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Zengcheng Kaifangfa and Zeros of Polynomials增乘開方法과 多項方程式의 解

Other Titles
增乘開方法과 多項方程式의 解
Authors
홍성사홍영희김창일
Issue Date
Dec-2020
Publisher
한국수학사학회
Keywords
East Asian mathematics; polynomial equations; zengcheng kaifangfa; Ruffini-Horner method; multiple zeros of polynomials; word problems.
Citation
한국수학사학회지, v.33, no.6, pp.303 - 314
Journal Title
한국수학사학회지
Volume
33
Number
6
Start Page
303
End Page
314
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/975
DOI
10.14477/jhm.2020.33.6.303
ISSN
1226-931X
Abstract
Extending the method of extractions of square and cube roots in Jiuzhang Suanshu, Jia Xian introduced zengcheng kaifangfa in the 11th century. The process of zengcheng kaifangfa is exactly the same with that in Ruffini-Horner method introduced in the 19th century. The latter is based on the synthetic divisions, but zengcheng kaifangfa uses the expansions of binomial expansions. Since zengcheng kaifangfa is based on binomial expansions, traditional mathematicians in East Asia could not relate the fact that solutions of polynomial equation $p(x) = 0$ are determined by the linear factorization of $p(x)$. The purpose of this paper is to reveal the difference between the mathematical structures of zengcheng kaifangfa and Ruffini-Honer method. For this object, we first discuss the reasons for zengcheng kaifangfa having difficulties to connect solutions with linear factors. Furthermore, investigating multiple solutions of equations constructed by tianyuanshu, we show differences between two methods and the structure of word problems in the East Asian mathematics.
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