洪正夏의 天元術과 增乘開方法

Abstract

Tianyuanshu and Zengcheng Kaifangfa introduced in the Song–Yuan dynasties andtheir contribution to the theory of equations are one of the most important achievementsin the history of Chinese mathematics. Furthermore, they became the mostfundamental subject in the history of East Asian mathematics as well. The operations,or the mathematical structure of polynomials have been overlooked by traditionalmathematics books. Investigation of GuIlJib (九一集) of Joseon mathematicianHong JeongHa reveals that Hong’s approach to polynomials is highly structural. For the expansion ofΠnk=1(x + ak), Hong invented a new method whichwe name Hong JeongHa’s synthetic expansion. Using this, he reveals that the processesin Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.