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Topic: Qin Jiushao

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	Technique of Finding One. (Site not responding. Last check: 2007-10-10)
		Qin jiushao described this method using counting board (rod numerals) diagrams.
		Using his counting board as reference, Qin jiushao started by placing 65 in the upper right of the counting board with four squares, 83 in the lower right, 1 at the upper left and nothing in the lower left.
		He then proceeded as follows, quoting Qin jiushao, "first divide right bottom by right top, multiply the quotient obtained by the top left and [add it to] the bottom left, [at the same time replacing the bottom right by the remainder of the division].
	www.brunssum.net /~joshua/China/Mathematics/history/Finding1.htm (288 words)

	Qin_Jiushao biography
		Qin Jiushao, also known as Ch'in Chiu-Shao, was born at the time of the Nan (Southern) Sung dynasty.
		By 1233 Qin was himself the sheriff of a subprefecture in Szechwan province and at this time he was instructed in writing poetry by an official from Chengdu, in central Szechwan province.
		It is recorded that Qin cheated his friend Wu Qian so that he became the owner of some of his land, and also that Qin punished a female member of his household by confining her without food.
	www-groups.dcs.st-and.ac.uk /~history/Biographies/Qin_Jiushao.html (1995 words)

	Qin Jiushao (Site not responding. Last check: 2007-10-10)
		Qin Jiushao's literary name was Daogu and was born in Sichuan in 1202.
		Qin Jiushao was reputed to be extremely clever, and skilful in astronomy, the theory of music, mathematics, and architecture by his contemporaries.
		Later, Qin served the government in several offices but because he was boastful, obsessed with his own advancement, extravagant and corrupted, so he was several times relieved off his duties.
	www.math.sfu.ca /histmath/China/13thCenturyAD/Qin.html (243 words)

	The Ta-Yen Rule
		The Ta-Yen rule is a method created by a man named Qin Jiushao to solve simultaneous linear congruences (indeterminate analysis).
		Qin Jiushao provided us with quite a detailed procedure for doing this.
		In order to reduce the moduli m1, m2, m3,..., mn to ones that are relatively primed to each other, we have to first find the least common multiple of them.
	www.brunssum.net /~/joshua/China/Mathematics/history/Ta-Yen.htm (633 words)

	Re: Chinese rod numerals
		The historian of science George Sarton characterised one of these, Qin Jiushao, as "one of the greatest mathematicians...
		Qin developed methods for solving problems which would in western terms involve equations of up to the power 10.
		131,132) reproduces pages from the work of two of Qin's contemporaries in which rod numerals appear in the text: the second example is particularly striking as showing a sequence of normal written characters with the rod numerals used as ordinary numbers.
	www.mail-archive.com /unicode@unicode.org/msg21554.html (1020 words)

	[No title]
		Qin Jiushao (c. 1202—1261) of China published this solution in 1247; the theorem’s name honors his accomplishment.
		You can find Qin’s solution in section 6.3.2 of A History of Mathematics 2e by Victor J. Katz, which also shows Qin’s attractive counting board implementation of the Euclidean Algorithm.
		We will see the CRT for the integers (where Qin solved it), but it holds in a much broader algebraic setting.
	www.math.utk.edu /~rdavis/Math504/Lecture12.doc (1120 words)

	Qin Jiushao and Ta-Yen rule (Site not responding. Last check: 2007-10-10)
		It was in 1247 that a general method for solving systems of linear congruences was discovered by a man named Qin Jiushao (1202 - 1261).
		He authored a book called Shushu jiuzhang translated to Mathematical Treatise in Nine Sections which contains this general rule.
		Qin Jiushao named this general rule the Ta-Yen Rule.
	www.math.sfu.ca /histmath/China/13thCenturyAD/QinTa.html (61 words)

	Bibliography of History of Science From 1900
		"Qin Jiushao Cewang Jiuwen Zaoshu Zhi Shentao" `ãèî‘ª—]ã—â‘¢p”V[“¢ (Studies of Qin Jiushao's Nine Surveying Questions) in pp.290-303 of Qian Baocong, 1964b.
		"Qin Jiushao Shi Ruhe Dechu Qiu Dingshu Fangfa De" `ãèî¥”@½“¾o’è”•û—@“I (How were the Methods of Finding Dingshu Obtained by Qin Jiushao).
		"Qin Jiushao Qiu 'Dingshu' Fangfa De Chengjiu He Que xian" `ãèî’è”•û—@“I¬Aaã× (Achievements and Deficiencies in Qin Jiushao's Methods of Finding Dingshu (Modulus)).
	www2.nkfust.edu.tw /~jochi/bib2.htm (2673 words)

