1. Chinese Mathematics: Rebecca And Tommy ch'in chiushao is a thirteenth century Chinese sage who around 1247 AD composed the nine sections of mathematics. He also developed a scheme for the solution of numerical equations. http://www.roma.unisa.edu.au/07305/chin.htm

Ch'in Chiu-Shao Ch'in Chiu-Shao is a thirteenth century Chinese sage who around 1247 AD composed the nine sections of mathematics. He also developed a scheme for the solution of numerical equations. In 1913, in his book titled 'The Development in Mathematics in China and Japan', Yoshio Mikam published a simplification of Ch'in Chiu-Shao process. The process is summed up, below in table, using the equation:- If we solve this as a quadratic, we find four real approximate roots:- x = + or - 76, x = + or - 265 For some reason Ch'in Chiu-Shao takes his first approximation 800 to solve this equation (as seen in the table below). This solution in the table needs to be read up from the bottom. Root x x Absolute x x x 1st degree x x x x 2nd degree x x x x x 3rd degree 4th degree select here for the timeline of events select here to return to the Chinese home page

2. Ch'in ch'in chiushao. ch'in chiu-shao was a genius in mathematics and was also accomplishedin poetry, fencing, archery, riding, music and architecture. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Ch'in.html

Ch'in Chiu-Shao Born: 1202 in Szechwan (now Sichuan), China Died: 1261 in Kwangtung, China Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ch'in Chiu-Shao was a genius in mathematics and was also accomplished in poetry, fencing, archery, riding, music and architecture. He wrote Mathematical Treatise in Nine Sections which appeared in 1247. It contains simultaneous integer congruences, the Chinese Remainder Theorem, and considers algebraic equations, areas of geometrical figures and linear simultaneous equations. This work on congruences was rediscovered by Gauss Lebesgue and Stieltjes Article by: J J O'Connor and E F Robertson List of References (3 books/articles) Mathematicians born in the same country Cross-references to History Topics A history of Zero Other references in MacTutor Chronology: 1100 to 1300 Honours awarded to Ch'in Chiu-Shao (Click a link below for the full list of mathematicians honoured in this way) Lunar features Crater Kuo Shou Ching Other Web sites Simon Fraser University Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index History Topics Societies, honours, etc.

3. Ch'in Biography of ch'in chiushao (1202-1261) ch'in chiu-shao. Born 1202 in Szechwan (now Sichuan), China http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Ch%27in.html

Ch'in Chiu-Shao Born: 1202 in Szechwan (now Sichuan), China Died: 1261 in Kwangtung, China Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Ch'in Chiu-Shao was a genius in mathematics and was also accomplished in poetry, fencing, archery, riding, music and architecture. He wrote Mathematical Treatise in Nine Sections which appeared in 1247. It contains simultaneous integer congruences, the Chinese Remainder Theorem, and considers algebraic equations, areas of geometrical figures and linear simultaneous equations. This work on congruences was rediscovered by Gauss Lebesgue and Stieltjes Article by: J J O'Connor and E F Robertson List of References (3 books/articles) Mathematicians born in the same country Cross-references to History Topics A history of Zero Other references in MacTutor Chronology: 1100 to 1300 Honours awarded to Ch'in Chiu-Shao (Click a link below for the full list of mathematicians honoured in this way) Lunar features Crater Kuo Shou Ching Other Web sites Simon Fraser University Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index History Topics Societies, honours, etc.

