• Title/Summary/Keyword: Shisuo Kaifangfa

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Kaifangfa and Translation of Coordinate Axes (개방법(開方法)과 좌표축(座標軸)의 평행이동(平行移動))

  • Hong, Sung Sa;Hong, Young Hee;Chang, Hyewon
    • Journal for History of Mathematics
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    • v.27 no.6
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    • pp.387-394
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    • 2014
  • 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.

Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa (홍정하(洪正夏)의 천원술(天元術)과 증승개방법(增乘開方法))

  • Hong, Sung Sa;Hong, Young Hee;Kim, Young Wook
    • Journal for History of Mathematics
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    • v.27 no.3
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    • pp.155-164
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    • 2014
  • 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.