	The science of mathematics is looked at with such importance in China that it is considered one of the six basic arts
		It was not until the thirteenth century A.D. when a man named Qin Jiushao began to represent this blank space with ‘0’(Reserve reading).
		Even without a number to represent the absence of a place value calculations were beginning to be worked out thanks largely in part to the invention of counting rods.
		A widely excepted theory is that the text was a long work in progress and compiles the mathematical knowledge of many from the Zhou, Qin, and Han periods.
	mcel.pacificu.edu /as/students/math/math.htm (2360 words)

	Chinese History - Song Dynasty å®, Liao é¼, Jin é‘, Western Xia è¥¿å¤ science, technology, and ...
		Qin Guan ç§¦è§ wrote the first Chinese book about breeding silkworms: Canshu è ¶æ¸ "Silkworm Book".
		The most important Song mathematicians were Jia Xian è³æ², Shen Kua æ²æ¬, Qin Jiushao ç§¦ä¹é¶ (wrote Shushu jiuzhang æ•¸æ¸ä¹ç« "A Mathematical Book in Nine Chapters"), and Yang Hui æ¥è¼.
		Jia Xian invented a numerical solution of equations by using a method similar to the Pascal triangle.
	www.chinaknowledge.de /History/Song/song-tech.html (5262 words)

	Qin Jiushao - MSN Encarta
		Qin Jiushao (1202?-1261?), Chinese mathematician, born in Sichuan.
		Qin's fame rests on one great book, Mathematical Treatise in Nine Sections (1247)....
		Become a subscriber today and gain access to:
	encarta.msn.com /encyclopedia_761579457/Qin_Jiushao.html (39 words)

	Chinese Mathematics : Rebecca And Tommy
		It was not until 1247 that Qin Jiushao (c 1202-1261) published a general method for solving systems of linear congruence's in his book called 'Shushu jiuzhang (Mathematical Treatise in Nine Sections)' (Katz, 1992, p188).
		A book clearly influenced by the old chiu chang suan shu, as were a majority of Chinese mathematical works.
		NOTE: This method was taken from Katz (1992) but written in my own words which I believe to be easier to understand.
	www.roma.unisa.edu.au /07305/remain.htm (529 words)

	Financial Cryptography: How the Chinese avoided insider fraud for over a millenium - The Chinese Remainder Theorem
		The statement of the theorem is that up to the product of all the moduli, the remainders are unique.
		Also, Qin Jiushao provided an algorithm for finding the number given the remainders.
		In his original example, he would make his two disciples measure the distance between his home and a river by holding hands and stepping together, one counting 23, the other counting 17.
	www.financialcryptography.com /mt/archives/000623.html (1152 words)

	Amazon.fr : The History Of Mathematics: From Mesopotamia to Modernity: Livres en anglais: Luke Howard Hodgkin (Site not responding. Last check: 2007-10-10)
		Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics.
		The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwasizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields.
		An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.
	www.amazon.fr /History-Mathematics-Mesopotamia-Modernity/dp/0198529376 (373 words)

	Qin - reviewed, comprehensive listings
		Qin Jiushao 1202 - 1261 Full MacTutor biography [Version for printing] List of References (16 books/articles) Mathematicians born in the same country Other Web sites Previous (Alphabetically) Next Biographies index JOC/EFR © December 2003 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/Mathematicians/Qin_Jiushao.html
		University of Cambridge / Mathematics / Statistical Laboratory / People / Li Qin Li Qin Li Qin Email address: L.G.Qin@statslab.cam.ac.uk Go to Statistical Laboratory Members.
		Pei Qin in Dept of Engineering Science, University of Oxford
	www.chinainformation.co.uk /qin/index.shtml (230 words)

	Men of Mathematics
		After the Nazi’s assumed power, Hilbert saw Gottingen lose its prominence.
		Qin Jiushao (1202-1261 CE) Chinese: Specialty: Generalist, Astronomy
		He grew up in the midst of the war under which Genghis Khan conquered much of Northern China.
	www.olypen.com /chinook/new_page_7.htm (3260 words)

	Web-and-Flow Hotlist: Biography of a Mathematician (Site not responding. Last check: 2007-10-10)
		Learn what important contribution this person made to the field of mathematics.
		Agnesi, Einstein, Archimedes, Aristarchus, Aristotle, Aryabhata, Bernoulli, Boethius, Brahe, Cantor, Copernicus, Descartes, Eratosthenes, Erdos, Escher, Euclid, Euler, Fermat, Feynman, Fibonacci, Galileo, Hawking, Hipparchus, Hippocrates, Hubble, Hypatia, Kepler, Khayyam, Koch, Mandelbrot, Mercator, Mobius, Ohm, Pascal, Peano, Plato, Ptolemy, Pythagoras, Qin Jiushao, Sierpinski, Venn, Yang Hui.
		Write a 3-5 page paper, double-spaced, presenting what you discover.
	www.web-and-flow.com /members/mdriscol/folder21/hotlist.htm (111 words)

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