21. Horner's Rule rule, the same rule was invented by Isaac Newton in 1669 and actually the first personto describe it was the Chinese mathematician Ch in chiushao in the 1200s http://www.fact-index.com/h/ho/horner_s_rule.html

Main Page See live article Alphabetical index Horner's rule When numerically computing values of polynomials, Horner's rule (or Horner's method Horner's Schema ) is one of the first basic computation rules one must learn. Assume you want to evaluate the value of a polynomial: You see that in order to carry out this evaluation for a given and given coefficients , you need to perform multiplications and additions, given that you preserve the powers of between the additions. (Else it will demand something like ( n n )/2 multiplications!) William George Horner observed in (columbi egg) that as additions are easier to perform than multiplications (especially if you want to compute this using a computer ), if you rewrite the polynomial evaluation as follows: then may be evaluated recursively using only multiplications and additions. This may be easily implemented in a computer program where a[] is a vector of the coefficients, with the most significant coefficient first, thusly (pseudo code): Historical Notice Even though William George Horner is credited with this rule, the same rule was invented by

22. Lexikon - Chinesischer Restsatz Definition Erklärung Bedeutung in chiu-shao aus dem Jahr 1247 ist eine Aussage über simultane http://www.net-lexikon.de/Chinesischer-Restsatz.html

Suche: Info Mitglied werden A B ... Impressum Beta 0.71 powered by: akademie.de Wikipedia PHP PostgreSQL ... englischen Lexikon Google News zum Stichwort Chinesischer Restsatz Definition, Bedeutung, Erkl¤rung im Lexikon Artikel auf Englisch: Chinese remainder theorem Chinesischer Restsatz ist der Name mehrerer ¤hnlicher Theorem e der abstrakten Algebra und Zahlentheorie Inhaltsverzeichnis 1 Simultane Kongruenzen ganzer Zahlen 1.1 Teilerfremde Moduln 1.2 Allgemeiner Fall 2 Aussage f¼r Hauptidealringe ... 3 Aussage f¼r allgemeine Ringe Simultane Kongruenzen ganzer Zahlen Eine simultane Kongruenz ganzer Zahlen ist ein System von linearen Kongruenzen f¼r die alle x bestimmt werden sollen, die s¤mtliche Kongruenzen gleichzeitig l¶sen. Wenn eine L¶sung x existiert, dann sind mit M := kgV( m m m m n ) die Zahlen x kM (k in Z ) genau alle L¶sungen. Es kann aber auch sein, dass es gar keine L¶sung gibt. Teilerfremde Moduln Die Originalform des Chinesischen Restsatzes aus einem Buch des chinesischen Mathematikers Ch'in Chiu-Shao aus dem Jahr ist eine Aussage ¼ber simultane Kongruenzen f¼r den Fall, dass die Moduln teilerfremd sind. Sie lautet:

23. FDC China 30f Ch'in Chiu-Shao FDC China 30f Ch in chiushao FDC. Ch in chiu-shao was born in Szechuan,China, in 1202 and died in Kwangtung, China, in 1261. During http://www.unicover.com/EA8RCUMN.HTM

FDC China 30f Ch'in Chiu-Shao Ch'in Chiu-Shao was born in Szechuan, China, in 1202 and died in Kwangtung, China, in 1261. During his lifetime, he made significant contributions to the field of mathematics. He was also accomplished in poetry, archery, fencing, riding, music and architecture. Among his many accomplishments, he wrote his celebrated mathematical treatise, "Shu-shu chiu-chang" or "Mathematical Treatise in Nine Sections," which appeared in 1247. Standard Number: None Stock Number (SKU): US$ Price: Information about Ordering: If you plan to order any of the above items you can do it any of three ways: Use Express Shopping : Simply click the "Add to Cart" Button for the item you want to order. This puts the item in your Express Shopping Cart, where you can change the quantity or remove it. When you've finished putting items in your Express Shopping Cart, Go to the Shopping Cart and choose your options from there. Use QuickNavigation. You'll want to be sure to write down the following "8-character Order Blank Code": BUTA-JS01 Also be sure to copy down the Stock Number (SKU) of each item you wish to order.

