History of mathematics in China

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History of mathematics in China

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Abstract

"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.

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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[...] 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 was solved using science and mathematics, including the construction of canals, dams . According to legend, a mythological Emperor Yu received a divine gift from a Lo river tortoise. [...]

[...] For example would be written as: 2 1000 + 3 10 Complements - The linear units of measure were as follows (they were deduced from natural things or from the sizes of human body): 1 zhang = height of human 1 bu = 2 kui (very widespread) 1 kui = step of human 1 foot (in English) 30 cm hu = thickness' thread produced by the silkworm - The notion of fraction was widespread, it was associated with the notion of division: form: x fen zhi y corresponds to the numerator = and y to the denominator = remarkable terms: = half in English) 1/3 = shao ban 1/2 = zhong ban 2/3 = tai ban 1/4 = ruo ban When they don't obtain exact results, the Chinese express them in the form: A + a'/a is a whole number) - decimal numbers: the only sign used ( ) played the role of our current decimal point) examples: was written as: would appear as: - positive and negative numbers: in fact, the Chinese used little negative numbers (only for intermediate calculations), because mathematics helped them to solve problems of everyday life or some concrete situations. [...]

[...] 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. Of course, the dating using units of length is not conclusive. Consider the fact that Britain changed to a decimal currency in 1970. [...]

[...] Notions of limits and infinitesimals appear in this chapter. Liu Hui whose commentary of 263 AD has become part of the text attempts to find the volume of a sphere. gives an approximate formula which he shows to be incorrect, then charmingly writes:- Let us leave the problem to whoever can tell the truth. Chapter Civil Engineering. Here there are 28 problems on the construction of canals, ditches, dykes, etc. Volumes of solids such as prisms, pyramids, tetrahedrons, wedges, cylinders and truncated cones are calculated. [...]

[...] 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. This leads to an interesting question which historians have as yet no convincing answer, namely were the European formulas taken directly from those of China. Liu Hui Born: about 220 in Wei, China Died: about 280 in China Liu Hui lived in the Kingdom of Wei so it is likely that he worked in what is now the Shansi province in north-central China. [...]

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