• Journal for History of Mathematics
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• v.19 no.1
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• pp.79-90
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• 2006

The purpose of this paper is to derive the ratios of trigonometric special angles from Euclid's by constructing regular pentagon and decagon. The intention of this paper is started from recognizing that teaching of the special angles in secondary math classroom excessively depends on algebraic approaches rather geometric approaches which are the origin of the trigonometric ratios. In this paper the method of constructing regular pentagon and decagon is reviewed and the geometric relationship between this construction and trigonometric special angles is derived. Through such geometric approach the meaning of trigonometric special angles is analyzed from a geometric perspective and pedagogical ideas of teaching these trigonometric ratios is suggested using history of mathematics.

• 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.29 no.2
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• pp.73-88
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• 2016

To introduce materials related to our traditional mathematics and to reinterpret modernly them could be a good tool to find the cultural values of them. We analyzed the degree for utilization of the history of mathematics in the middle school textbooks developed depending on the 2009 revised mathematics curriculum. Through this, we suggest the need for research on concrete and practical teaching and learning materials development utilizing the history of mathematics. We reinterpret, in modern style based on the curriculum, two subjects dealt with in 'GakDeungByeonHyeongSeupYu', the first theme of 'SanSulGwanGyeon' written by Lee Sang Hyuk. We expansively reconstruct the original samples up to regular decagon so that students might figure out the situation of all regular polygon using a kind of mathematics software GeoGebra. Also this process is constructed on the basis of the curriculum for an implementation the secondary school classes.

• Journal of the Korean Society of Clothing and Textiles
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• v.32 no.2
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• pp.167-178
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• 2008

Despite the fact that chogakpos are part of our wonderful Kyubang(the women's quarters in the Chosun Dynasty) culture with their own unique beauty and artistic values, there has been no scientific and objective proof of their aesthetic values. Once they are proved for their beauty through scientific analysis, they will be recognized worldwide along with our unique culture. The methodology included a review of related literature and theses along with magazines, periodicals, and Internet books. The analysis of lines parting, the dimensions of chogakpos were carried out over 108 pieces introduced in Old Pojagis by Heo Dong-hwa. As for line parting, the dimensions of chogakpos were measured to see if the golden and Geumgang ratio could be applied and to discover their unique partition ratio. As a result, there was the presence of the golden ratio applied to them with the golden curves from golden triangles and rectangles also found therein. The Yeoijumunbo confirmed that there was the golden ratio between the radius of a circle and a side of a regular decagon inscribed in the circle. The common line ratio among the squares, isosceles triangles, wanes, and overlapping rectangles was around 1:1.31, which means that there was a unique line ratio in the traditional chogakpos. Furthermore, the ratio of 1:1.31 was close to the Geumgang ratio commonly used in the traditional buildings of Korea.