A Discussion on the Significance of the Discovery of Mathematics Bamboo Slips from Thewarring States Period, Qin and Han Dynasty

The recent acquisitions of archaeological findings of bamboo slips inmany institutions inChina provide us a good significance for the study of development of mathematics in Ancient China. These includes the Tsinghua University (arithmetic table, dated from the Warring States period), the YueluAcademy (bamboo slips of the book “mathematics”, QinDynasty), the BeijingUniversity (bamboo slips of mathematics, dated in the Qin Dynasty), and the Hubei Museum (Han bamboo slips of mathematics at the found on “land of sleeping tiger”, Han Dynasty). Firstly, it gives us rare first-hand information on the knowledge of mathematics in Ancient China. Secondly, it helps to clarify that the nihilistic attitude holds by some scholars on the development of early Chinese mathematics was unfounded. Thirdly, it provided strong evidence in the study of Chinese mathematics, that the major methods and mathematics problems in Jiuzhang Suanshu (Nine Chapters) was completed in early Qin period. Most importantly, it provides reliable literature to support that the first peak of mathematics achievement in China was in the Spring and Autumn and Warring States period. In the past, the statement was only supported by the evidence of the work of Jiuzhang Suanshu and its explanations and remarks made by Liu Hui. 1 The recent discovery of mathematics bamboo slips from the Warring States Period, Qin and Han Dynasty From 1983 to early 1984, about 200 mathematical bamboo slips “Suanshu shu” were discovered in Jingzhou Zhangjiashan Han Tomb No. 247 in Hubei. There was less significant harvest for 20 years in unearthed mathematical bamboo slips since then. Then there were much news on discovery of mathematical bamboo slips from theWarring States Period, Qin andHanDynasty in the past 10 years. The news of discovery excited the circle of the scholars in history of Chinese mathematics. Some of the discovered bamboo slips have been treated and studied, some are under treatment. We introduce as follow these discoveries according to the date of history of these mathematical bamboo slips: Calculation table (suanbiao), Warring States Period, collection of Tsinghua University The Centre of research and protection for relics of the Tsinghua University has a collection of calculation table (suanbiao) dating from the Warring States Period. The book has 21 bamboo slips and is dated 2300 years from now. The whole table consists of 441 unit cells, in the form of 19 rows time 19 columns. 192 A Discussion on the Significance The right column and the upper column start from bottom to above and from left to right. It could be reads in order, from 12 to the cardinal number 1 to 9 and then all two-digit number. Their products were recorded at the intersection of the cells. Therefore, the table is a multiplication in the form of 9 times 9; the rest is the extension of the table.1 Wooden Book of 9 times 9 table, Qin Dynasty, unearthed in Liye Town, Hunan In the year 2002, a multiplication table made from wood2 dating from the Qin Dynasty in the form of 9 times 9 was unearthed from an old well in Liye Town of Hunan (湘西). There are in total 113 characters. Most of the bamboo slips of 9 times 9 multiplication table unearthed in 20th century were incomplete, and this table from the Qin Dynasty is a complete 9 times 9 table. Bamboo slip≪shu≫, QinDynasty, collection of Yuelu AcademyHunanUniversity In December 2007, The Yuelu Academy in Hunan University had purchased a batch of bamboo slips from the antiques market in Hong Kong. Those bamboo slips were examined by a group of experts and it was confirmed that these were dated from Qin Dynasty. We are most interested in that collection of slips under the name “Shu”(mathematics). At present, 236 bamboo slips in Shu has been arranged and numbered, with 18 pieces of them not in good conditions (without numbering). The better-preserved slips are about 27.5 cm in length and 0.5 to 0.6 cm in width. There are three braided rope at the upper, middle and lower part of each bamboo slip. “Shu” was printed at the back of bamboo slip numbered 0956, which make the name of the book.3 In the format of “Shu”, a complete problem (suan ti) generally consisted of four parts, conditions, questions, answers and method. Only a few of the problems was given a title. There are 19 exemplars of methods (shu) in the book. For example, “he fen shu” (xx) and pithy for multiplication. There are 34 bamboo slips with the record of ratio of volume and weight of grains and their rate of exchange. Another 3 bamboo slips recorded measurement and units. The content of≪shu≫ from Qin Dynasty included arithmetic operation of fractions, areas of fields, crop yield, ratios of grains and its rate of exchange, shuaifen, shaoguang, volume, ying bu zu, gougu, yingjun and zu wu quan etc.4 There was only one Gougu problem, and is in consistencewith the gougu geyuan in GouGuChapter in Jiuzhang Suanshu, with simple and unsophisticated wordings.5 Mathematical bamboo slip, Qin Dynasty, collection of the Beijing University In early 2010, a friend from Hong Kong donated a batch of bamboo slips to the Beijing University. Among these slips, there are in total 400 slips written with mathematics, a big proportion in this batch of slips. According to preliminary study, these mathematical bamboo slips is close to those bamboo slips Shu from Qin Dynasty by Yuelu Academy, Suanshu shu from Han Dynasty and the Jiuzhang Suanshu. 1Tsinghua’s new development of bamboo slip. “The recent development of the jian”, from the website of the Fudan University’s Research Centre of Unearthed Literature and Ancient Text: http://www.gwz.fudan.edu.cn/ShowPost.asp?ThreadID=3522, 2010-8-10 2HunanProvinceArchaeological ResearchOffice: Brief report ofHunanLong ShanLi YeWarring States Period – ancient city of Qin Dynasty, No.1 well excavation. “Wen Wu” vol. 1, 2003. 3Chen Songchang : Content summarization of the bamboo slips from Qin Dynasty in Yuelu Academy. “Wen Wu” vol. 3, 2009. 4Xiao Can, Zhu Hanmin: Major contents and historical value of the bamboo slips “shu” from Qin Dynasty in Yuelu Academy. “Research of Chinese History” vol. 3, 2009. 5Xiao Can, Zhu Hanmin: New evidence of gougu – related research of the bamboo slips “shu” from Qin Dynasty in Yuelu Academy. “Research of the history of natural science” Paper 29, vol 3, 2010.