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Zheng Xuan’s mathematical world – Zheng’s method of mathematical observing, landscape and historical contributions
Author: Zhu Yiwen
Source: Vol. 48, Issue 11
Content Summary: As a master of the two academic studies, Zheng Xuan has covered the various works of the ancient and modern texts, and has also carefully studied calculations and is good at “Nine Chapters of Achievement”. However, in the past, the academic community has not discussed its math. Judging from the San Rong Notes of Zheng Xuan, he quoted Zheng people as saying “nine numbers”, implying that “Nine Chapters of Achievement” originated from “Zhou Rong”, and mentioned the “corn method” and the application of “Pythagorean method”. He often gives the algorithm the key points or results without giving calculation details, and uses them to eliminate the differences between classics or versions. His annotations also use mathematics, thus creating a textual context for developing mathematics for later scholars. In the same period, Liu Xin proposed that mathematics is the concept of “leuth, erecting, and pursuing the basics of law”; in the second year of Guanghe, the Dali Yuanhu and the License established this concept and the authority of “Nine Chapters of Calculation”. In the late Donghan period, the chapters and sentences of the academic chapters were single, and compared with Zheng Guan, Xu Shen, Ma Rong and others, Zheng Xuan was better at applying mathematics and calculations for a long time. Therefore, the notes of Zheng’s “Nine Chapters of Achievement” have the dual importance of politics and academic compliance. However, based on his academic research, later Confucianism developed a relatively independent computational tradition with traditional computation represented by “Nine Chapters of Achievement”, which deviated from Zheng Xuan’s original aspiration to use mathematics to read.
Keywords: Zheng Xuan, “Nine Chapters of Achievement”, Study, Calculation, Liu Xin, San Rong
Author introduction: Zhu Yiwen, associate professor at the Department of Philosophy of Zhongshan, Guangzhou and the Institute of Logic and Awareness. The purpose of the important discussion is mathematical history and mathematics philosophy, chess history and gaming civilization.
1. Media
As the master of the two schools of learning, Zheng Xuan (127-200) reads the community and integrates ancient and modern literature. “Later Han Book·Zheng Xuanyu” says that Zheng’s name is “The Three Symbols” and “Nine Chapters of Calculation” and also says “Xuan is good at Calculation”. [1] From this we can see that Zheng Xuan has certain ideas in geography and mathematics [2]. However, compared with its academic research, the academic community has discussed its scientific knowledge and thinking for a long time. [3] However, the relationship between Zheng Xuan and modern Chinese mathematics has always been paid attention to. Modern mathematical historian Money Baocong (1892-1974) believed that “The Nine Chapters of Achievement” is similar to Xu Shen’s “Shi Wen Jiezi”. It is a part of Confucianism in the early years of Dong and Han, and is closely related to Confucian traditional thinking.” He also said that “The compilation of “The Nine Chapters of Achievement” is closely related to the Confucian scholars from the ancient literature school in the early years of Dong and Han”, and mentioned three scholars, Zheng (?-83), Ma Hu (Ma Rong’s brother), and Ma Rong (79-166). [4] Guo Shuchun believed that Zheng Xuan “had actually formed a mathematical middle school with Liu Hong, Xu Yue and others”, and said that “Liu Hui studied “Zhou Rong” through Zheng Xuan’s annotation, and Zheng Xuan’s annotation became one of the direct data that he had ‘taken what he saw’ when he annotated the “Nine Chapters”.” [5] Liu Hong (Aboutique)129-190) wrote “Qian Xiangyu”, Xu Yue (born at the end of Donghan), and “Nine Chapters of Calculation” in the fourth year of Jingyuan, Liu Hui (263), and they were both famous geographical calculationists at that time. These insights in the academic world have determined the relationship between Donghan school and the editor of “Nine Chapters of Achievement”, determined the influence of Zheng Xuan on Liu Hui’s notes, and left a space for further research.
