• Journal for History of Mathematics
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• v.24 no.2
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• pp.31-46
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• 2011

[ ${\ll}$ ]n divisions of figures(${\pi}{\varepsilon}{\rho}{\acute{\iota}}\;{\delta}{\iota}{\alpha}{\iota}{\rho}{\acute{\varepsilon}}{\sigma}{\varepsilon}{\omega}{\nu}\;{\beta}{\iota}{\beta}{\lambda}{\acute{\iota}}o{\nu}$)${\gg}$ is one of the works written by Euclid, but little known to us. In this paper, we introduce this Euclid's book on divisions of figures with its brief history, analyse its contents, and discuss how to use it in mathematics education.

• East Asian mathematical journal
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• v.32 no.4
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• pp.483-500
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• 2016

Ancient Greek mathematician Euclid left three books about mathematics. It's 'The elements', 'The data', 'On divisions of figure'. This study is based on the analysis of Euclid's 'On divisions of figure'. 'On divisions of figure' is a book about the construction of the shape. Because, there are thirty six proposition in 'On divisions of figure', among them 30 proposition are for the construction. In this study, based on the 'On divisions of figure' we explore the direction for construction education. The results were as follows. First, the proposition of 'On divisions of figure' shall include the following information. It is a 'proposition presented', 'heuristic approach to the construction process', 'specifically drawn presenting', 'proof process'. Therefore, the content of textbooks needs a qualitative improvement in this way. Second, a conceptual basis of 'On divisions of figure' is 'The elements'. 'The elements' includes the construction propositions 25%. However, the geometric constructions contents in middle school area is only 3%. Therefore, it is necessary to expand the learning of construction in the our country mathematics curriculum.

• Journal of the Korean Society for Library and Information Science
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• v.1
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• pp.1-58
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• 1970

As to the structure of author tables for the Korean libraries using the Korean alphabet Hangul for filing, no other system is understood more relevant to author notations than the analytico-synthetic system. The Korean character consists of syllables respectively dividual into 'consonant+vowel' or 'consonant+vowel+consonant,' with the first element a consonant and the second a vowel. When these elements are synthesized with figure representation, they make an enumerative two-figure table. Individualizing and assigning, therefore, are done without listing many en-tries on the table or looking up notations in ready-made enumerative author tables. We still do not have general agreements in form of entry, reading of the Japanese and Chinese names, transliteration of foreign words, and filing system. What is more, so flexible and hospitable a notation system should be adopted as to meet the anticipated changes. The writer introduces an author notation system that could make 150,000 divisions by combinating figures, thus making it possible to endure changes through readjustments. It is considered effective, convenient, and efficacious for individualization.

• Publications of The Korean Astronomical Society
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• v.28 no.2
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• pp.25-36
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• 2013

Chumsungdae is an ancient astronomical observatory whose main role was doing 'chunmoon'. It was administrate by a royal advisory agency on state affairs. The observers observed the heaven on the observatory platform, recorded peculiar events, and watched and interpreted the signs displayed in the heaven. Chumsungdae is an stonemasonry which represents almanac principles with its peculiar shapes and the numbers of strata and stones. The numbers were thoroughly invented to match exactly the almanac constants. Chumsungdae is comprised largely of three main parts, namely the square base, the stratified cylindrical body, and the top #-shaped stonework, and the total number of stones is 404. The number of the strata (27) and the height of the cylindrical body (27 尺) stand for the days in a sidereal month (27.3 days), which implies that the motion of the Moon with respect to the stars was given more priority than to the Sun at that time of geocentricism. And the cylindrical body was thoroughly designed to consist of 365 stones, which is of course the number of days in a solar year. In addition, there are 12 strata each under and above the south entrance and this in sum makes the 24 divisions of the year. Also there is 182 stones below the 13th stratum and this represents the number of days in the winter ~ summer solstice period, and the rest 183 stones the vice versa. The #-shaped top stonework was aligned in such a way that one of the diagonals points the direction of sunrise on the winter solstice. The square base also layed with the same manner. The south entrance was built 16 degrees SE, and the upright direction of the right pillar stone coincides with the meridian circle. This was a kind of built-in standard meridian circle facilitating the observations. In a symbolic sense, Chumsungdae was thought as the tunnel reaching the heaven, where the observers wished to be enlightened with the signs and inspirations in need. With the craftsmanship and skill, the builder reinforced the stratified cylindrical body with two sets of #-shaped beam stones, piercing at a right angle at 19th ~ 20th and 25th ~ 26th strata. Likewise, by placing the double #-shaped stonework with 8 beam stones on the platform of the observatory, both the stability of the stonemasonry and a guard rail for the nightly observers were securely provided.