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Topic: The Nine Chapters on the Mathematical Art

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	Wikinfo \| Nine
		In probability, the nine is a logarithmic measure of probability of an event, defined as the negative of the base-10 logarithm of the probability of the event's complement.
		Nine babies born into a single birth are called nonuplets, although not one baby born into a set of nonuplets has ever survived infancy.
		Nine (九 pinyin jiu3) is considered a good number in Chinese culture because it sounds the same as the word "longlasting" (久 pinyin jiu3).
	www.wikinfo.org /wiki.php?title=nine (751 words)

	Qwika - similar:Zhu_Shijie
		The Nine Chapters on the Mathematical Art (九章算術) is a Chinese mathematics book, probably composed in the 1st century AD, but perhaps as early as 200 BC.
		Mathematics Portal Mathematics is often defined as the study of topics such as quantity, structure, space, and change.
		Mathematics, in nearly every society, is used in fields such as the natural sciences, eng...
	www.qwika.com /rels/Zhu_Shijie (1568 words)

	The science of mathematics is looked at with such importance in China that it is considered one of the six basic arts
		It is the importance that the Chinese place on mathematics that caused it to be one of the most influential cultures in the history of the world in terms of mathematical breakthroughs.
		Chapter five is the least accurate of the chapters due to a poor knowledge of the value of pi.
		The mathematical knowledge of the Chinese was so ahead of their time it is not surprising that scholars had a hard time believing it.
	mcel.pacificu.edu /as/students/math/math.htm (2360 words)

	Upto11.net - Artist Profile for The 9
		Perhaps Antonín Dvoand#345;ák was also superstitious about the number nine, because he wrote no symphonies after his New World Symphony, which is nowadays considered his Ninth, but which he thought was his Eighth because he considered the score of his early C minor Symphony lost forever.
		A polygon with nine sides is called an enneagon (technically) or nonagon (in common usage).
		Nine (and#20061; pinyin jiand#468;) is considered a good number in Chinese culture because it sounds the same as the word "longlasting" (and#20037; pinyin jiand#468;).
	www.upto11.net /artistprofile.php?ar=138850 (1126 words)

	Nine chapters
		The Jiuzhang suanshu or Nine Chapters on the Mathematical Art is a practical handbook of mathematics consisting of 246 problems intended to provide methods to be used to solve everyday problems of engineering, surveying, trade, and taxation.
		In this final chapter there are 24 problems which are all based on right angled triangles.
		The Nine Chapters on the Mathematical Art was certainly an important text, so may have had its units of length brought up to date as it evolved.
	www-groups.dcs.st-and.ac.uk /~history/HistTopics/Nine_chapters.html (2000 words)

	nine chapters
		The Jiuzhang suanshu or the Nine Chapters on Mathematical Art is the most famous Chinese mathematical text.
		It is not dissimilar to Euclid's Elements, which were written around 600 years before the Nine Chapters.
		Nine Chapters is an interesting work as it sums up the mathematical knowledge of China at the time when it was written.
	www.mathsisgoodforyou.com /artefacts/ninechapters.htm (384 words)

	Math Maze - Be Maze-merised - History of Math
		The Nine Chapters on the Mathematical Art is a Chinese mathematics book, believed to be written in the 1st century AD or even earlier.
		Nine Chapters on the Mathematics have had numerous achievements in Arithmetic, Geometry and Algebra.
		In the history of Arabic Mathematics, one of its greatest achievements is the introduction of "Arabic Numerals".
	library.thinkquest.org /05aug/01951/history.htm?country=babylonia (2564 words)

	sangaku math (Site not responding. Last check: 2007-10-19)
		Mathematics is called the "universal language" precisely because it deals with provable theorems that are not subject to interpretation.
		Mathematics is only considered "creative" at the cutting edge of knowledge and even that creativity is fleeting as hypotheses are proven and disproved.
		Mathematical theorems were no longer means to an end and "calculate the area of this circle" became as much of a spiritually enriching exercise as answering the Koan "what is the sound of one hand clapping", or trimming a bonsai tree.
	www.loyola.edu /maru/sangaku.html (5033 words)

