap. The present study purposed to make a comparative analysis of the formative pattern of Chogakp and tessellation in order to show the superiority of Korean Kyubang(the women's quarters called Kyubang in the Chosun Dynasty) culture. As for the research method, we analyzed relevant materials to examine the geometric characteristics and formative principles of tessellation. In addition, we analyzed the formative pattern of Chogakpo using Photographs. The scope of this study was limited to 148 old Chogakpos contained in Huh Dong-hwa's 'Yetpojagi'. According to the results of this research, similarities between Chogakpo and tessellation were as follows. First, in a regular polygon, the face was divided into regular triangles, squares and two or more regular polygons. Second, in a polygon, the face was divided into triangles and quadrangles. Third, the symmetry of tessellation was applied to Cintamani pattern Pojagi. Differences between Chogakpo and tessellation were as follows. First, different from Chogakpo, tessellation had various formative patterns utilizing different regular polygons including hexagons. Second, there was no overlapping repetition in tessellation. Third, there was no free pattern in tessellation.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.12 s.177
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• pp.205-210
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• 2005

This paper addresses the correlation between the change of file size and the scanning path build time by the slicing height of STL file. Though the study about STL file has been achieved quite actively scanning path build time using STL file is not investigated so much to be satisfied. The file size depends on the number of polygon created by the slicing height specified. And this number of polygons increases in a regular rate. The correlation between the number of polygons and the scanning path build time is examined and verified.