History of mathematics in China

David B.

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History of mathematics in China

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Résumé
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"Chinese mathematics" was defined by Chinese in ancient times as the "art of calculation". This art was both a practical and a spiritual one. Like in Europe, many traces of calculations and solutions of equations were found by archaeologists. Today, these archaeological discoveries enable us to assert that Chinese civilization was very advanced compared to the other civilizations in the field of mathematics. But how did Chinese mathematics evolve through the centuries and on which concepts and discoveries were they precursor of modern mathematics? These numerical inscriptions contained both tally and code symbols which were based on a decimal system and they employed a positional value system. This proves that the Chinese were among the first civilizations to understand and efficiently use a decimal numeration system. Moreover, the ancient Chinese civilization was the first to discover many mathematical concepts, such as the pi number (π), the existence of zero, the magic squares or the Pascal's triangle. All these discoveries, which nowadays constitute the fundamental bases of arithmetics, were discovered centuries later in Occident. Then, during the 1st century A.D., the Chinese worked out the most famous of the mathematical treaties of ancient China, the "Jiuzhang Suanshu". This treaty, also called "Arithmetic in Nine Sections", is the most well-known and influential Chinese mathematical text.

Sommaire

Introduction.
Brief history.
The Chinese counting system.
1. Origins.
2. Schemes of notation.
3. Rod numeral system.
4. Traditional system (still used nowadays).
5. Complements.
Instruments to calculate.
1. Chinese counting boards.
2. The abacus.
The Chinese discoveries.
1. Computation of Pi.
2. Magic squares.
3. Pascal's triangle.
Chinese problems.
1. The broken bamboo problem.
2. The hundred fowl problem.
3. The rice problem.
Nine chapters on the mathematical art.
1. Land surveying.
2. Millet and rice.
3. Distribution by proportion.
4. Short width.
5. Civil engineering.
6. Fair distribution of goods.
7. Excess and deficit.
8. Calculation by square tables.
9. Right angled triangles.
Liu Hui.
Conclusion.

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Extraits

[...] In Problem 32 an accurate approximation is given for p. This is discussed in detail in Liu Hui's biography. Chapter Millet and Rice. This chapter contains 46 problems concerning the exchange of goods, particularly the exchange rates among twenty different types of grains, beans, and seeds. The mathematics involves a study of proportion and percentages and introduces the rule of three for solving proportion problems. Many of the problems seem simple an excuse to give the reader practice at handling difficult calculations with fractions. [...]

[...] has dominated the history of Chinese mathematics. It served as a textbook not only in China but also in neighbouring countries and regions until western science was introduced from the Far East around 1600 AD. Now although European science does not appear to have reached China in sixteenth century, it has been pointed out that a number of mathematical formulas and rules which were widely used in Europe during that century are essentially identical to formulas written down in the Nine Chapters on the Mathematical Art. [...]

[...] Perhaps the most important is to examine the units of length, volume and weight which appear in the various problems. Standard decimal units of length were established in China around 200 BC and later further subdivisions occurred. That the basic units are used, but not the later subdivisions, leads to a date of shortly after 200 BC. In Liu Hui's commentary subdivisions introduced around 250 AD are used, which is in line with this commentary being written in 263 AD. [...]

[...] The numeration system used in the modern world had its origins 34 centuries ago in Shang China. However, mathematics in China began much earlier in the development of the Chinese calendar, flood-control measures, administration, and so on. The need to control the flood-prone rivers of China, such as the Yangtze and Yellow Rivers, was an important factor in the development of mathematics in ancient China. The problem of providing a safe environment in a water-dependent society were solved using science and mathematics, including the construction of canals, dams . [...]

[...] 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. There is one major difference which we must examine right at the start of this article and this is the concept of proof. It is well known what that Euclid, for example, gives rigorous proofs of his results. 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. [...]

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