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Liu Yi and Hong Jung Ha's Kai Fang Shu  

Hong, Sung-Sa (Department of Mathematics, Sogang University)
Hong, Young-Hee (Department of Mathematics, Sookmyung Women's University)
Kim, Young-Wook (Department of Mathematics, Korea University)
Publication Information
Journal for History of Mathematics / v.24, no.1, 2011 , pp. 1-13 More about this Journal
Abstract
In Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法) of Yang Hui suan fa(楊輝算法)), Yang Hui annotated detailed comments on the method to find roots of quadratic equations given by Liu Yi in his Yi gu gen yuan(議古根源) which gave a great influence on Chosun Mathematics. In this paper, we show that 'Zeng cheng kai fang fa'(增乘開方法) evolved from a process of binomial expansions of $(y+{\alpha})^n$ which is independent from the synthetic divisions. We also show that extending the results given by Liu Yi-Yang Hui and those in Suan xue qi meng(算學啓蒙), Chosun mathematican Hong Jung Ha(洪正夏) elucidated perfectly the 'Zeng cheng kai fang fa' as the present synthetic divisions in his Gu il jib(九一集).
Keywords
Solutions of polynomial equations; Liu Yi(劉益); Yang Hui(楊輝); Xiang jie jiu zhang suan fa(詳解九章算法); Yang Hui suan fa(楊輝算法); Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法); Yong le da dian(永樂大典); Suan xue qi meng(算學啓蒙); Zeng cheng kai fang fa(增乘開方法); Hong Jung Ha(洪正夏); Gu il jib(九一集);
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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