24. List Of Mathematicians - Wikipedia, The Free Encyclopedia 19, 1996); Shiingshen Chern (October 26, 1911 - ); Alexey Chervonenkis(Russia); Ch in chiu-shao (China, 1200s); Sarvadaman Chowla http://en.wikipedia.org/wiki/List_of_mathematicians

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25. List Of People By Name Ch - Wikipedia, The Free Encyclopedia cattle baron; Chiu, Alex, (born 1971), discoverer of immortality rings;chiushao, Ch in, mathematician. Chl-Chm. Chladni, Ernst, (1756 http://en.wikipedia.org/wiki/List_of_people_by_name:_Ch

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26. Cultural History Of East Asian Science, Technology, And Medicine Urlich Libbrecht, Chinese Mathematics in the Thirteenth Century, the ShuShuChiu-Chang of Ch in chiu-shao (Cambridge MIT Press, 1973), selections. http://uts.cc.utexas.edu/~rhart/courses-chicago/easci/

An Introduction to Sources in the History of East Asian Science, Technology, and Medicine HIST 150 / EALC 150 / HIPSS 292 / CHSS 390 Winter 2001 Tuesday, Thursday 1:30-2:50 p.m. Henry Hinds Laboratory for the Geophysical Sciences, Room 180 Roger Hart office: Social Sciences Research Building, Room 206 office hours: Tuesdays 3-6 p.m. Introduction Course Requirements Class attendance is mandatory. Students may choose one of the following two options: (1) Before the first class of each week write a brief summary of the primary and required secondary readings assigned for that week (but not the supplementary readings), to be sent to me by email by 10 p.m. Monday evening. Students should complete reading notes for nine of the ten weeks. Notes on the primary sources should summarize the material, usually in one paragraph. Notes on the secondary readings should usually be two short paragraphs one summarizing the central argument and one offering critical analysis. The reading notes should total 2 to 3 pages per week. These will be graded and will serve as the basis for class discussions. Grading: reading assignments 70%; class participation 30%. (2) Students interested in a particular topic should complete a final paper of 10 pp. for undergraduates and 20 pp. for graduate students. Students should consult me as early as possible on possible topics. An outline and bibliography are due by February 13; a first draft must be turned in by February 27; and the final draft is due March 8. Grading: final paper 70%; class participation 30%.

27. HPS 297 Syllabus Winter 97 Urlich Libbrecht, Chinese Mathematics in the Thirteenth Century, the ShuShuChiu-Chang of Ch in chiu-shao (Cambridge MIT Press, 1973), chaps. 1-2. http://uts.cc.utexas.edu/~rhart/courses-stanford/chinesescience/

A CULTURAL HISTORY OF CHINESE SCIENCE, TECHNOLOGY, AND MEDICINE History 297A / History 397A / HPS 297 Winter 1998 Undergraduate / Graduate Colloquium Wednesday 3:15-5:05 History Corner (Building 200), Room 230 Roger Hart Office: History Corner, Room 27 Office hours: T Th 2:00-3:00, and by appt. INTRODUCTION This course adopts an interdisciplinary approachdrawing on cultural history, anthropology, gender studies, and philosophyto the study of Chinese science, technology, and medicine analyzed in its intellectual, social, and cultural context. The course is designed for students interested in i) the history, philosophy and anthropology of science, technology, and medicine; ii) East Asian studies; iii) studies of 'non-Western' cultures. We will also critically assess the conclusions on 'culture' derived from the received historiography on Chinese science, and examine emerging trends in current research. Knowledge of Chinese is not required for the course. COURSE REQUIREMENTS i) Class attendance is mandatory. ii) Reading assignments: before class you must write a brief summary and critique of the readings, to be sent to me by email. Notes on each of the readings should usually be about two paragraphsone summarizing the central argument and one offering critical analysisfor a total of 2-5 pages per week. These will be graded (distinguished, satisfactory, or unsatisfactory) and will serve as the basis for class discussions. Students are encouraged to rewrite the assignments on the basis of our class discussions.

