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The Spread of Traditional Chinese Mathematics in the Sinosphere and Its 11 Influence

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The Spread of Traditional Chinese Mathematics in the Sinosphere and Its 11 Influence The Spread of Traditional Chinese Mathematics in the Sinosphere and Its 11 Influence Zelin Xu Contents 11.1 Mathematical Exchanges Between China and Korea ................................... 414 11.2 Traditional Chinese Mathematics in Japan .............................................. 417 11.3 Traditional Chinese Mathematics in Vietnam ........................................... 423 Abstract The Sinosphere refers to China, the birthplace of Chinese characters, and its surrounding areas, including Vietnam, Korean Peninsula, Japan, and the ancient Ryukyu Kingdom. With the language of Chinese as the medium, China’s neigh- boring countries and ethnic groups learned not only national systems, political thoughts, and various kinds of knowledge from China’s different dynasties and developed similar cultures and values, but more importantly, traditional Chinese mathematics had great influence on these neighboring countries. Keywords Sinosphere · Traditional Chinese mathematics · Chinese astronomical calendar · Korean mathematics The Sinosphere refers to China, the birthplace of Chinese characters, and its sur- rounding areas, including Vietnam, Korean Peninsula, Japan, and the ancient Ryukyu Kingdom. In ancient times, people with farming culture were mainly distributed in these areas, and their leaders were crowned by ancient Chinese emperor who enjoyed tribute presented to them. In history, these countries used Chinese characters in writing or mixed it with their own characters. Ancient officials Z. Xu (*) Institute of History, School of Humanities, Donghua University, Shanghai, China © Springer Nature Singapore Pte Ltd. 2021 413 X. Jiang (ed.), The High Tide of Science and Technology Development in China, History of Science and Technology in China, https://doi.org/10.1007/978-981-15-7847-2_11 414 Z. Xu and intellectuals mostly used classical style of writing (known as Han Wen or Chinese written language in Japan, Vietnam, and Korea) as their written language. With the language of Chinese as the medium, China’s neighboring countries and ethnic groups learned national systems, political thoughts, and various kinds of knowledge from China’s different dynasties and developed similar cultures and values. The influence of Chinese science and technology culture on neighboring countries is one demonstration. 11.1 Mathematical Exchanges Between China and Korea As a close neighbor of China, Korea paid tributes to ancient China and received conferred titles in different dynasties. Its culture, science and technology are deeply influenced by Chinese culture. In the history of mathematics exchanges in Sinosphere, Dongsuan (literally means eastern calculation, Korea’s traditional math- ematics), derived from Zhongsuan, or Chinese calculation, has inherited Chinese mathematics culture successively, preserving many related ancient literature and systems of Chinese calculation, providing many academic resources for Hesuan (literally means Japanese calculation, Japanese traditional mathematics) as well. Chinese astronomical calendar was introduced to Korea in the Qin and Han Dynasties (221–220 AD). According to Houhanshu-Xunli liezhuan (Book of the Later Han-biographies of benevolent officials), during the early years of the west Han Dynasty (206 BC-25 AD), the descendant of the noble Langya Family, Wang Zhong, from Buqi (in Shandong Province) moved to Korean Peninsula to avoid chaos and rebellion of empress Lv’s family. Korea was in the early days of Wei’s reign back then and had frequent communications with the Han Dynasty. In 108 BC, Emperor Wu of the Han Dynasty destroyed the Wei Family of Korea and set up four prefectures, namely, Zhenfan, Lintun, Lelang, and Xuantu, bringing the connections between Korea and China closer. Wang Jing, the eighth grandson of Wang Zhong, lived in Nehan County, Lelang Prefecture. He studied the Book of Changes when he was still young, and he read widely, “has good commands of astronomy and many other skills.” From Wang Zhong to Wang Jing, generations of immigrants spread the astronomy and mathematics of the Han Dynasty to the Korean Peninsula. According to the ancient Japanese documents, such as the Kojiki or records of ancient matters and Nihon Shoki, or the Chronicles of Japan, in the third century, Wang Ren from Baekje brought Chinese culture from mainland to Japan. In the sixth century, Wang Daoliang from Baekje, Wang Baosun, Guan Le, and other so-called naturalized people brought many Chinese science knowledge including calendars into Japan. Therefore, during the Qin and Han Dynasties, Chinese immigrants introduced Chinese calculation along with other cultures into the Korean Peninsula. From