4. References For Ch'in References for ch'in chiushao. VK Zharov, On two problems in the treatise 'Ninebooks on mathematics' by Ch'in Chiu Shao (Russian), Istor.-Mat. Issled. http://www-gap.dcs.st-and.ac.uk/~history/References/Ch'in.html

References for Ch'in Chiu-Shao Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles: Y Mikami, The development of mathematics in China and Japan (Leipzig-New York, 1913), 63-78. V K Zharov, On two problems in the treatise 'Nine books on mathematics' by Ch'in Chiu Shao (Russian), Istor.-Mat. Issled. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Ch'in.html

5. Ch'in Chiu-shao To Christian Of Brunswick. Alphabetic Index To Entries. The Colu 2001. Ch’in Chiushao to Christian of Brunswick. Ch’in Chiu-shao. Chinchón,Luis Jerónimo Fernández de Cabrera Bobadilla Cerda y Mendoza, conde de. http://www.bartleby.com/65/index51.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. chinchona Chindaswinth Chindwinn Chinese ... Chinook, indigenous people of North America

6. Ch'in Chiu-shao To Christian Of Brunswick. Alphabetic Index To Entries. The Colu ch'in chiushao to Christian of Brunswick. Alphabetic Index to Entries. The Columbia Encyclopedia, Sixth Edition. 2001 http://www.bartelby.com/65/index51.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. chinchona Chindaswinth Chindwinn Chinese ... Chinook, indigenous people of North America

7. Ch'in Chiu-shao. The Columbia Encyclopedia, Sixth Edition. 2001 The Columbia Encyclopedia, Sixth Edition. 2001. Ch’in Chiushao.(ch n chy -shou) (KEY) , c.1202–1261, Chinese mathematician. http://www.bartleby.com/65/ch/Chinchiu.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. (ch n chy -shou) ( KEY Mathematical Treatise in Nine Sections CONTENTS INDEX GUIDE BIBLIOGRAPHIC RECORD ... NEXT Search Amazon: Click here to shop the Bartleby Bookstore Welcome Press Advertising ... Bartleby.com

8. Ch'in Chiu-shao. The Columbia Encyclopedia, Sixth Edition. 2001 Chin Chiushao. (ch n chy -shou) (KEY) , c.12021261, Chinese mathematician. http://www.bartelby.com/65/ch/Chinchiu.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia World Factbook Columbia Gazetteer American Heritage Coll. Dictionary Roget's Thesauri Roget's II: Thesaurus Roget's Int'l Thesaurus Quotations Bartlett's Quotations Columbia Quotations Simpson's Quotations English Usage Modern Usage American English Fowler's King's English Strunk's Style Mencken's Language Cambridge History The King James Bible Oxford Shakespeare Gray's Anatomy Farmer's Cookbook Post's Etiquette Bulfinch's Mythology Frazer's Golden Bough All Verse Anthologies Dickinson, E. Eliot, T.S. Frost, R. Hopkins, G.M. Keats, J. Lawrence, D.H. Masters, E.L. Sandburg, C. Sassoon, S. Whitman, W. Wordsworth, W. Yeats, W.B. All Nonfiction Harvard Classics American Essays Einstein's Relativity Grant, U.S. Roosevelt, T. Wells's History Presidential Inaugurals All Fiction Shelf of Fiction Ghost Stories Short Stories Shaw, G.B. Stein, G. Stevenson, R.L. Wells, H.G. Reference Columbia Encyclopedia PREVIOUS NEXT ... BIBLIOGRAPHIC RECORD The Columbia Encyclopedia, Sixth Edition. (ch n chy -shou) ( KEY Mathematical Treatise in Nine Sections CONTENTS INDEX GUIDE BIBLIOGRAPHIC RECORD ... NEXT Search Amazon: Click here to shop the Bartleby Bookstore Welcome Press Advertising ... Bartleby.com

9. Ch'in Chiu-shao ch'in chiushao , c. 1202 1261 , Chinese mathematician. http://infoplease.lycos.com/ce6/people/A0811903.html

Educational GamesTeachers ZoneNutritionHouse Works ... Body Works All Infoplease All Almanacs General Entertainment Sports Biographies Dictionary Encyclopedia AlmanacsAtlasDictionaryEncyclopedia ... Encyclopedia Ch'in Chiu-shao [chin chy OO -shou] Pronunciation Key Ch'in Chiu-shao c. 1202 , Chinese mathematician. He pioneered in the study of indeterminate analysis in his Mathematical Treatise in Nine Sections of 1247. The text existed only in manuscript form for several centuries and still has not been fully translated or investigated. Like many traditional Chinese mathematical works, it reflects a Confucian administrator's concern with calendrical, mensural, and fiscal problems. chinchilla Infoplease HomeDaily AlmanacWorldSports ... Business Development Your use of this website constitutes acceptance of the Lycos Network and Entertainment Family Zone Reference Family Zone Recipes/Entertaining Grandparents Gardening ... Health Books

