当开方术遇到一元高次方程  

The Kaifangshu (Extraction of a Root) Meeting with the Higher-order Equation with One Variable

作　　者：段耀勇 周畅 DUAN Yaoyong;ZHOU Chang(School of Intelligence Policing,China People’s Police University,Langfang,Hebei,065000;College of Science,Xi’an University of Posts&Telecommunications,Xi’an,Shannxi,710121)

机构地区：[1]中国人民警察大学智慧警务学院,河北廊坊065000 [2]西安邮电大学理学院,陕西西安710121

出　　处：《自然辩证法通讯》2021年第1期90-93,共4页Journal of Dialectics of Nature

基　　金：国家自然科学基金“中国、日本以及西方的消元方法的比较研究”(项目编号:11701446)。

摘　　要：开方术是中国古代数学中的内容,最先出现在《九章算术》中的《少广》章,他是中国传统数学中发展较为完善和成熟的一个分支。后来经过宋元时期的发展,演变为求解一元高次方程一个实根的增乘开方算法。如果方程恰好只有一个正的实根,解决起来顺理成章。如果方程有两个正根,开方术得到的是哪一个根?为什么这一个就是所要求的根?如果方程有多个正根,开方术如何求出这些正根?这些问题都是中国传统数学必须面对和需要解决的问题。另外,中国解方程的方法"开方术"也必然的无法回避方程的负数根、复数根以及方程论的相关问题,而对这些问题的梳理和介绍,可以为大家提供认识方程论的另一种视角,从中可以体现认识数学的多种进路。One of the most advanced and mature elements in Chinese traditional mathematical algorithm,the extraction method first occurred in The Nine Chapters.It was later developed into two methods (Zengchengkaifang and Lichengshisuo),an effective method to solve the equations with one unknown for one positive solution.If the equation has two positive roots,which one is the one obtained by the Kaifangshu,and why is this one the required root?If the equation has more than one positive root,how can we get them by the method?These problems,together with those pertaining to the negative root,the complex root and the theory of equations,had to be faced with and solved in Chinese traditional mathematics.A review of these problems can provide us with another perspective of understanding of the same issue developed in other cultures.

关 键 词：开方术 立成释锁 增乘开方 一元高次方程 方程论 

分 类 号：N0[自然科学总论—科学技术哲学]