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산대셈 개방법(開方法)에 대한 <산학정의>의 독자적 성취: 어림수[商] 배열법 개선을 통한 증승개방법(增乘開方法)의 정련(精鍊)
강민정 한국수학사학회 2018 Journal for history of mathematics Vol.31 No.6
The KaiFangFa開方法 of traditional mathematics was completed in JiuZhang SuanShu{九章算術} originally, and further organized in Song宋, Yuán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. SanHak JeongEui{算學正義} basically used the latter and improved the estimate-value array by referring to the written-calculation in ShuLi JingYun{數理精蘊}. As a result, ZengChengKai\-FangFa was more refined so that the KaiFangFa algorithm is more consistent. 전통산학의 開方法은 漢代의 《九章算術》에서 原型이 완성되었고, 宋·元代에 한층 더 구조화되었다. 전자는 다항전개식의 계수를 이용하는 釋鎖開方法이고, 후자는 기계적인 수치 조작만으로 해를 얻는 增乘開方法이다. 《算學正義》는 기본적으로 증승개방법을 사용하되 《數理精蘊》의 筆算 개방법을 참조하여 어림수[商] 배열법을 개선하였다. 그 결과 증승개방법에 기계적 구조성을 강화하여 더욱 일관된 알고리듬을 갖추도록 精鍊하는 독자적 성취를 이루었다.
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김창일,윤혜순,Kim, Chang-Il,Yun, Hye-Soon 한국수학사학회 2009 Journal for history of mathematics Vol.22 No.4
중국 산학에서 방정식 풀이 방법은 고법(古法)과 구장산술(九章算術)의 개방술(開方術), 개입방술(開立方術)을 시작으로 가헌(賈憲)의 개방석쇄법(開方釋鎖法)을 걸쳐 증승개방법(增乘開方法)으로 완성된다. 본 논문에서는 이 방법들을 알아보고 조선의 산학자들이 그들의 산서에서 사용한 해법을 연구한다. we know that Zeng Cheng Kai Fang Fa is the generalization of the method of square roots and cube roots of ancient <Jiu zhang suan shu> through the investigation of China mathematics. In this paper, we have research on traditional solutions equations of China mathematics and the development solutions of equations used by Chosun mathematicians.
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Kaifangfa and Translation of Coordinate Axes
홍성사,홍영희,장혜원,Hong, Sung Sa,Hong, Young Hee,Chang, Hyewon The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.6
Since ancient civilization, solving equations has become one of the most important subjects in mathematics and mathematics education. The extractions of square roots and cube roots were first dealt in Jiuzhang Suanshu in the setting of subdivisions. Extending these, Shisuo Kaifangfa and Zengcheng Kaifangfa were introduced in the 11th century and the subsequent development became one of the most important contributions to mathematics in the East Asian mathematics. The translation of coordinate axes plays an important role in school mathematics. Connecting the translation and Kaifangfa, we find strong didactical implications for improving students' understanding the history of Kaifangfa together with the translation itself although the latter is irrelevant to the former's historical development.
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Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa
홍성사,홍영희,김영욱,Hong, Sung Sa,Hong, Young Hee,Kim, Young Wook The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.3
Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of $\prod_{k=11}^{n}(x+a_k)$, Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.
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