11/23/2023 0 Comments Ancient chinese abacus factsThey also started to pursue more abstract mathematical problems (although usually couched in rather artificial practical terms), including what has become known as the Chinese Remainder Theorem. The Chinese went on to solve far more complex equations using far larger numbers than those outlined in the “Nine Chapters”, though. By an approximation using a regular polygon with 192 sides, he also formulated an algorithm which calculated the value of π as 3.14159 (correct to five decimal places), as well as developing a very early form of both integral and differential calculus. It was particularly important as a guide to how to solve equations – the deduction of an unknown number from other known information – using a sophisticated matrix-based method which did not appear in the West until Carl Friedrich Gauss re-discovered it at the beginning of the 19th Century (and which is now known as Gaussian elimination).Īmong the greatest mathematicians of ancient China was Liu Hui, who produced a detailed commentary on the “Nine Chapters” in 263 CE, was one of the first mathematicians known to leave roots unevaluated, giving more exact results instead of approximations. A textbook called “Jiuzhang Suanshu” or “ Nine Chapters on the Mathematical Art” (written over a period of time from about 200 BCE onwards, probably by a variety of authors) became an important tool in the education of such a civil service, covering hundreds of problems in practical areas such as trade, taxation, engineering and the payment of wages. Early Chinese Method of Solving EquationsĮarly Chinese method of solving equationsīut the main thrust of Chinese mathematics developed in response to the empire’s growing need for mathematically competent administrators. But soon, bigger magic squares were being constructed, with even greater magical and mathematical powers, culminating in the elaborate magic squares, circles and triangles of Yang Hui in the 13th Century (Yang Hui also produced a triangular representation of binomial coefficients identical to the later Pascals’ Triangle, and was perhaps the first to use decimal fractions in the modern form). The Lo Shu Square, an order three square where each row, column and diagonal adds up to 15, is perhaps the earliest of these, dating back to around 650 BCE (the legend of Emperor Yu’s discovery of the square on the back of a turtle is set as taking place in about 2800 BCE). In particular, magic squares – squares of numbers where each row, column and diagonal added up to the same total – were regarded as having great spiritual and religious significance. There was a pervasive fascination with numbers and mathematical patterns in ancient China, and different numbers were believed to have cosmic significance. Lo Shu magic square, with its traditional graphical representation ![]() The use of the abacus is often thought of as a Chinese idea, although some type of abacus was in use in Mesopotamia, Egypt and Greece, probably much earlier than in China (the first Chinese abacus, or “suanpan”, we know of dates to about the 2nd Century BCE). ![]() This was largely because there was no concept or symbol of zero, and it had the effect of limiting the usefulness of the written number in Chinese. ![]() Written numbers, however, employed the slightly less efficient system of using a different symbol for tens, hundreds, thousands, etc. It was, therefore, a decimal place value system, very similar to the one we use today – indeed it was the first such number system, adopted by the Chinese over a thousand years before it was adopted in the West – and it made even quite complex calculations very quick and easy. The simple but efficient ancient Chinese numbering system, which dates back to at least the 2nd millennium BCE, used small bamboo rods arranged to represent the numbers 1 to 9, which were then places in columns representing units, tens, hundreds, thousands, etc. Even as mathematical developments in the ancient Greek world were beginning to falter during the final centuries BCE, the burgeoning trade empire of China was leading Chinese mathematics to ever greater heights.
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