{"title":"一个被忽视的文本:胡适、朱载予的插补新方法","authors":"Gang Li, Anjing Qu","doi":"10.1007/s00407-025-00348-6","DOIUrl":null,"url":null,"abstract":"<div><p>This paper translates and interprets a neglected and significant original text in Zhu Zaiyu’s 朱載堉 (1536–1611) calendar system. The invention and application of Guo Shoujing’s 郭守敬 (1231–1316) <i>hushi geyuan</i> 弧矢割圓 was a great change in the concept of constructing calendar system. In this text we argue that, by giving the relationship between <i>xian</i>-<i>hu</i> 弦弧 ratio and <i>shi</i> 矢, Zhu Zaiyu provided a new method of <i>hu shi</i> 弧矢新術 with higher accuracy than Guo Shoujing’s. Furthermore, we retrieved the construction of the new method of <i>hu shi</i> and discovered the crucial fact that Zhu Zaiyu created a new interpolation method. According to Zhu Zaiyu, a linear interpolation was used to modify the coefficient in each single step, then by repeating the steps, a high-order polynomial function could be constructed. Zhu Zaiyu’s interpolation was mechanical, and the polynomial function constructed by this method was categorized as the type of Newton interpolation, notably in modern terms. The critical purpose of ancient Chinese calendar compilers in interpolation was to construct higher order polynomial function; crucially, Zhu Zaiyu gave a general solution to this problem.</p></div>","PeriodicalId":50982,"journal":{"name":"Archive for History of Exact Sciences","volume":"79 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2025-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A neglected text: the new method of Hu Shi and Zhu Zaiyu’s interpolation\",\"authors\":\"Gang Li, Anjing Qu\",\"doi\":\"10.1007/s00407-025-00348-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper translates and interprets a neglected and significant original text in Zhu Zaiyu’s 朱載堉 (1536–1611) calendar system. The invention and application of Guo Shoujing’s 郭守敬 (1231–1316) <i>hushi geyuan</i> 弧矢割圓 was a great change in the concept of constructing calendar system. In this text we argue that, by giving the relationship between <i>xian</i>-<i>hu</i> 弦弧 ratio and <i>shi</i> 矢, Zhu Zaiyu provided a new method of <i>hu shi</i> 弧矢新術 with higher accuracy than Guo Shoujing’s. Furthermore, we retrieved the construction of the new method of <i>hu shi</i> and discovered the crucial fact that Zhu Zaiyu created a new interpolation method. According to Zhu Zaiyu, a linear interpolation was used to modify the coefficient in each single step, then by repeating the steps, a high-order polynomial function could be constructed. Zhu Zaiyu’s interpolation was mechanical, and the polynomial function constructed by this method was categorized as the type of Newton interpolation, notably in modern terms. The critical purpose of ancient Chinese calendar compilers in interpolation was to construct higher order polynomial function; crucially, Zhu Zaiyu gave a general solution to this problem.</p></div>\",\"PeriodicalId\":50982,\"journal\":{\"name\":\"Archive for History of Exact Sciences\",\"volume\":\"79 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2025-04-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archive for History of Exact Sciences\",\"FirstCategoryId\":\"98\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00407-025-00348-6\",\"RegionNum\":2,\"RegionCategory\":\"哲学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"HISTORY & PHILOSOPHY OF SCIENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archive for History of Exact Sciences","FirstCategoryId":"98","ListUrlMain":"https://link.springer.com/article/10.1007/s00407-025-00348-6","RegionNum":2,"RegionCategory":"哲学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"HISTORY & PHILOSOPHY OF SCIENCE","Score":null,"Total":0}
A neglected text: the new method of Hu Shi and Zhu Zaiyu’s interpolation
This paper translates and interprets a neglected and significant original text in Zhu Zaiyu’s 朱載堉 (1536–1611) calendar system. The invention and application of Guo Shoujing’s 郭守敬 (1231–1316) hushi geyuan 弧矢割圓 was a great change in the concept of constructing calendar system. In this text we argue that, by giving the relationship between xian-hu 弦弧 ratio and shi 矢, Zhu Zaiyu provided a new method of hu shi 弧矢新術 with higher accuracy than Guo Shoujing’s. Furthermore, we retrieved the construction of the new method of hu shi and discovered the crucial fact that Zhu Zaiyu created a new interpolation method. According to Zhu Zaiyu, a linear interpolation was used to modify the coefficient in each single step, then by repeating the steps, a high-order polynomial function could be constructed. Zhu Zaiyu’s interpolation was mechanical, and the polynomial function constructed by this method was categorized as the type of Newton interpolation, notably in modern terms. The critical purpose of ancient Chinese calendar compilers in interpolation was to construct higher order polynomial function; crucially, Zhu Zaiyu gave a general solution to this problem.
期刊介绍:
The Archive for History of Exact Sciences casts light upon the conceptual groundwork of the sciences by analyzing the historical course of rigorous quantitative thought and the precise theory of nature in the fields of mathematics, physics, technical chemistry, computer science, astronomy, and the biological sciences, embracing as well their connections to experiment. This journal nourishes historical research meeting the standards of the mathematical sciences. Its aim is to give rapid and full publication to writings of exceptional depth, scope, and permanence.