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東洋 數學에서 多項方程式의 解Zeros of Polynomials in East Asian Mathematics

Other Titles
Zeros of Polynomials in East Asian Mathematics
Authors
홍성사홍영희김창일
Issue Date
Dec-2016
Publisher
한국수학사학회
Keywords
East Asian mathematics; zeros of polynomials; polynomial equations; tianyuanshu; kaifangfa; Suanxue Qimeng; 구장산술이래 동아시아의 전통수학은 수학적 구조를 실생활의 문제 해결을 통하여 들어내었다. 따라서 다항방정식은 상수항이 없는 다항식 $p(x)$와 양의 실수 $a_0$를 사용하여 $p(x)=a_0$ 형태를 사용하였다. 이런 제약은 방정식론의 구조적 발전에 방해가 되었다. 11세기 천원술 (天元術)이 도입되면서 다항방정식은 $p(x)=0$ 형태로 되었지만 천원술은 일부 수학자들만 사용하였다. 한편 동아시아 수학자들은 방정식의 해법에 집중하면서 다항방정식의 해의 개념이 이루어지지 못하였다. 한편 산학계몽은 동아시아 한중일 삼국의 방정식론이 서로 다른 길을 따라 발전하게 되는 계기가 된 것도 보인다.
Citation
한국수학사학회지, v.29, no.6, pp.317 - 324
Journal Title
한국수학사학회지
Volume
29
Number
6
Start Page
317
End Page
324
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/3199
DOI
10.14477/jhm.2016.29.6.317
ISSN
1226-931X
Abstract
Since Jiuzhang Suanshu, mathematical structures in the traditional East Asian mathematics have been revealed by practical problems. Since then, polynomial equations are mostly the type of $p(x) = a_0$ where $p(x)$ has no constant term and $a_0$ is a positive number. This restriction for the polynomial equations hinders the systematic development of theory of equations. Since tianyuanshu (天元術) was introduced in the 11th century, the polynomial equations took the form of $p(x)=0$, but it was not universally adopted. In the mean time, East Asian mathematicians were occupied by kaifangfa so that the concept of zeros of polynomials was not materialized. We also show that Suanxue Qimeng inflicted distinct developments of the theory of equations in three countries of East Asia.
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