• (The)Study of the Eastern Classic
• /
• no.48
• /
• pp.147-167
• /
• 2012

This paper was investigated by comparing "Sok-Mong-Gu Bun-Ju"(續蒙求分註) and "Mong-Gu"(蒙求). As a result, "Mong-Gu" was organized around the person anecdotes, "Sok-Mong-Gu Bun-Ju" is annotated with the person anecdotes. So the text show an differences were found on the configuration. Thus It reveal that "Sok-Mong-Gu Bun-Ju" is a tome and convenient to use the report has been made by scholars can be clarified.

• Journal for History of Mathematics
• /
• v.21 no.4
• /
• pp.1-10
• /
• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.