the fourth century to the seventh century, tripartite confrontation among Koguryo, Baekje, and Silla was formed on the Korean Peninsula, leading to closer connections with Chinese culture. In 372 AD, Koguryo began to set up Taixue, or imperial knowledge schools, with Sinology as its main teaching content. The calendar calculation of Yuan-jia li, created by Liu Song of the Southern Dynasty of China, was 11 The Spread of Traditional Chinese Mathematics in the Sinosphere and Its... 415 adopted by Baekje at that time. According to Nihon Shoki,inthefifth century, some Chinese descendants who immigrated to Lelang and Daifang county and immigrants from Baekje of Koreans were called “people who cross the ocean” or “naturalized people.” They traveled to Japan from Baekje located in the south of Korea, mastering all kinds of handicrafts and having good commands of Chinese, and brought all kinds of techniques to Japan. Among them, those who were called “doctors” or “teachers” were employed by the Japanese court in ministry of appointment and ministry of finance in charge of document record, foreign affair document, accounting, tax collection, etc. As a result, Chinese culture was introduced to Japan, including knowledge of arithmetic, computing skills, and calendar. According to Nihon Shoki, Japanese imperial court sent envoys to Baekje in 553 AD for doctor of medicine, geomancy, and calendar, bringing back “divination books, almanacs and different medicines” to Japan. So, the next year, Wang Daoliang, or Shide, the doctor of geomancy; Wang Baosun, or Gude, the doctor of calendar; and others came to Japan from Baekje. During the Sui and Tang Dynasties (581–907), the exchanges of astronomy and mathematics between China and Korea saw important development. In 676, Silla unified Korea and in 682 established imperial college imitating the system of Tang Dynasty, bringing Chinese calculation books and mathematics systems to Korea. The records of the history of the Three Kingdoms of Korea documented literature of Silla which mentioned the Nine Chapters, or The Nine Chapters on the Mathemat- ical Art, the Classic of Zhui, or Zhui Shu (Methods for Interpolation). However, these two books, San Kai and Liu Zhang, have not been recorded in Book of Sui, Old Book of Tang, and New Book of Tang. Korea directly adopted the Chinese calendar for a long time. In the second year of Linde during the reign of Emperor Gaozong in the Tang Dynasty (665), Linde calendar created by Li Chunfeng was issued, which was used until 728 AD. According to the Records of the Three Kingdoms, in the first year of Yongchun during the reign of Emperor Gaozong of the Tang Dynasty (692), monks from Silla returned to their home country after studying the calendar in China and “presented the astronomical map” to the king of Silla. In 718, Silla established the system of clepsydra imitating the Tang Dynasty. In the second year of Tanbao of Tang (749), Silla followed China, “appointed one doctor of astronomy and six doctors of clepsydra,” gradually forming a complete astronomical organization system. From 766 to 779, Jin Yan from Silla went to Tang to study astronomy and calendar and returned to serve as doctor of heaven in Silla. Goryeosa or History of Goryeo records that “the calendar was changed in the previous Tang Dynasty and it was then changed for twenty-two times. However, Goryeo used the same calendar until Emperor Zhongxuan of Goryeo announced to change the calendar of Shoushi in the Yuan Dynasty.” From the time of Silla to the time of Emperor Zhongxuan of Goryeo (1309–1313), the Xuanming calendar of Tang xu’ang was adopted in Korea for 400 years. Compared with the calendar of the Han Dynasty, the calculation method of the calendar of Sui and Tang Dynasty was improved in both the astro- nomical accuracy and the mathematical method. For example, the method of adjusting the sun, the method of second differences interpolation, the difference table, and the table containing the tangent function value were all advanced 416 Z. Xu mathematical methods in the world at that time. These mathematical knowledge along with Chinese calendar were introduced into the Korean Peninsula. In 918, Wang Jian established the Goryeo Dynasty and inherited the former dynasty’s mathematics system due to the tradition of Confucianism and imperial examination. According to volume 188 of Supplementary Documents for Reference, “election examination,” the arithmetic examination in the Korean Dynasty was still dominated by the Chinese calculation. The latest arithmetic books popular in China at that time were also introduced to Korea at that time. Xiejia could be the arithmetic book Xiecha micro arithmetic book in the Song Dynasty. The reign of Li Family for over 500 years in Korea witnessed a golden age of Korea culture. During its peak time, the fourth generation of the Shizong Dynasty (1419–1450),
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