1. 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

2. HighBeam Research: ELibrary Search: Results 3. CH IN chiushao The Columbia Encyclopedia, Sixth Edition; January 10, 2004CH IN chiu-shao Ch in chiu-shao , c.1202-1261, Chinese mathematician. http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_thesauru

3. HighBeam Research: ELibrary Search: Results 1. CH IN chiushao The Columbia Encyclopedia, Sixth Edition; January 10, 2004 CH IN CHIU- SHAO Ch in Chiu- shao , c.1202-1261, Chinese mathematician http://www.highbeam.com/library/search.asp?FN=AO&refid=ency_refd&search_thesauru

4. Qin_Jiushao Qin Jiushao, also known as Ch in chiushao, was born at the time ofthe Nan (Southern) Sung dynasty. His ancestors came from Lu-chun http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Qin_Jiushao.html

Qin Jiushao Born: 1202 in Puzhou (Anyue), Szechwan province, China Died: 1261 in Meizhou (now Meixian), Guangtong province, China Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Main index Qin Jiushao , also known as Ch'in Chiu-Shao , was born at the time of the Nan (Southern) Sung dynasty. His ancestors came from Lu-chun in Shantung province and some biographies quote this incorrectly as his birthplace. His father, Qin Jiuyu (or Ch'in Chiu-yu), was a graduate who worked as an official in local administration. In around 1219, when Qin was about seventeen years old, his father was working as a prefect of Bazhou. At this time Qin volunteered for the army, which was putting down a rebellion, and served for a while. Qin's father moved to Hang-chou, the capital of the Nan Sung, in around 1224 and Qin went with his father. He wrote in the preface to his famous work Shushu Jiuzhang (see for example [3]):- In my youth I was living in the capital, so that I was able to study in the Board of Astronomy; subsequently, I was instructed in mathematics by a recluse scholar. We know that Qin was a rebellious youth, famous for his many love affairs, who disliked authority [1]:-

5. Ch'in Chiu-Shao --  Encyclopædia Britannica Ch in chiushao Encyclopædia Britannica Article. MLA style Ch in chiu-shao. Encyclopædia Britannica. 2004. Encyclopædia Britannica Premium Service. http://www.britannica.com/eb/article?eu=2201

6. A-Z Browse Results - Encyclopædia Britannica te Ch engtu ch i Ch i Ch i Ju-shan Ch i-chia culture Ch i-lien Mountains ch i-linCh i-ying Ch iang-t ang Ch ien-lung Ch ih-feng ch in Ch in chiu-shao Ch in http://www.britannica.com/eb/alpha?search=Cez

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 Cultural Literacy 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 Respectfully Quoted 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 ... Click here to download the Dictionary and Thesaurus Search Amazon: Click here to shop the Bartleby Bookstore Welcome Press Advertising ... Bartleby.com

8. Children, Delinquent To Chorazin. Alphabetic Index To Entries. The Columbia Ency Chincha. chinch bug. chinchilla. Ch’in chiushao. Chinchón, Luis Jerónimo Fernándezde Cabrera Bobadilla Cerda y Mendoza, conde de. chinchona. Chindaswinth. http://www.bartleby.com/65/index51.html

Select Search All Bartleby.com All Reference Columbia Encyclopedia World History Encyclopedia Cultural Literacy 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 Respectfully Quoted 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. children, delinquent to Chorazin

9. Ch'in Chiu-shao encyclopediaEncyclopedia Ch in chiushao, chin chyOO-shou PronunciationKey. Related content from HighBeam Research on Ch in chiu-shao. http://www.infoplease.com/cgi-bin/id/A0811903.hmtl

HOTWORDS CITE PRINT EMAIL in All Infoplease Almanacs Biographies Dictionary Encyclopedia Home Almanacs Atlas Dictionary ... D-Day Infoplease Tools Periodic Table Conversion Tool Perpetual Calendar Year by Year ... Site Map Also from Infoplease Search Infoplease Info search tips Search Biographies Bio search tips 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. The Columbia Electronic Encyclopedia, chinchilla Related content from HighBeam Research on: Effect of antecedent soil water regime and rice straw application time on [CH.sub.4] emission from rice cultivation. (Australian Journal of Soil Research) MEDIA / Ch. 11 Hungrily Eyes Ch. 9's Mets

10. Ch'in Chiu-shao Site Map. encyclopediaEncyclopedia Ch in chiushao, chin chyOO-shou PronunciationKey. Ch in chiu-shao , c. 1202–1261, Chinese mathematician. http://www.factmonster.com/cgi-bin/id/A0811903.hmtl

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. The Columbia Electronic Encyclopedia, chinchilla Print this page Cite this page AD AD AD ADS Link to Fact Monster Add Fact Monster search to your site ... Privacy Brought to you by:

11. AllRefer Encyclopedia - Ch'in Chiu-shao (Mathematics, Biographies) - Encyclopedi Ch in chiushao, Mathematics, Biographies. Ch in chiu-shaochin chyOO-shouPronunciation Key, c.1202–1261, Chinese mathematician. http://reference.allrefer.com/encyclopedia/C/Chinchiu.html