In recent years, the author has focused on studying mathematical literature in Confucian classical annotations and found that Confucians in the Southern and Northern Dynasties, Sui and Tang Dynasties developed relatively independent algorithmic traditions that were different from the “Nine Chapters of Arithmetic” (called “calculation” by the Qing people), [6], and this algorithmic tradition has always been extended to the late Qing Dynasty. [7] Specifically, the “artistic” of “Nine Chapters of Achievement” has the characteristics of “construction”, “mechanization” and “integration of theory in calculation”, and its application is broad; in contrast, the traditional foundation of algorithms in academic research does not take into account, but only uses books for calculation and reasoning, and only occurs when the annotations of mathematics by later generations such as Zheng Xuan. [8] Under this research and study, we will ask whether Zheng Xuan’s own mathematics can also be Confucian tradition? The author believes that the bottom line can be denied. However, why did Zheng adopt this method of introductory practice, and why did this method have such a big impact on the development of mathematics in later generations? In order to answer these questions, we must further analyze the relationship between Zheng Xuan and modern Chinese mathematics or “Nine Chapters of Arithmetics” and promote Chinese mathematical history and historical history. This is the goal of this article.
Zheng and Zheng Xuan quoted “Nine Chapters of Achievements” to annotate
In the process of observing the group, Zheng Xuan used many thinking resources. In the past, the academic community paid more attention to the ideological thoughts used by Zheng Xuan in this. [9]In fact, Zheng Xuan also used mathematics in large quantities. In terms of the general view, Zheng’s usage of mathematics has three levels: First, he discussed the relationship between mathematics and Zhou Rong; secondly, his mathematical betting provides the textual context of mathematics developed in later generations; finally, his goal is to use mathematics as something to eliminate or harmonize the differences between various classics. The above briefly describes it.
Zheng Xuan’s gift study has had a great impact on later generations, so there is a saying that “Tender is a teaching”. In this protecting online car and horse tax, Zheng’s notes on “Zhou Rong” “Nine Numbers” have a great impact on the development of mathematical knowledge among his predecessors. “Zhou Rong·Diguan·Baoshi” says: “Harding the countryBaozhuangThe Tao is the six teachings of teaching. One is the five gifts, the second is the six joys, the third is the five shooting, the fourth is the five jing, the fifth is the sixth book, and the sixth is the nineth number.” Zheng Xuan quoted Zheng people: “Nine numbers, square fields, corn, difference, small fortune, business achievements, equalization, equations, winning lack, and side keys. Now there are heavy differences, Xijie, and Juquan.” [10] This is to explain the “nine numbers” into nine items related to mathematics. The nine-chapter volumes of the current version of “Nine Chapters of Achievement” are: square fields, corn, decay, low-cost, business achievements, equal gain, lack of profit, equations, and sentence stocks. Declining is difference, and lack of profit means lack of reward. Therefore, Zheng Xuan led the public to the “Nine Chapters of Achievement” (only the lack of profit and the order of equations, and the differences between the side and the sentence stock). The academic community generally believes that this explains the inheritance between the nine numbers of “Zhou” and “Nine Chapters of Achievement”. In fact, because of Zheng Xuantong’s “Nine Chapters of Calculation”, he quoted Zheng’s approach to constructing the relationship between “Nine Numbers” in “Zhou Rong” to “Nine Numbers” in “Zhou Rong”. Through this relationship, Zheng Xuan introduced mathematics to “Baoying ContractZhou Rong”, and hinted that “Nine Chapters of Achievement” was derived from it. Liu Hui’s preface to the “Nine Chapters of Achievement” says: “According to the Zhou dynasty, there are nine numbers and nine numbers, so the “Nine Chapters” is the case.” [11] Without doubt, we will continue to use and determine Zheng Xuan’s explanation.
Zheng Xuan’s notes directly mentioned the “corn method” or “corn method”. Zheng’s notes on “Zhou Rong·Kao Gong Ji” “㮚 is the quantity” says, “In the present method of corn, two liters are less than 81 fen.” [12] Zheng’s notes o
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