	The Nine Chapters on the Mathematical Art - Wikipedia, the free encyclopedia
		It lays out an approach to mathematics that centres on finding the most general methods of solving problems, which may be contrasted with the approach common to ancient Greek mathematicians, who tended to deduce propositions from an initial set of axioms.
		Nevertheless we may note that the method of chapter 7 was not found in Europe until the 13th century, and the method of chapter 8 is not found before the sixteenth century.
		He analyses the procedures of the Nine Chapters step by step, in a manner which is clearly designed to give the reader confidence that they are reliable, although he is not concerned to provide formal proofs in the Euclidean manner.
	en.wikipedia.org /wiki/The_Nine_Chapters_on_the_Mathematical_Art (656 words)

	80.07.11: A Chronological History of ¹ with Developmental Activities in Problem Solving
		The scribe Ahmes assumed that the area of a circular field with a diameter of nine units is the same as the area of a square with a side of eight units.
		In the third century Liu Hui, an important commentator on the Nine Chapters, derived the figure 3.14 by use of a regular polygon of 96 sides and the approximation 3.14159 by considering a polygon of 3072 sides.
		In the Nine Chapters on the Mathematical Art, the area of the circle was found by taking three fourths the square on the diameter or onetwelfth the square of the circumference.
	www.yale.edu /ynhti/curriculum/units/1980/7/80.07.11.x.html (2706 words)

	The history of matrices
		In the treatise's seventh chapter, "Too much and not enough," the concept of a determinant first appears, nearly two millennia before its supposed invention by the Japanese mathematician Seki Kowa in 1683 or his German contemporary Gottfried Leibnitz (who is also credited with the invention of differential calculus, separately from but simultaneously with Isaac Newton).
		More uses of matrix-like arrangements of numbers appear in chapter eight, "Methods of rectangular arrays," in which a method is given for solving simultaneous equations using a counting board that is mathematically identical to the modern matrix method of solution outlined by Carl Friedrich Gauss (1777-1855), also known as Gaussian elimination.
		The elevation of the matrix from mere tool to important mathematical theory owes a lot to the work of female mathematician Olga Taussky Todd (1906-1995), who began by using matrices to analyze vibrations on airplanes during World War II and became the torchbearer for matrix theory.
	www.ualr.edu /lasmoller/matrices.html (470 words)

	Math 232 Linear Algebra Home Page (Site not responding. Last check: 2007-10-19)
		This perhaps was what great art was -- a momentary apprehension of the plane at a point in the line.
		Liu Hui, about 220 to 280 AD, known for his commentary on the Nine Chapters on the Mathematical Art, a practical handbook of mathematics written in China in 200 BC.
		One of the giants of mathematics, Gauss was said to be able to calculate before he could even talk.
	people.carleton.edu /~rdobrow/courses/232f06/home.html (221 words)

	China
		In 1261 Yang Hui wrote a Detailed analysis of the Nine Chapters on the Mathematical Art, the classical Chinese handbook of mathematics.
		Little is known about Zhang Qiujian, a learned teacher, except that he wrote a Mathematical Manual in which he outlined the calculation of square and cube roots, solving of equations and systems of equations, sum of arithmetic series, proportions and fractions, and geometry.
		K Takeda, The characteristics of Chinese mathematics in the Ming dynasty (Japanese), J.
	members.shaw.ca /rzamar/mathtrail/china.htm (872 words)