10. 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

11. Ch'in Chiu-shao Gherman Alexeyvich Komlev ch'in chiushao. Artist Gherman Alexeyvich Komlev http://kids.infoplease.lycos.com/ce6/people/A0811903.html

Search For: Lycos Zone Home Family Zone Teachers Zone Encyclopedia Ch'in Chiu-shao [chin chy OO -shou] Pronunciation Key Ch'in Chiu-shao c. 1202 , Chinese mathematician. He pioneered in the study of indeterminate analysis in his Mathematical Treatise in Nine Sections of 1247. The text existed only in manuscript form for several centuries and still has not been fully translated or investigated. Like many traditional Chinese mathematical works, it reflects a Confucian administrator's concern with calendrical, mensural, and fiscal problems. chinchilla Awards and Press Citing Fact Monster Lycos Worldwide Lycos Zone Privacy Statement

12. Ch'in Chiu-shao encyclopediaEncyclopedia ch'in chiushao, chin chyOO-shou PronunciationKey. ch'in chiu-shao , c. 1202–1261, Chinese mathematician. http://www.factmonster.com/ce6/people/A0811903.html

Encyclopedia Ch'in Chiu-shao [chin chy OO -shou] Pronunciation Key Ch'in Chiu-shao c. 1202 , Chinese mathematician. He pioneered in the study of indeterminate analysis in his Mathematical Treatise in Nine Sections of 1247. The text existed only in manuscript form for several centuries and still has not been fully translated or investigated. Like many traditional Chinese mathematical works, it reflects a Confucian administrator's concern with calendrical, mensural, and fiscal problems. chinchilla AD AD AD AD AD Print this page Cite this page Awards and Press Link to Fact Monster Add Fact Monster search ... Privacy

13. References For Ch'in References for ch'in chiushao. Biography in Dictionary of Scientific Biography (New York 1970-1990). http://www-gap.dcs.st-and.ac.uk/~history/References/Ch%27in.html

References for Ch'in Chiu-Shao Biography in Dictionary of Scientific Biography (New York 1970-1990). Articles: Y Mikami, The development of mathematics in China and Japan (Leipzig-New York, 1913), 63-78. V K Zharov, On two problems in the treatise 'Nine books on mathematics' by Ch'in Chiu Shao (Russian), Istor.-Mat. Issled. Main index Birthplace Maps Biographies Index History Topics ... Anniversaries for the year JOC/EFR December 1996 School of Mathematics and Statistics University of St Andrews, Scotland The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/References/Ch'in.html

14. Ch'in Chiu-shao encyclopediaEncyclopedia ch'in chiushao, chin chyOO-shou PronunciationKey. ch'in chiu-shao , c. 1202–1261, Chinese mathematician. http://print.factmonster.com/ce6/people/A0811903.html

15. Ch'in Chiu-shao ch'in chiushao. c.1202-1261, Chinese mathematician. He pioneered in the study ofindeterminate analysis in his Mathematical Treatise in Nine Sections of 1247. http://www.slider.com/enc/11000/Ch'in_chiu-shao.htm

Hour Glass Home Encyclopeadia C Cau - Cen ... Rope Ladders Trellian WebPage Slider Search: The Web Encyclopaedia Shopping Index Help Encyclopaedia Ch'in chiu-shao c.1202-1261, Chinese mathematician. He pioneered in the study of indeterminate analysis in his Mathematical Treatise in Nine Sections of 1247. The text existed only in manuscript form for several centuries and still has not been fully translated or investigated. Like many traditional Chinese mathematical works, it reflects a Confucian administrator's concern with calendrical, mensural, and fiscal problems. Add URL Advertise Contact Us

