• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.39-54
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• 2005

In Chinese Mathematics, Jia Xian(要憲) introduced Zeng cheng kai fang fa(增乘開方法) to get approximations of solutions of Polynomial equations which is a generalization of square roots and cube roots in Jiu zhang suan shu. The synthetic divisions in Zeng cheng kai fang fa give ise to two concepts of Fan il(飜積) and Yi il(益積) which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) obtained the sufficient conditions for Fan il and Yi il for quadratic equations and proved them in the middle of 19th century.

• Bulletin of the Korean Chemical Society
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• v.23 no.8
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• pp.1062-1066
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• 2002

The complexes [Ni(L)(INT)2]${\cdot}$5H2O (1) and [Cu(L)(H2O)](Cl)(INT)${\cdot}$3H2O (2) (L = 3,14-dimethyl-2,6,13,17-tetraazatricyclo[14,4,01.18 ,07.12 ]docosane, INT = isonicotinate) have been prepared and characterized by X-ray crystallography, electronic absorption, and cyclic voltammetry. The crystal structure of 1 reveals an axially elongated octahedral geometry with two axial isonicotinate ligands. The electronic spectra, magnetic moment, and redox potentials of 1 also show a high-spin octahedral geometry. However, 2 shows that the coordination environment around the copper atom is a distorted square-pyramid with an axial water molecule. The spectra and electrochemical behaviors of 2 are also discussed.

• Journal of Astronomy and Space Sciences
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• v.32 no.1
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• pp.73-80
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• 2015

The Yang-gyeong-gyu-il-ui (兩景揆日儀) is a kind of elevation sundial using three wooden plates. Sang-hyeok Lee (李尙爀, 1810~?) and Byeong-cheol Nam (南秉哲, 1817~1863) gave descriptions of this sundial and explained how to use it in their Gyu-il-go (揆日考) and Ui-gi-jip-seol (儀器輯說), respectively. According to Gyu-il-go (揆日考) there are two horizontal plates and two vertical plates that have lines of season and time. Subseasonal (節候) lines are engraved between seasonal (節氣) lines, subdividing the interval into three equal lines of Cho-hu (初候, early subseason), Jung-hu (中候, mid subseason) and Mal-hu (末候, late subseason); there are 13 seasonal lines for a year, thus resulting in 37 subseasonal lines; also, there are 12 double-hour (時辰) lines for a day engraved on these plates. The only remaining artifact of Yang-gyeong-gyu-il-ui was made in 1849 (the $15^{th}$ year of Heon-jong) and is kept at the Korea University Museum. We have compared and analyzed Yang-gyeong-gyu-il-ui and similar western sundials. Also, we have reviewed the scientific aspect of this artifact and built a replica. Yang-gyeong-gyu-il-ui is a new model enhanced from the miniaturization development in the early Joseon Dynasty and can be applied to the southern part of the tropic line through a structure change.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.273-289
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• 2018

The KaiFangFa開方法 of traditional mathematics was completed in ${\ll}$JiuZhang SuanShu九章算術${\gg}$ originally, and further organized in Song宋 $Yu{\acute{a}}n$元 dinasities. The former is the ShiSuoKaiFangFa釋鎖開方法 using the coefficients of the polynomial expansion, and the latter is the ZengChengKaiFangFa增乘開方法 obtaining the solution only by some mechanical numerical manipulations. ${\ll}$SanHak JeongEui算學正義${\gg}$ basically used the latter and improved the estimate-value array by referring to the written-calculation in ${\ll}$ShuLi JingYun數理精蘊${\gg}$. As a result, ZengChengKaiFangFa was more refined so that the KaiFangFa algorithm is more consistent.