28. Math History - Middle Ages 1247, Ch in chiushao writes Mathematical Treatise in Nine Sections. It containssimultaneous integer congruences and the Chinese Remainder Theorem. http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MmiddleAges.htm

29. GIOVAROSI S FORMULA in chiu-shao riportatanel suo celebre trattato del 1247 Shu- shu chiu- chang (Trattato di http://utenti.lycos.it/sandro999/

...E QUANDO L'ULTIMO RAGGIO SI SPENSE DANDO LUOGO ALLE TENEBRE DELL'ETERNA NOTTE LA LUCE INTELLETTUALE INCOMINCIAVA A RIFULGERE.... EVOLUZIONE ARMONIOSAMENTE ALTERNANTE METODO "GENERALE" PER LA RISOLUZIONE DI TUTTE LE EQUAZIONI NUMERICHE Gioacchino Giovarosi Matematico cieco e violinista Dall’Ipsia De Amicis la verifica-conferma della “procedura generalizzata”per la risoluzione delle equazioni numeriche esposta dal prof. Sandro Stocchi. L'equazione di partenza di grado n (n può assumere qualsiasi valore: negativo o positivo, razionale, irrazionale o trascendente) si presenta nella forma "canonica" dell'equazione di Wang Hsiao-Thung (+VII sec.). tutte le equazioni possono"in generale" essere ricondotte alla forma canonica o "ideale" per l'applicazione della formula Giovarosi. Le due formule a confronto: quella del matematico cinese Ch'in Chiu-Shao riportata nel suo celebre trattato del 1247 "Shu- shu chiu- chang" (Trattato di Matematica in Nove Sezioni) e quella di Giovarosi (1939) presente nel suo lavoro "Complementi d'Algebra relativi alla risoluzione dell'equazione di ordine superiore". La formula generale per la risoluzione di tutte le equazioni numeriche ad una sola incognita Gioacchino Giovarosi GIOVAROSI La vita di un genio : Gioacchino Giovarosi nasce a Roma nel +1889 dove vive fino all’età di 20 anni. Cieco fin dalla nascita per una difterite oculare,studia alla scuola Sant’Alessio (zona Aventino), istituto per non vedenti dove impara anche a suonare il violino, a rilegare libri e a scrivere con il sistema Braille. Si trasferisce poi a Terni ,si sposa ed ha un figlio che mantiene sfruttando il suo talento di virtuoso del violino. In questo periodo della sua vita il Giovarosi veniva accompagnato ogni mattina sui ponti di questa città e qui mestamente iniziava a suonare il suo violino; ma certamente dal suo strumento di lavoro evolveVano al cielo note musicali armoniose che si alternavano a numeri celesti e a formule matematiche.

30. List Of Mathematicians - Reference Library 1933 1996); Shiing-shen Chern (October 26,1911 - ); Alexey Chervonenkis(Russia); Ch in chiu-shao (China, 1200s); Sarvadaman Chowla http://www.campusprogram.com/reference/en/wikipedia/l/li/list_of_mathematicians.

Reference Library: Encyclopedia Main Page See live article Alphabetical index List of mathematicians The famous mathematicians are listed below in English alphabetical transliteration order (by surname A B C ... Z A Niels Henrik Abel (Norway, Ralph H. Abraham (USA, University of California, Santa Cruz Wilhelm Ackermann (Germany, Maria Gaetana Agnesi (Italy, Lars Valerian Ahlfors , (Finland, Ahmes , (Egypt, roughly around 17th century BC Jean le Rond d'Alembert (France, Abu Ja'far Muhammad Ibn Musa Al-Khwarizmi (Persia, Alexander Anderson (Scotland, André-Marie Ampere , (France, Apollonius of Perga (Asia Minor, 265 B.C 170 B.C Archimedes (Syracuse, 287 B.C 212 B.C Aristotle (Greece, 384 B.C 322 B.C Vladimir Arnol'd (Russia, Emil Artin (Austria, Michael Francis Atiyah (Britain, B Charles Babbage (United Kingdom, John Baez Alan Baker (Britain, Stefan Banach (Poland, Grigory Isaakovich Barenblatt (Russia, USA, Isaac Barrow (England, Thomas Bayes (England, Eric Temple Bell (Scotland, USA, Jakob Bernoulli (Switzerland, Johann Bernoulli (Switzerland, Joseph Louis Francois Bertrand (France

31. Reading List On History Of Special Topics In Mathematics Medieval Mathematics. Ulrich Libbrecht, Chinese Mathematics in the Thirteenth CenturyThe Shushu chiu-chang of Ch in chiu-shao (Cambridge MIT Press, 1973). http://www.dean.usma.edu/math/people/rickey/hm/mini/bib-katz.html

