Chinese

An analysis of early Chinese mathematics has demonstrated论证、说明 its unique development compared to other parts of the world, leading scholars to assume an entirely independent development. The oldest extant mathematical text from China is the Zhoubi Suanjing, variously dated to between 1200 BC and 100 BC, though a date of about 300 BC during the Warring States Period战国时期 appears reasonable. However, the Tsinghua Bamboo Slips竹简, containing the earliest known decimal multiplication table十进制乘法表 (although ancient Babylonians had ones with a base of 60), is dated around 305 BC and is perhaps the oldest surviving mathematical text of China.

Of particular note is尤其值得注意的是 the use in Chinese mathematics of a decimal positional notation system, the socalled "rod竿、棒 numerals" in which distinct ciphers were used for numbers between 1 and 10, and additional ciphers for powers of ten. Thus, the number 123 would be written using the symbol for "1", followed by the symbol for "100", then the symbol for "2" followed by the symbol for "10", followed by the symbol for "3". This was the most advanced number system in the world at the time, apparently in use several centuries before the common era时代 and well before the development of the Indian numeral system. Rod numerals allowed the representation of numbers as large as desired and allowed calculations to be carried out on the suan pan, or Chinese abacus算盘. The date of the invention of the suan pan is not certain, but the earliest written mention dates from AD 190, in Xu Yue's Supplementary增补地 Notes on the Art of Figures.

The oldest existent work on geometry in China comes from the philosophical Mohist墨家的 canon准则、经典 c. 330 BC, compiled by the followers of Mozi (470–390 BC). The Mo Jing described various aspects of many fields associated with physical science, and provided a small number of geometrical theorems as well. It also defined the concepts of circumference周长, diameter直径, radius半径, and volume.

In 212 BC, the Emperor Qin Shi Huang commanded all books in the Qin Empire other than officially sanctioned许可 ones be burned. This decree法令 was not universally obeyed, but as a consequence of this order little is known about ancient Chinese mathematics before this date. After the book burning of 212 BC, the Han dynasty (202 BC–220 AD) produced works of mathematics which presumably很可能 expanded on works that are now lost. The most important of these is The Nine Chapters on the Mathematical Art, the full title of which appeared by AD 179, but existed in part under other titles beforehand. It consists of 246 word problems involving agriculture, business, employment of geometry to figure height spans范围、跨度 and dimension尺寸、规模 ratios比例 for Chinese pagoda佛塔 towers, engineering, surveying, and includes material on right triangles. It created mathematical proof for the Pythagorean theorem, and a mathematical formula公式 for Gaussian高斯 elimination消去、淘汰（高斯消元法）. The treatise also provides values of π, which Chinese mathematicians originally approximated as 3 until Liu Xin (d. 23 AD) provided a figure of 3.1457 and subsequently后来 Zhang Heng (78–139) approximated pi as 3.1724, as well as 3.162 by taking the square root of 10. Liu Hui commented on the Nine Chapters in the 3rd century AD and gave a value of π accurate to 5 decimal places小数位 (i.e. 3.14159). Though more of a matter of computational stamina计算耐力 than theoretical insight洞察力, in the 5th century AD Zu Chongzhi computed the value of π to seven decimal places (i.e. 3.141592), which remained the most accurate value of π for almost the next 1000 years. He also established创立 a method which would later be called Cavalieri's principle卡瓦列里原理 to find the volume of a sphere.球体

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来源： https://www.cnblogs.com/valar-morghulis/p/13697352.html