	Chinese mathematics
		Unlike the Greeks, Chinese developed their mathematics in relation to the problems of everyday life - their most famous work on mathematics Jiuzhang suanshu or Nine Chapters on the Mathematical Art is a tribute to this practical approach to mathematics in general.
		The oldest known, complete, Chinese mathematical text is a work on astronomy, which shows how to measure the positions of the heavenly bodies by using sun-dials of a kind.
		The mathematical syllabus that was the basis for the examination consisted of ten, now most famous, Chinese mathematical texts.
	www.mathsisgoodforyou.com /topicsPages/general/chinese.htm (233 words)

	Mathematical classics
		As a consequence Li Chunfeng together with Liang Shu, an expert in mathematics from the ministry of education, and Wang Zhenru, a teacher from the national university and others were ordered by imperial decree to annotate the ten mathematical texts such as the Wucao suanjing or the Sunzi suanjing.
		Perhaps the most important mathematics which is included in the Zhoubi suanjing is related to the Gougu rule, which is the Chinese version of the Pythagoras Theorem.
		This is a small work consisting of nine problems and it was originally written as part of his commentary on Chapter Nine of The Nine Chapters on the Mathematical Art but later removed and made into a separate work by Li Chunfeng and his colleagues during the creation of The Ten Mathematical Classics.
	www-history.mcs.st-andrews.ac.uk /HistTopics/Mathematical_classics.html (1884 words)

	Math 4312 (Site not responding. Last check: 2007-10-19)
		The Nine Chapters on the Mathematical Art, a compilation of practical problems and solutions, was used for centuries; over the centuries, commentaries were written to explain or derive rules.
		A new attitude toward mathematics appeared in Greece beginning in the 6th century BCE: it was no longer enough to calculate numerical answers; it was necessary to prove the results were correct.
		With their discovery of irrational numbers, they were forced to adjust their mathematical philosophy and this enabled Greeks to develop new theories.
	cms.dt.uh.edu /faculty/BecerraL/Spring2005/4312_calendar.htm (1728 words)

	History of Algebra
		China and the Nine Chapters of Mathematical Art
		The Nine Chapters of Mathematical Art was a recording of the development of early Chinese mathematics.
		It’s main purpose was, however, to present the knowledge acquired in the study of astronomy, so it wasn’t specific to mathematics.
	library.thinkquest.org /C0110248/algebra/history1.htm (535 words)

	History of mathematics - Gurupedia
		Also see The Nine Chapters on the Mathematical Art for information about the development of mathematics in China.
		The study of structure starts with numbers, firstly the familiar natural numbers and integers and their arithmetical operations, which are recorded in elementary algebra.
		Discrete mathematics is the common name for those fields of mathematics useful in computer science.
	www.gurupedia.com /h/hi/history_of_mathematics.htm (585 words)

	Mathematics - History and Culture
		The problems posed here often involve fundamental mathematical methods and notions, but their chief appeal is their capacity to tease and delight.
		The Nine Chapters was the standard mathematics textbook in China for about two thousand years.
		Unlike modern mathematics in which numbers and concepts are expressed in a universal mathematical notation, the numbers and concepts found in native cultures occur and are expressed in many distinctive ways.
	iweb.tntech.edu /AGutek/BOOKS/Math-History/history.htm (1384 words)

	Development of Math in China3
		However, there are several existing Chinese applied mathematics texts, which are collections of problems and solutions organized in chapters according to their practical applications.
		These texts proves that the Chinese were the first society to use some of the most basic and advanced mathematical principles and concepts utilized in modern times.
		The oldest existing Chinese texts containing formal mathematical theories were produced during the Han period.
	saxakali.com /COLOR_ASP/developcm3.htm (440 words)

	History of Mathematics: China (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-10-19)
		The Nine Chapters on the Mathematical Art (Jiuzhang Suanshu) (c.
		Originally appendix to commentary on Ch 9 of the Nine Chapters.
		Jiushang suanshu zhu (Commentary on the `Nine Chapters of the Mathematical Art')
	aleph0.clarku.edu.cob-web.org:8888 /~djoyce/mathhist/china.html (1907 words)

