4. Qin Jiushao (c. 1202–1261) was the first to introducethe zero symbol into Chinese mathematics. Before thisinnovation, blank spaces were used instead of zeros inthe system of counting rods. One of the most importantcontribution of Qin Jiushao was his method of solvinghigh order numerical equations. Referring to Qinssolution of a 4th order equation, Yoshio Mikami put it:"Who can deny the fact of Horners illustrious processbeing used in China at least nearly six long centuriesearlier than in Europe?" Qin also solved a 10th orderequation. 24.05.2012 4
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6. Mathematics in China emerged independently by the11th century BC. The Chinese independently developedvery large and negative numbers, decimals, a place valuedecimal system, a binarysystem, algebra, geometry, and trigonometry. Knowledgeof Chinese mathematics before 254 BC is somewhatfragmentary, and even after this date the manuscripttraditions are obscure. Dates centuries before theclassical period are generally considered conjectural byChinese scholars unless accompanied by verifiedarchaeological evidence, not just in mathematics, in adirect analogue with the situation in the Far West.Neither Western nor Chinese archaeological findingscomparable to those for Babylonia or Egypt are known. 24.05.2012 6
7. As in other early societies the focus wason astronomy in order to perfect theagricultural calendar, and other practical tasks, andnot on establishing formal systems. Axiomic proof wasthe strength of ancient Greek mathematician; ancientChinese mathematicians excelled at place valuedecimal device computation, algorithm developmentand algebra, the weakness of their Greekcounterparts. The algorithm and algebra tradition ofancient Chinese together with the axiomic deductionof Greece formed the two equally important pillars ofworld mathematics. While the Greek mathematicsdeclined in the west during the mediaval times, theachievement of Chinese algebra reached its zenithduring the same period. 24.05.2012 7
8. 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.24.05.2012 8
9. Suan shu shuThe Suàn shù shū (writings on reckoning) is an ancient Chinese text onmathematics approximately seven thousand characters inlength, written on 190 bamboo strips. It was discovered together withother writings in 1984 when archaeologists opened a tomb atZhangjiashan in Hubei province. From documentary evidence this tomb is known to have been closed in186 BC, early in the Western Han dynasty. While its relationship tothe Nine Chapters is still under discussion by scholars, some of itscontents are clearly paralleled there.The text of the Suan shu shu is however much less systematic thanthe Nine Chapters, and appears to consist of a number of more or lessindependent short sections of text drawn from a number of sources.Some linguistic hints point back to the Qin dynasty. 24.05.2012 9
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12. In the third century Liu Hui wrote his commentary on theNine Chapters and also wrote Haidao suanjing which dealtwith using Pythagorean theorem (already known by the 9chapters), and triple, quadruple triangulation forsurveying; his accomplishment in the mathematicalsurveying exceeded those accomplished in the west by amillennium. He was the first Chinese mathematician tocalculate π=3.1416 with his π algorithm. He discoveredthe usage of Cavalieris principle to find an accurateformula for the volume of a cylinder, and also developedelements of the integral andthe differential calculus during the 3rd century CE. 24.05.2012 12
13. Four outstanding mathematiciansarose during the SongDynasty and YuanDynasty, particularly in the twelfthand thirteenth centuries:YangHui, Qin Jiushao, Li Zhi (LiYe), and Zhu Shijie. Yang Hui, QinJiushao, Zhu Shijie all usedthe Horner-Ruffini method sixhundred years earlier to solve certaintypes of simultaneousequations, roots, quadratic, cubic, andquartic equations. Yang Hui was alsothe first person in history to discoverand prove "Pascals Triangle", alongwith its binomial proof (although theearliest mention of the Pascalstriangle in China exists before theeleventh century AD). Li Zhi on theother hand, investigated on a form ofalgebraic geometry. 24.05.2012 13
14. Precious Mirror of the FourElementsSi-yüan yü-jian《四元玉鑒》, or Precious Mirror of theFour Elements, was writtenby Chu Shi-jie in 1303 AD and itmarks the peak in thedevelopment of Chinese algebra.The four elements, calledheaven, earth, man andmatter, represented the fourunknown quantities in hisalgebraic equations. The Ssy-yüanyü-chien deals with simultaneousequations and with equations ofdegrees as high as fourteen. Theauthor uses the method of fanfa, today called Hornersmethod, to solve these equations. 24.05.2012 14
15. However after the overthrow ofthe Yuan Dynasty China becamesuspicious of knowledge it used.The Ming Dynasty turned away frommath and physics in favorof botany and pharmacology.At this period, the abacus whichfirst appeared in Song dynasty nowovertook the counting rods andbecame the preferred computingdevice. Zhu Zaiyu, Prince ofZheng who invented the equaltemperament used 81 position abacusto calculate the square root andcubic root of 2 to 25 figureaccuracy. 24.05.2012 15
16. However, this switching from counting rods to abacus to gainspeed in calculation was at a high cost, causing the stagnationand decline of Chinese mathematics. The pattern rich layoutof counting rod numerals on counting board inspired manyChinese inventions in mathematics, such as cross multiplyprincipe of fractions, method for solving linear equations. Thepattern rich counting rods inspired Japanese mathematician toinvent the concept of matrix. In Ming dynasty, mathematicianswere fascinated with perfecting algorithms for abacus, manymathematical works devoted to abacus mathematics appearedin this period, at the expense of new ideas creation. 24.05.2012 16
17. Despite the achievements of Shen and Guos work intrigonometry, another substantial work in Chinesetrigonometry would not be published again until1607, with the dual publication of EuclidsElements by Chinese official and astronomer XuGuangqi (1562–1633) and the Italian Jesuit MatteoRicci (1552–1610).[43]A revival of math in China began in the late nineteenthcentury, when Joseph Edkins, Alexander Wylie and LiShanlan translated works on astronomy, algebra anddifferential-integral calculus into Chinese, publishedby London Missionary Press in Shanghai. 24.05.2012 17
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