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In particular arithmetic and geometric progressions are used in some of the problems. Direct proportion, inverse proportion and compound proportion are all studied. Here there are 20 problems which again involve proportion, many involving different sums given to or owed by officials of various different ranks. Many of the problems seem simple an excuse to give the reader practice at handling difficult calculations with fractions. The mathematics involves a study of proportion and percentages and introduces the rule of three for solving proportion problems. This chapter contains 46 problems concerning the exchange of goods, particularly the exchange rates among twenty different types of grains, beans, and seeds. This is discussed in detail in Liu Hui's biography. In Problem 32 an accurate approximation is given for π.
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The types of shapes for which the area is calculated include triangles, rectangles, circles, trapeziums. It then proceeds to further area problems which do not use the material on fractions which appears somewhat misplaced. The Euclidean algorithm method for finding the greatest common divisor of two numbers is given. It looks first at area problems, then looks at rules for the addition, subtraction, multiplication and division of fractions. This consists of 38 problems on land surveying. Let us now give a short description of each of the nine chapters of the book.Ĭhapter 1: Land Surveying.
#Math illustrations help with formulas how to
For example in Chemla shows that Chinese mathematicians certainly understood how to give convincing arguments that their methodology for solving particular problems was correct.
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Recent work has begun to correct this false impression and understand that there are different understandings of "proof". This however is simply an example of historians well versed in mathematics which is essentially derived from Greek mathematics, thinking that Chinese mathematics was inferior since it was different. Failure to see similar rigorous proofs in Chinese works such as the Nine Chapters on the Mathematical Art led to historians believing that the Chinese gave formulas without justification. It is well known what that Euclid, for example, gives rigorous proofs of his results. There is one major difference which we must examine right at the start of this article and this is the concept of proof. It has played a fundamental role in the development of mathematics in China, not dissimilar to the role of Euclid's Elements in the mathematics which developed from the foundations set up by the ancient Greeks. The Jiuzhang suanshu or Nine Chapters on the Mathematical Art is a practical handbook of mathematics consisting of 246 problems intended to provide methods to be used to solve everyday problems of engineering, surveying, trade, and taxation.