	Read This: Historical Modules for the Teaching and Learning of Mathematics
		By providing copious and relevant activities, students and teachers are invited into first-hand experiences of the mathematics of the past, enriching their standard work, and obtaining valuable motivation for some important ideas.
		After a tour of the development of algebraic notation in Egypt, China, India, and the Middle East, a review of proportions is presented as a discussion of problems from ancient texts — the Nine Chapters of the Mathematical Art, the Rhind Papyrus, Bhaskara's Lilavati, the Treviso Arithmetic and Euclid's Elements.
		Mathematics is much more than a technical and lifeless skill in calculation.
	www.maa.org /reviews/HistoricalModules.html (662 words)

	book title
		The nine chapters on the mathematical art is a classic text: the most important mathematical source in China during the past 2000 years, and comparable in significance to Euclid's Elements in the West.
		This volume contains the first complete English translation of the Nine Chapters, together with two commentaries written in the 3rd century (by Liu Hui) and 7th century AD, and a further commentary by the translators.
		Tony Lun is a Senior Lecturer in the Department of Mathematics and Statistics, Monash University, and has published many papers on general relativity.
	www.lib.monash.edu.au /collections/monash-authors/2000/0198539363.html (195 words)

	Amazon.com: The Nine Chapters on the Mathematical Art: Companion and Commentary: Books: Shen Kangshen,John N. ... (Site not responding. Last check: 2007-10-19)
		This volume contains the first complete English translation of the Nine Chapters, together with two commentaries written in the 3rd and 7th centuries AD, and a further commentary by the translators.
		The Nine Chapters contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs.
		The Nine Chapters quickly acquired a distinguished reputation, and was the standard mathematics textbook in China and the surrounding regions until Western science was introduced in about 1600.
	www.amazon.com.cob-web.org:8888 /Nine-Chapters-Mathematical-Art-Commentary/dp/0198539363 (846 words)

	No title
		Sample pages about the first problem of Chapter 8 (the one in my first lecture).
		Chapter IV (from finite to infinite dimensional “linear algebra”).
		These two chapters are about linear transformations in finite dimensional vector spaces.
	www.math.ucla.edu /~xinweiyu/115a.3.06s/index.html (496 words)

	UNT Libraries Recent Acquisitions (Site not responding. Last check: 2007-10-19)
		The nine chapters on the mathematical art : companion and commentary / Shen Kangsheng, John N. Crossley, Anthong W.-C. Lun.
		A contextual history of mathematics : to Euler / Ronald Calinger with the assistance of Joseph E. Brown and Thomas R. West.
		The mathematical analysis of logic : being an essay towards a calculus of deductive reasoning / George Boole ; with a new introduction byJohn Slater.
	www.library.unt.edu /newacqs/2000_03/math.htm (712 words)

	[No title]
		Through the course the students will be introduced to mathematical methods and algorithms used historically to solve financial problems, from Mesopotamian mathematical tablets to Chinese problems to medieval calculations to the mathematical advances of the enlightenment.
		Shen Kangshen, John N. Crossley, Anthony W. Lun, Nine Chapters on the Mathematical Arts, The Nine Chapters on the Mathematical Art : Companion and Commentary, selected problems for analysis.
		Reading G&R Chapter 2, 9 (Malmendier and Neal) Hansmann, Henry, Kraakman, Reinier H. and Squire, Richard C., "Law and the Rise of the Firm" (January 2006).
	www.library.yale.edu /eli/fall06/goetzmann/proposal.doc (2914 words)

	Liu Hui - Wikipedia, the free encyclopedia
		He estimated pi to 3.141014 with a 192 sided polygon and later calculated pi as 3.14159 by using a 3079 sided polygon.
		His estimation is made with a method similar to Archimedes.
		The Nine Chapters used the value 3 as π, but Zhang Heng had previously estimated it to the square root of 10;
	en.wikipedia.org /wiki/Liu_Hui (253 words)

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