Reading List on History of Special Topics in Mathematics Prepared by Victor Katz. Ancient Mathematics Otto Neugebauer, The Exact Sciences in Antiquity (Princeton: Princeton University Press, 1951) B. L. van der Waerden, Science Awakening I (New York: Oxford University Press, 1961) B. L. van der Waerden, Geometry and Algebra in Ancient Civilizations (New York: Springer, 1983) Richard J. Gillings, Mathematics in the Time of the Pharaohs (Cambridge: MIT Press, 1972) Li Yan and Du Shiran, Chinese Mathematics: A Concise History , translated by John N. Crossley and Anthony W. C. Lun (Oxford: Clarendon Press, 1987) B. Datta and A. N. Singh, History of Hindu Mathematics (Bombay: Asia Publishing House, 1961) (reprint of 1935-38 original) Denise Schmandt-Besserat, Before Writing: From Counting to Cuneiform (Austin: University of Texas Press, 1992) Greek Mathematics Thomas Heath, A History of Greek Mathematics (New York: Dover, 1981) (reprint of 1921 original) Wilbur Knorr, The Evolution of the Euclidean Elements (Dordrecht: Reidel, 1975)

32. HISTORIA MATHEMATICA VOLUME 2, PAGES 253424, AUGUST 1975 350353 Chinese Mathematics in the Thirteenth Century The ShuShuChiu-Chang of Ch in chiu-shao by Ulrich Libbrecht (Lam Lay Yong http://www.math.uu.nl/ichm/hm/02253424.html

Volume Index Previous VOLUME 2, PAGES 253424, AUGUST 1975 REVIEWS `Boethius' Geometrie II by Menso Folkerts (G. P. Matvievskaya) ............................................ 339341 Diderot by Arthur M. Wilson (Charles C. Gillispie) .......................................... 342344 Einstein. Zhizn, Smert, Bessmertie by B. G. Kuznetsov (Martin Dyck) ................................................... 344347 Women in Mathematics by Lynn M. Osen (Mary E. Williams) .............................................. 348349 Georgii Nikolaevich Nikoladze by A. N. Bogolyubov (Esther Portnoy) ..................................................... 349 Babbage, La Macchina Analitica by Mario G. Losano (Umberto Forti) ................................................. 350353 Chinese Mathematics in the Thirteenth Century: The Shu-Shu Chiu-Chang of Ch'in Chiu-Shao by Ulrich Libbrecht (Lam Lay Yong) .................................................. 353355 English-Greek Mathematical Dictionary by C. P. Tzelekis (S. P. Zervos) ....................................................... 355

33. Chinese Mathematicians: Rebecca And Tommy Diagram List. Diagram 1 Titled Ch in chiushao Source Coolidge, JL(1963) The mathematics of Great Amateurs, pg 194. Diagram 2 Titled http://www.roma.unisa.edu.au/07305/pict.htm

Diagram List Diagram 1 Titled: Ch'in Chiu-Shao Source: Coolidge, J.L. (1963) The mathematics of Great Amateurs , pg 194 Diagram 2 Titled: The 'Hsuan-thu' Source: Swetz, F.J. and Kao, T.I. (1977) Was Pythagoras Chinese , pg 14 Diagram 3 Titled: Pictorial Representation of Method 1 Source: Swetz, F.J. and Kao, T.I. (1977) Was Pythagoras Chinese , pg 27 Diagram 4 Titled: Pictorial Representation of Method 2 Source: Swetz, F.J. and Kao, T.I. (1977) Was Pythagoras Chinese , pg 27 Diagram 5 Titled: Pictorial Representation of Method 3 Source: Swetz, F.J. and Kao, T.I. (1977) Was Pythagoras Chinese , pg 28 Diagram 6 Titled: Zhu Shijiei triangle Source: Stillwell, J. (1989) Mathematics and its History , pg 137 Diagram 7 Titled: Lo Shu Source: Needham, J. (1959) Science and Civilization In China: Volume 3, Mathematics and the Sciences of the Heavens and Earth Diagram 8 Titled: Ho Thu Source: Needham, J. (1959) Science and Civilization In China: Volume 3, Mathematics and the Sciences of the Heavens and Earth Diagram 9 Titled: Modern Representation of Lo Shu Source: Needham, J. (1959)

