In details

Oriental Mathematics (part 3)


The Chinese civilization, as well as the Indian civilization, are much older than the Greek and Roman civilizations, but no older than the Egyptian and Mesopotamian civilizations.

Historical context

Chinese civilization originated on the banks of the Yangtze and Yellow rivers. We can divide Chinese history into four major periods:

  • Ancient China (2000 BC - 600 BC)
  • Classical China (600 BC - 221 AD)
  • Imperial China (221 AD - 1911 AD)
  • Modern China (AD 1911 - today)

Although ancient China was ruled by Hsia, Shang, and Chou monarchies, royal power was in the hands of numerous small lords, rulers of small towns. This period was characterized by countless wars, population taxes and much poverty of the people.

During the classical period, the philosopher Confucius preached a total social and political restructuring. Confucius preached respect for the authorities, caring for poverty, humility, ethics on the part of rulers and not doing to others what we do not want them to do to us. Confucius could not in life get his ideas accepted by the aristocracy. In the same period Taoism was created by Chang Tzu (399 BC - 295 BC), who proclaimed an order in the universe and recommended peace and governmental benevolence. These concepts were created by virtue of your misrule and the misery of your subjects. In 200 BC the Han Dynasty created an empire that lasted until the end of classical China. This dynasty expanded the boundaries of China and adopted Confucianism as the official religion. Coming from India, Buddhism merged with Taoism and gained wide acceptance among the peasants.

In the imperial period, China was involved in various internal struggles. With the fall of the Han dynasty, you began to fight each other to exercise dominance in your regions. In 618 AD the Tang Dynasty unified China. After her followed the Sung and Yuan dynasties. These dynasties sponsored the arts and literature, thus creating the golden age. With this, China has reached great dimensions and much influence. The opening of Chinese trade with Europe is beginning to take place via the Middle East. Marco Polo's trips to Kublai Khan's court provided the first contact of Chinese civilization with the European market.

The Chinese empire lasted much longer than the Roman. It was only broken with the 1911 revolution. Importantly, unlike the Roman Empire, the Chinese emperors, especially Kublai Khan, produced a rich culture and a solid intellectual base. While Roman monarchs were generally illiterate military men, Chinese monarchs highly valued intellectuality. Because the Chinese were more interested in literature and art, Chinese mathematics and science lagged behind other subjects.

Mathematical Context

Historians find it very difficult to date mathematical documents from China. The oldest Chinese mathematics classic “Chou Pei Suang Ching” has a variation of almost a thousand years between its most likely writing dates. The biggest difficulty with dating this document is because it was written by several people at different times. Chou Pei indicates that in China geometry originated from measurement, as in Babylon, being an exercise in arithmetic or algebra. In this paper there are indications that the Chinese knew the Pythagorean theorem.

Another publication as old as Chou Pei is the math book "Chui Chang Suan Shu" (Nine chapters on the art of mathematics, circa 1200 BC). Among many subjects covered, attention is drawn to problems with land measurement, agriculture, societies, engineering, taxes, calculations, solutions of equations and properties of right triangles. At the same time the Greeks composed logically ordered treaties and systematically exposed. The Chinese followed the same Babylonian line, compiling collections with specific problems. Like the Egyptians, the Chinese alternated, in their experiments, precise and inaccurate, primitive and elaborate results. In this publication solutions of linear systems with positive and negative numbers appear.

Since the Chinese liked to solve systems, the diagrams were widely used by them. It is interesting to note that the magic square was first recorded by this people, even though its origin is older but unknown.

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Throughout its history, Chinese science has suffered from a number of problems that have prevented its continuity and improvement. In 213 a.c. The emperor of China had the existing books burned. Even if some copies were saved, the loss was irreparable. In the twentieth century, Mao-Tse-Tung, with his "Cultural Revolution" also promoted a widespread burning of books, considered "subversive".

There was probably cultural contact between India and China and between China and the West. Many say there was a Babylonian influence on Chinese mathematics, although China did not use sexagesimal fractions. The Chinese numbering system was decimal, but with different notations than those known at the time. They used the "bar" system (I, II, III, IIII, T). We cannot specify the age of this numbering system, but it is known to be prior to the positional notation system.

This bar notation was not simply used in calculating (writing) boards. Bamboo, ivory, or iron bars were carried in bags by the administrators for calculations to be made. This method was simpler and faster than the calculation performed with abacus, soroban or suan phan.

The Chinese knew the operations on common fractions using m.d.c. They worked with negative numbers through two bar collections (red for positive coefficients and black for negative ones), but they did not accept negative numbers as a solution to an equation.

Chinese mathematics is so different from the mathematics of other peoples at the same time that its development took place independently. Li Hui, in the third century, determined a value for Pi using first a regular 96-sided polygon (3,14) and then using a regular 3072-sided polygon (3.14159).

The highlight of Chinese mathematics occurred in the thirteenth century during the late Sung period. At this time the printing, the gunpowder, the paper and the compass were discovered. Chinese works of this time strongly influenced Korea and Japan. Many of these works disappeared from China in this period, reappearing only in the nineteenth century.

Yang Hui (1261 - 1275), talented mathematician worked with numerical series and presented a Chinese variation for the Pascal triangle.

From the Middle Ages in Europe it is well known that Chinese mathematics had no achievements compared to European and Near Eastern. Possibly China absorbed more math than it sent. Possibly the Chinese and Hindu sciences were influenced by one another during the first millennium of our era.

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