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丁若鏞의 算書 勾股源流의 多項式의 數學的 構造Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu

Other Titles
Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu
Authors
홍성사홍영희이승온
Issue Date
Oct-2016
Publisher
한국수학사학회
Keywords
Jeong Yag-yong; Gugo Wonlyu; Pythagorean polynomials; polynomial functions; 丁若鏞(1762--1836); 勾股源流; 피타고라스 多項式; 多項函數
Citation
한국수학사학회지, v.29, no.5, pp.257 - 266
Journal Title
한국수학사학회지
Volume
29
Number
5
Start Page
257
End Page
266
URI
https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/3249
DOI
10.14477/jhm.2016.29.5.257
ISSN
1226-931X
Abstract
This paper is a sequel to our paper ``Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu''. Although polynomials in the tianyuanshu induce perfectly the algebraic structure of polynomials, the tianyuan(天元) is always chosen by a specific unknown in a given problem, it can't carry out the role of the indeterminate in ordinary polynomials. Further, taking the indeterminate as a variable, one can study mathematical structures of polynomials via those of polynomial functions. Thus the theory of polynomials in East Asian mathematics could not be completely materialized. In the previous paper \cite{6}, we show that Jeong Yag-yong disclosed in his Gugo Wonlyu(勾股源流) the mathematical structures of Pythagorean polynomials, namely polynomials $p(a, b, c)$ where $a, b, c$ are the three sides gou(勾), gu(股), xian(弦) of a right triangle, respectively. In this paper, we show that Jeong obtained his results through his recognizing Pythagorean polynomials as polynomial functions of three variables $a, b, c$.
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