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http://dx.doi.org/10.14477/jhm.2015.28.6.301
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Mathematical Structures of Jeong Yag-yong's Gugo Wonlyu |

HONG, Sung Sa
(Dept. of Math., Sogang Univ.)
HONG, Young Hee (Dept. of Math., Sookmyung Women's Univ.) LEE, Seung On (Dept. of Math., Chungbuk National Univ.) |

Publication Information

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;

Citations & Related Records

- Reference

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 | JEONG Yag-yong, Gugo Wonlyu, Yeoyudang Jeonseo Boyu Four, Gyeongin Munhwasa, 1975.(丁若鏞, <<勾股源流>>, 與猶堂全書補遺四, 景仁文化社, 1975.) |

4 | JEONG Yag-yong, Gugo Wonlyu, chapter 1-3, National Library of Korea.(丁若鏞, <<勾股源流>> 1-3章, 國立中央圖書館, http://www.nl.go.kr.) |

5 | JING Yushu ed. ZhongGuo Lidai Suanxue Jicheng, Shandong Renmin Pub. Co., 1994.(靖玉樹編勘, <<中國歷代算學集成>>, 山東人民出版社, 1994.) |

6 | MEI Wending, Meishi Lishuan Quanshu, Tohoku University Library.(梅文鼎, <<梅氏曆算全書>>, 東北大學圖書館.) |