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Mathematical Structures of Jeong Yag-yong`s Gugo Wonlyu
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  • Journal title : Journal for History of Mathematics
  • Volume 28, Issue 6,  2015, pp.301-310
  • Publisher : The Korean Society for History of Mathematics
  • DOI : 10.14477/jhm.2015.28.6.301
 Title & Authors
Mathematical Structures of Jeong Yag-yong`s Gugo Wonlyu
HONG, Sung Sa; HONG, Young Hee; LEE, Seung On;
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 Abstract
Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.
 Keywords
Jeong Yag-yong;Gugo Wonlyu;polynomials of three indeterminates;algebraic structure;order structure;lexicographic order;
 Language
English
 Cited by
1.
정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 다항식(多項式)의 수학적(數學的) 구조(構造),홍성사;홍영희;이승온;

한국수학사학회지, 2016. vol.29. 5, pp.257-266 crossref(new window)
2.
정약용의 『구고원류』의 내용과 표현방법 분석,이경언;

한국수학사학회지, 2016. vol.29. 1, pp.1-16 crossref(new window)
1.
An Analysis of the Contents and Expression Methods of Jeong Yag-yong's 『Gugo Wonlyu』, Journal for History of Mathematics, 2016, 29, 1, 1  crossref(new windwow)
2.
Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu, Journal for History of Mathematics, 2016, 29, 5, 257  crossref(new windwow)
 References
1.
GUO ShuChun ed. ZhongGuo Kexue Jishu Dianji Tonghui Shuxuejuan, Henan Jiaoyu Pub. Co., 1993.(郭書春主編, <<中國科學技術典籍通彙>> 數學卷, 河南敎育出版社, 1993.)

2.
HONG Sung Sa, HONG Young Hee, KIM Chang Il, Gougushu in the 18th century Chosun, The Korean Journal for History of Mathematics 20(4) (2007), 1-22.(홍성사, 홍영희, 김창일, 18 世紀朝鮮의 句股術, 한국수학사학회지 20(4) (2007), 1-22.)

3.
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