34. Chinese Mathematics : Rebecca And Tommy Laws of signs (+1299); Ch in chiu-shao - solution of numeric equations; ZhuShijie - systems of equations; Horners method; Solution of polynomial equations. http://www.roma.unisa.edu.au/07305/timeline.htm

Time Line of Ancient Chinese Mathematics 2000 B.C. Magic squares discovered by Yu the Great 1000 - 500 B.C. Rod numerals Pythagoras theorem 300 - B.C. Square and cube roots Systems of linear equations Measurement of a circle Volume of a pyramid Chiu chang suah shu , most famous Chinese mathematical book Chou-pei, oldest of Chinese mathematical classics (300 B.C. ) 213 B.C. burning of related books and burial of protesting scholars Liu Hui - (263 - ?) mathematics of surveying Sun Zi - chinese remainder problem Zhang Quijian - hundred fowl problem Yi Xing - (683-727) first tangent table Jian Xian - pascal triangle Li Ye - (1192 - 1279) algebraic equations for geometry Qin Jiushao - (1202 - 1261) chinese remainder theorem (Ta-Yen) Yang Hui - (1270 - ?) first to study magic squares Laws of signs Ch'in Chiu-Shao - solution of numeric equations Zhu Shijie - systems of equations Horners method Solution of polynomial equations Counting rods Matteo Ricci - (1552 - 1610) entry of Western mathematics into China NOTE: This table was created through the cross referencing of all references select here to return to the Chinese home page

35. Full Alphabetical Index in chiu-shao (62) Ch http://alas.matf.bg.ac.yu/~mm97106/math/alphalist.htm

Full Alphabetical Index The number of words in the biography is given in brackets. A * indicates that there is a portrait. A Abbe , Ernst (602*) Abel , Niels Henrik (2899*) Abraham bar Hiyya (641) Abraham, Max Abu Kamil Shuja (1012) Abu Jafar Abu'l-Wafa al-Buzjani (1115) Ackermann , Wilhelm (205) Adams, John Couch Adams, J Frank Adelard of Bath (1008) Adler , August (114) Adrain , Robert (79*) Adrianus , Romanus (419) Aepinus , Franz (124) Agnesi , Maria (2018*) Ahlfors , Lars (725*) Ahmed ibn Yusuf (660) Ahmes Aida Yasuaki (696) Aiken , Howard (665*) Airy , George (313*) Aitken , Alec (825*) Ajima , Naonobu (144) Akhiezer , Naum Il'ich (248*) al-Baghdadi , Abu (947) al-Banna , al-Marrakushi (861) al-Battani , Abu Allah (1333*) al-Biruni , Abu Arrayhan (3002*) al-Farisi , Kamal (1102) al-Haitam , Abu Ali (2490*) al-Hasib Abu Kamil (1012) al-Haytham , Abu Ali (2490*) al-Jawhari , al-Abbas (627) al-Jayyani , Abu (892) al-Karaji , Abu (1789) al-Karkhi al-Kashi , Ghiyath (1725*) al-Khazin , Abu (1148) al-Khalili , Shams (677) al-Khayyami , Omar (2140*) al-Khwarizmi , Abu (2847*) al-Khujandi , Abu (713) al-Kindi , Abu (1151) al-Kuhi , Abu (1146) al-Maghribi , Muhyi (602) al-Mahani , Abu (507) al-Marrakushi , ibn al-Banna (12)

36. A Bibliographt Of Source Materials The Shushu chiu-chang of Ch in chiu-shao, Cambridge, MA MIT Press, 1973;Lebesque, H., Lecons sur l integration, Chelsea Publishing Company, 1974; http://www66.homepage.villanova.edu/thomas.bartlow/history/sourcebib.htm