16. Cen - Cha Ceylon Ceylon gooseberry, Cezanne, Paul Cf cgs system Ch'an Buddhism Ch'angchouCh'i-ch'i-ha-erh Ch'it'ai Ch'ien-lung Ch'ien-tang Ch'in ch'in chiu-shao Ch'in http://www.slider.com/enc/c_10.htm

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17. Chinese Remainder Theorem - Wikipedia The original form of the theorem, contained in a book by the Chinese mathematicianch'in chiushao published in 1247, is a statement about simultaneous http://www.wikipedia.org/wiki/Chinese_Remainder_Theorem

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help Chinese remainder theorem (Redirected from Chinese Remainder Theorem The Chinese remainder theorem is the name applied to a number of related results in abstract algebra and number theory Simultaneous congruences of integers The original form of the theorem, contained in a book by the Chinese mathematician Ch'in Chiu-Shao published in , is a statement about simultaneous congruences (see modular arithmetic ). Suppose n n k are positive integers which are pairwise coprime (meaning gcd n i n j ) = 1 whenever i j ). Then, for any given integers a a k , there exists an integer x solving the system of simultaneous congruences x a i mod n i ) for i k Furthermore, all solutions

18. 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)

19. Elementary Number Theory - Kenneth H. Rosen Chinese Remainder Theorem) Page 144 Biographical information about ch'in chiushaocan be found at the MacTutor History of Mathematics Archive at http//www http://www.aw.com/rosen/resourcesc_4.html

Annotated Web Links CHAPTER 4 Congruences Return to Annotated Web Links Home 4.1 Introduction to Congruences Page 127 Modular arithmetic is discussed at the Cut-the-Knot site at http://www.cut-the-knot.com/blue/Modulo.html (Modular Arithmetic) Biographical information about Karl Friedrich Gauss can be found at the MacTutor History of Mathematics Archive at http://www-groups.dcs.st-andrews.ac.uk/~history/Mathematicians/Gauss.html (Gauss) Page 134 You can find source code for a C program implementing the algorithm for modular exponentiation by repeated squaring and multiplying at http://www.mindspring.com/~pate/crypto/chap02.html 4.2 Linear Congruences Page 139 You can find an approach for solving linear congruences at http://www.unc.edu/~rowlett/Math81/notes/Oct06.html (linear congruences) Page 140 You can find source code for a C program that computes modular inverses at http://www.mindspring.com/~pate/crypto/chap02.html

20. 1Up Info > Ch'in Chiu-shao (Mathematics, Biographies) - Encyclopedia You are here 1Up Info Encyclopedia Mathematics, Biographies Ch'inChiushao. 1Up Info - A Portal with a Difference. ch'in chiu-shao. http://www.1upinfo.com/encyclopedia/C/Chinchiu.html

You are here 1Up Info Encyclopedia Mathematics, Biographies Ch'in Chiu-shao ... News Search 1Up Info ENCYCLOPEDIA Mathematics, Biographies Ch'in Chiu-shao Related Category: Mathematics, Biographies Ch'in Chiu-shao [ch n chy -shou] Pronunciation Key Mathematical Treatise in Nine Sections of 1247. The text existed only in manuscript form for several centuries and still has not been fully translated or investigated. Like many traditional Chinese mathematical works, it reflects a Confucian administrator's concern with calendrical, mensural, and fiscal problems. Related Resources and Utilities AMAZON All Products Books Magazines Popular Music Classical Music Video DVD Electronics Software Outdoor Living Wireless Phones Computers Outlet Read articles on eLibrary: Encyclopedia Topics History People Places Content on this web site is provided for informational purposes only. We accept no responsibility for any loss, injury or inconvenience sustained by any person resulting from information published on this site. We encourage you to verify any critical information with the relevant authorities. Home Contact Us Privacy Links Directory ©1Up Info

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