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Mathematics in China emerged independently by the 11th century BC.〔(Chinese overview )〕 The Chinese independently developed very large and negative numbers, decimals, a place value decimal system, a binary system, algebra, geometry, and trigonometry. Knowledge of Chinese mathematics before 254 BC is somewhat fragmentary, and even after this date the manuscript traditions are obscure. Dates centuries before the classical period are generally considered conjectural by Chinese scholars unless accompanied by verified archaeological evidence, in a direct analogue with the situation in the Far West. Neither Western nor Chinese archaeological findings comparable to those for Babylonia or Egypt are known. As in other early societies the focus was on astronomy in order to perfect the agricultural calendar, and other practical tasks, and not on establishing formal systems. Ancient Chinese mathematicians did not develop an axiomatic approach, but made advances in algorithm development and algebra. While the Greek mathematics declined in the west during the mediaeval times, the achievement of Chinese algebra reached its zenith in the 13th century, when Zhu Shijie invented the method of four unknowns. As a result of obvious linguistic and geographic barriers, as well as content, Chinese mathematics and the mathematics of the ancient Mediterranean world are presumed to have developed more or less independently up to the time when ''The Nine Chapters on the Mathematical Art'' reached its final form, while the ''Writings on Reckoning'' and ''Huainanzi'' are roughly contemporary with classical Greek mathematics. Some exchange of ideas across Asia through known cultural exchanges from at least Roman times is likely. Frequently, elements of the mathematics of early societies correspond to rudimentary results found later in branches of modern mathematics such as geometry or number theory. The Pythagorean theorem for example, has been attested to the time of the Duke of Zhou. Knowledge of Pascal's triangle has also been shown to have existed in China centuries before Pascal,〔(Frank J. Swetz and T. I. Kao: Was Pythagoras Chinese? )〕 such as by Shen Kuo. == Early Chinese mathematics == Simple mathematics on Oracle bone script date back to the Shang Dynasty (1600–1050 BC). One of the oldest surviving mathematical works is the ''Yi Jing'', which greatly influenced written literature during the Zhou Dynasty (1050–256 BC). For mathematics, the book included a sophisticated use of hexagrams. Leibniz pointed out, the I Ching contained elements of binary numbers. Since the Shang period, the Chinese had already fully developed a decimal system. Since early times, Chinese understood basic arithmetic (which dominated far eastern history), algebra, equations, and negative numbers with counting rods. Although the Chinese were more focused on arithmetic and advanced algebra for astronomical uses, they were also the first to develop negative numbers, algebraic geometry (only Chinese geometry) and the usage of decimals. Math was one of the ''Liù Yì'' (六艺) or ''Six Arts'', students were required to master during the Zhou Dynasty (1122–256 BC). Learning them all perfectly was required to be a perfect gentleman, or in the Chinese sense, a "Renaissance Man". Six Arts have their roots in the Confucian philosophy. The oldest existent work on geometry in China comes from the philosophical Mohist canon of 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 wealth of information on mathematics as well. It provided an 'atomic' definition of the geometric point, stating that a line is separated into parts, and the part which has no remaining parts (i.e. cannot be divided into smaller parts) and thus forms the extreme end of a line is a point.〔Needham, Volume 3, 91.〕 Much like Euclid's first and third definitions and Plato's 'beginning of a line', the ''Mo Jing'' stated that "a point may stand at the end (of a line) or at its beginning like a head-presentation in childbirth. (As to its invisibility) there is nothing similar to it."〔Needham, Volume 3, 92.〕 Similar to the atomists of Democritus, the ''Mo Jing'' stated that a point is the smallest unit, and cannot be cut in half, since 'nothing' cannot be halved.〔 It stated that two lines of equal length will always finish at the same place,〔 while providing definitions for the ''comparison of lengths'' and for ''parallels'',〔Needham, Volume 3, 92-93.〕 along with principles of space and bounded space.〔Needham, Volume 3, 93.〕 It also described the fact that planes without the quality of thickness cannot be piled up since they cannot mutually touch.〔Needham, Volume 3, 93-94.〕 The book provided word recognition for circumference, diameter, and radius, along with the definition of volume.〔Needham, Volume 3, 94.〕 The history of mathematical development lacks some evidence. There are still debates about certain mathematical classics. For example, the ''Zhou Bi Suan Jing'' dates around 1200–1000 BC, yet many scholars believed it was written between 300–250 BC. The ''Zhou Bi Suan Jing'' contains an in-depth proof of the ''Gougu Theorem '' (a special case of the Pythagorean Theorem) but focuses more on astronomical calculations. The abacus was first mentioned in the second century BC, alongside 'calculation with rods' (''suan zi'') in which small bamboo sticks are placed in successive squares of a checkerboard. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Chinese mathematics」の詳細全文を読む スポンサード リンク
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