History of Mathematics Bibliography of Source Materials Anthologies Baum, Robert J., Philosophy and Mathematics : From Plato to the Present , Freeman Cooper, 1973 Berrgren, Lennart, Borwein, Jonathan, and Borwein, Peter, Pi: A Source Book, Springer, 1997 Birkhoff, Garrett, ed., A Soucrebook in Classical Analysis , Cambridge: Harvard University Press, 1973 Calinger, Ronald, Classics in Mathematics , Englewood Cliffs, NJ: Prentice-Hall, Inc., 1995 Cohen, M. R. and I. E. Drabkin, A Source Book in Greek Science , New York: McGraw-Hill, 1948 Fauvel, John and Jeremy Gray, ed., The History of Mathematics: A Reader , London: Macmillan Press, 1987 Grant, Edward, A Source Book in Medieval Science , Cambridge, MA: Harvard U. Press Smith, David Eugene, ed., A Source Book in Mathematics , 2 vols., New York: Dover Publications, 1959 Struik, Dirk J., A Source Book in Mathematics, 12001800 , Princeton: Princeton University Press,1986 van Heijenoort, Jean, Frege and Godel: two fundamental texts in mathematical logic , Cambridge, MA: Harvard U. Press, 1970

37. ThinkQuest : Library : CultureQuest Ch in chiushao Culture Chinese Area of Study Mathematic Century 13 ContributionHe wrote Mathematical Treatise in nine sections treats equations of a http://library.thinkquest.org/C008444/pages/library/info/asian.html

Index Cultures CultureQuest CultureQuest is a site dedicated to educating people about the contributions of scientists of various cultures to the scientific community. It is does so in a way that is appealing to both adults and children, offering games, and recipes to make the learning process more interesting. It is available in 3 languages. Visit Site 2000 ThinkQuest Internet Challenge Languages French Spanish Students Micah Hill Regional Career High School, New Haven, CT, United States eric Hill Regional Career High School, Milford, CT, United States Julius Hill Regional Career High School, New Haven, CT, United States Coaches Linda Hill Regional Career High School, New Haven, CT, United States Phil Hill Regional Career High School, New Haven, CT, United States Want to build a ThinkQuest site? The ThinkQuest site above is one of thousands of educational web sites built by students from around the world. Click here to learn how you can build a ThinkQuest site. Privacy Policy

38. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï Tommaso Ceva Born 20 Dec 1648 in Milan, Italy Died 3 Feb 1737 in Milan, ItalyCh in, Ch in chiushao Born 1202 in Szechwan (now Sichuan), China Died 1261 http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=C

39. Milestones In MathematicsHistory 1, 1, 2, 3, 5, 8, 13 . . . 1247. Ch in chiushao (Chinese) gives numerical methodof solving equations. 1427. al-Kahi (Arabic) first uses decimal fractions. 1515. http://www.cs.wustl.edu/~qingfeng/misc/mathhist.html

Milestones in Mathematics History 20,000 BC Carved notches in wood represent numbers. 3500 BC Numbers based on place value (base 60) used in Sumeria. The Sumerians had no symbol for zero. They used an empty space to represent a zero in the middle of a number but had no way to represent zero on the end of a number. Thus they could distinguish 15 from 105 but could not tell 15 from 150. 2000 BC Mesopotamians solve quadratic equations. 1900 BC Egyptians apply basic geometry to solve practical problems. 1900 BC Pythagorean Theorem a + b = c discovered by Babylonians 1700 BC Babylonians find approximate value of r(2). But don't tell how they did it. 1700 BC A'hmosé (Egyptian) describes methods of mathematical problem solving. One of the earliest "textbooks." 547 BC Thales (Greek) introduces deductive proofs. 520 BC Pythagoras (Greek) founds brotherhood based on mathematics. 500 BC Greeks use abacus, the first mechanical calculating device (probably invented by Babylonians). 460 BC Zeno (Greek) devises paradoxes such as "Achilles and the Tortoise." Achilles and the Tortoise Achilles races a tortoise that has a head start. First, Achilles must run to the point where the tortoise started the race. While he does that, the tortoise moves a little farther. So Achilles must run to where the tortoise is now but again the tortoise moves a little farther. Since this can be repeated indefinitely, Achilles can never catch up to the tortoise.

40. List Of Mathematicians - Wikipedia, The Free Encyclopedia Chaitin (USA, ; Pafnuty Lvovich Chebyshev, (Russia, (May 16, 1821 December 8, 1894); Ch in chiu-shao (China, 1200s); Sarvadaman http://www.phatnav.com/wiki/wiki.phtml?title=List_of_mathematicians

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