| 当开方术遇到一元高次方程 |
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| 引用本文： | 段耀勇,周畅. 当开方术遇到一元高次方程[J]. 自然辩证法通讯, 2021, 0(1): 90-93 |
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| 作者姓名： | 段耀勇 周畅 |
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| 作者单位： | 中国人民警察大学智慧警务学院;西安邮电大学理学院 |
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| 基金项目： | 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)。 |
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| 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...
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| 关 键 词： | 开方术 立成释锁 增乘开方 一元高次方程 方程论 |
The Kaifangshu (Extraction of a Root) Meeting with the Higher-order Equation with One Variable |
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| DUAN Yaoyong,ZHOU Chang. The Kaifangshu (Extraction of a Root) Meeting with the Higher-order Equation with One Variable[J]. Journal of Dialectics of Nature, 2021, 0(1): 90-93 |
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| Authors: | DUAN Yaoyong ZHOU Chang |
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| Affiliation: | (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) |
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| Abstract: | 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. |
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| Keywords: | Kaifangshu Lichengshisuo Zengcheng Kaifang The higher-order equation with one variable Theory of equations |
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