• East Asian mathematical journal
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• 제31권4호
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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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• 제30권3호
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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.

• 한국수학사학회지
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• 제22권2호
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• pp.99-116
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• 2009

본 연구에서는 18세기 출판된 '자와 컴퍼스의 방법'에 제시된 정다각형의 작도방법들 중에서 오류를 포함하는 작도를 분석하였다. 정7각형과 정9각형은 자와 컴퍼스를 이용하여 작도불가능 하다는 것이 알려져 있지만, '자와 컴퍼스의 방법'에서는 이들 정다각형을 작도하는 두 가지 방법이 제시되어 있다. 본 연구에서는 이들 작도가 오류를 포함하고 있음을 보였고, 이에 관련된 몇몇 정다각형 작도 방법도 오류를 포함하고 있음을 보였다. 이를 통해 정다각형 작도문제의 해결을 위한 노력에서 성공적이지 못한 시도에 관련된 새로운 자료를 제공할 것으로 기대된다.

• 한국수학사학회지
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• 제14권1호
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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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• 제26권4호
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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.

• 한국수학사학회지
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• 제21권2호
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• pp.119-134
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• 2008

본 연구에서는 1709년 러시아에서 출판되었고, 다양한 작도문제의 해결방법이 기술된 '자와 컴퍼스의 방법'을 분석하였다. 이 책에 제시된 정삼각형, 정사각형, 정오각형, 정육각형, 정8각형, 정10각형의 작도방법을 소개하고, 이에 관련된 다양한 논의를 시도하였다. 이를 통해 정다각형 작도에 관련된 역사-발생적 연구를 위한 새로운 자료를 제공할 것으로 기대된다.

• 한국수학사학회지
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• 제14권2호
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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.

• 대한수학교육학회지:수학교육학연구
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• 제27권3호
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• pp.581-598
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• 2017

독일 르네상스의 대표적인 예술가인 뒤러는 정다각형 작도법을 정리하였다. 이 논문에서는 뒤러의 정다각형 작도를 둘러싼 배경과 실제 내용을 살펴보았다. 이어 교육적인 활용 방안을 탐색하기 위해, 첫째, 유클리드 원론의 작도와 뒤러 작도의 차이를 도출하고, 둘째, 각 작도를 오늘날의 기호로 표현하고, 셋째, 기본 작도를 추출하였다. 마지막으로, 정다각형 작도로 만들 수 있는 형태 문양들을 살펴보았다. 이는 초등학교 고학년에서 융합교육, 영재교육, 활동주의교육에 관한 자료 개발에 기초가 될 수 있을 것이다.

• 한국의류학회지
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• 제30권6호
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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.

• 한국정밀공학회지
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• 제22권12호
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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.