Mathematical Structures of Jeong Yag-yong`s Gugo Wonlyu

- 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;

HONG, Sung Sa; HONG, Young Hee; LEE, Seung On;

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;

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