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- Sommaire
- Extraits
- Descriptif
- À propos de l'auteur
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Publiez vos documents !History of mathematics in China
Résumé de l'exposé
?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 (?), 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 de l'exposé
- Introduction.
- Brief history.
- The Chinese counting system.
- Origins.
- Schemes of notation.
- Rod numeral system.
- Traditional system (still used nowadays).
- Complements.
- Instruments to calculate.
- Chinese counting boards.
- The abacus.
- The Chinese discoveries.
- Computation of Pi.
- Magic squares.
- Pascal's triangle.
- Chinese problems.
- The broken bamboo problem.
- The hundred fowl problem.
- The rice problem.
- Nine chapters on the mathematical art.
- Land surveying.
- Millet and rice.
- Distribution by proportion.
- Short width.
- Civil engineering.
- Fair distribution of goods.
- Excess and deficit.
- Calculation by square tables.
- Right angled triangles.
- Liu Hui.
- Conclusion.
Extraits de l'exposé
[...] 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. [...]
[...] Liu Hui wrote a commentary on the Nine Chapters on the Mathematical Art in 263 AD. He believed that the text which he was commentating on was originally written around 1000 BC but incorporated much material from later eras. He wrote in the Preface:- In the past, the tyrant Qin burnt written documents, which led to the destruction of classical knowledge. Later, Zhang Cang, Marquis of Peiping and Geng Shouchang, Vice-President of the Ministry of Agriculture, both became famous through their talent for calculation. [...]
[...] These first eleven problems involve unit fractions are all of the following type, where n = 12: Suppose a field has width 1/2 + 1/3 + . + 1/n. What must its length be if its area is Problems 12 to 18 involve the extraction of square roots, and the remaining problems involve the extraction of cube roots. 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. [...]
[...] Open the first canal and the cistern fills in 1/3 day; with the second, it fills in 1 day; with the third, in 21/2 days; with the fourth, in 3 days, and with the fifth in 5 days. If all the canals are opened, how long will it take to fill the cistern? [Answer: 15/74 of a day] Chapter Excess and Deficit. The 20 problems give a rule of double false position. Essentially linear equations are solved by making two guesses at the solution, then computing the correct answer from the two errors. For example to solve ax + b = c we try x = and instead of we get c + d. [...]
À propos de l'auteur
David B.Etudiant- Niveau
- Grand public
- Etude suivie
- sciences...
- Ecole, université
- IEP...
Descriptif de l'exposé
- Date de publication
- 2006-04-29
- Date de mise à jour
- 2006-04-29
- Langue
- anglais
- Format
- Word
- Type
- dissertation
- Nombre de pages
- 24 pages
- Niveau
- grand public
- Téléchargé
- 1 fois
- Validé par
- le comité de lecture