iCHSTM 2013 Programme • Version 5.3.6, 27 July 2013 • ONLINE (includes late changes)
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The Tsinghua multiplication table
Feng Lisheng | Tsinghua University, China
Xu Yibao | Borough of Manhattan Community College, The City University of New York, United States

In July of 2008 an alumnus of Tsinghua University in Beijing donated 2,388 bamboo strips, along with some wooden tablets, to his alma mater. These bamboo strips, presumably stolen by robbers from an ancient tomb somewhere in mainland China, were smuggled to Hong Kong where they were sold through an antiques dealer. These bamboo strips are very important documents. A substantial number of these bamboo strips concern Chinese classics and history, but a tiny portion, 21 strips in all, are about mathematics. When put together, they form a perfect and complete multiplication table. This presentation discusses the structure of the Tsinghua multiplication table, and shows how it may be used to multiply a two-digit number by another two-digit number, and even two-digit mixed numbers with one-half by another mixed two-digit number and one-half. The table may also be used to carry out divisions and even the extraction of square roots of certain numbers. The Tsinghua multiplication table is sophisticated—it not only provides solid evidence that the Chinese had a decimal place value system at least as early as the Warring States period (475‒221 BCE), but it also indicates that mathematics had been well developed in China by the third century BCE.