History of Fanji and Yiji
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In Chinese Mathematics, Jia Xian(賈憲)introduced zengcheng kaifangfa(增乘開方法)to get approximations of solutions of polynomial equations which is a generalization of square roots and cube roots in Jiuzhang Suanshu. The synthetic divisions in zeng- cheng kaifangfa give rise to two concepts of Fan ji(fanji)and Yi ji(yiji)which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(Nam Byeong-gil)and Lee Sang Hyuk(Lee Sang- hyeog)obtained the sufficient conditions for Fan ji and Yi ji for quadratic equations and proved them in the middle of 19th century.
Abstract
In Chinese Mathematics, Jia Xian(賈憲)introduced zengcheng kaifangfa(增乘開方法)to get approximations of solutions of polynomial equations which is a generalization of square roots and cube roots in Jiuzhang Suanshu. The synthetic divisions in zeng- cheng kaifangfa give rise to two concepts of Fan ji(fanji)and Yi ji(yiji)which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(Nam Byeong-gil)and Lee Sang Hyuk(Lee Sang- hyeog)obtained the sufficient conditions for Fan ji and Yi ji for quadratic equations and proved them in the middle of 19th century.