AllRefer Channels :: Health Yellow Pages Reference Weather SEARCH : in Reference May 31, 2004 You are here : AllRefer.com Reference Encyclopedia Mathematics, Biographies ... Ch'in Chiu-shao By Alphabet : Encyclopedia A-Z C Ch'in Chiu-shao, Mathematics, Biographies Related Category: Mathematics, Biographies Ch'in Chiu-shao [chin chy OO -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. Encyclopedia U com Check out around 175,000 brief encyclopedia articles on almost all topics. Related Categories: People Science and Technology Science and Technology Mathematics ... Biographies More articles from AllRefer Reference on Ch'in Chiu-shao Encyclopedia U com Check out around 175,000 brief encyclopedia articles on almost all topics. 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. About Us Contact Us Privacy Links Directory ... Link to AllRefer.com

12. AllRefer Encyclopedia - Encyclopedia Topics C : Ches - Chm - Reference China grass • China Incident • china marks • Chinan • chinaware • Chincha• chinch bug • chinchilla • Ch in chiu-shao • Chinchon, Luis http://reference.allrefer.com/encyclopedia/topics-a-z/C6.html

AllRefer Channels :: Health Yellow Pages Reference Weather SEARCH : in Reference May 31, 2004 You are here : AllRefer.com Reference Encyclopedia Encyclopedia Topics A-Z ... com Check out around 175,000 brief encyclopedia articles on almost all topics. 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. About Us Contact Us Privacy Links Directory ... AllRefer.com

13. Apronyms: CH'IN CHIU SHAO Awfully Peculiar Racket Ordinary Names Yield Meanings, Surprisingly! APRONYM.100%, CH IN CHIU SHAO, Composed Haiku, Investigated Numbers Congruences. http://apronyms.com/gonym.php?ap=CH'IN CHIU SHAO

14. Apronyms: CH'IN CHIU SHAO Expansion. Composed Haiku, Investigated Numbers Congruences. His InterestingUnderstandings Stieltjes Has Afterwards Observed. Credit/Explanation. http://apronyms.com/cgi-bin/gonym?CH'IN CHIU SHAO&mode=onlinestack

15. 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://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/~DZ6B93.htm

Ch'in Chiu-Shao Born: 1202 in Szechwan (now Sichuan), China Died: 1261 in Kwangtung, China Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page 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 References (3 books/articles) References elsewhere in this archive: There is a Crater Kuo Shou Ching (possibly named after this mathematician) on the moon. You can see a list of lunar features named after mathematicians. Other Web sites: Simon Fraser, Canada Previous (Chronologically) Next Biographies Index Previous (Alphabetically) Next Welcome page History Topics Index Famous curves index ... Search Suggestions JOC/EFR December 1996 The URL of this page is: http://www-history.mcs.st-andrews.ac.uk/history/Mathematicians/Ch'in.html

16. C Index Cayley, Arthur (1158*) Cech, Eduard (465*) Cesàro, Ernesto (186), Ceulen, Ludolphvan (223) Ceva, Giovanni (296) Ceva, Tommaso (172) Ch in chiushao (62) Ch http://intranet.woodvillehs.sa.edu.au/pages/resources/maths/History/C.htm

Names beginning with C The number of words in the biography is given in brackets. A * indicates that there is a portrait. Cajori , Florian (85*) , Alberto (879*) Callippus Campanus of Novara (171) Campbell , John (74*) Camus , Charles (61) Cantelli , Francesco (104) Cantor , Georg (3100*) Cantor , Moritz (498*) Caramuel y Lobkowitz, (227) , Constantin (267*) Carcavi , Pierre de (439) Cardan , Girolamo (2818*) Carlyle , Thomas (372*) Carnot, Lazare Carnot, Sadi Carroll , Lewis (266*) Carslaw , Horatio (525*) Cartan , Elie (406*) Cartan, Henri Cartwright , Dame Mary (110*) Cassels , John (418*) Casorati , Felice (95*) Cassini , Giovanni (309*) Castel , Louis (172) Castelnuovo , Guido (384*) Castigliano , Alberto (456) Castillon , Johann (162) Catalan Cataldi , Pietro (308) Cauchy , Augustin (2467*) Cavalieri , Bonaventura (565*) Cayley , Arthur (1158*) Cech , Eduard (465*) , Ernesto (186) Ceulen , Ludolph van (223) Ceva, Giovanni Ceva, Tommaso Ch'in Chiu-Shao (62) Ch'ung Chi Tsu Chandrasekhar , Subrahmanyan (236*) Chang , Sun-Yung (620*) Chaplygin , Serg (366*) Chapman , Sydney (792*) Chasles , Michel (154*) , Gabrielle du (154*) Chebotaryov , Nikolai (409*) Chebyshev , Pafnuty (255*) Chern , Shiing-shen (627*) Chevalley , Claude (369*) Chi Tsu Ch'ung (127*) Chisholm Young , Grace (112*) Chowla , Sarvadaman (819*) Christoffel , Elwin (1580*) Chrysippus Chrystal , George (2763*) Chu Shih-Chieh (80) Chuquet , Nicolas (299) Church , Alonzo (171*) Civita , Tullio Levi- (418*) Clairaut , Alexis (2087*) Clapeyron , Benoit (525*) Clarke , Samuel (284) Clausen , Thomas (357) Clausius , Rudolf (110*)

17. RSA Conference 2004 During the 13th century, a patriotic poet, musician, archer, and student of calendricalcomputation and mathematics named Ch’in chiushao joined the military http://2004.rsaconference.com/theme.aspx

The Guardian of Treasures. An Imperial Emblem of Vigilance. RSA Conference 2004 offers a unique industry forum for professionals with a vital interest in information security. The Conference lays the foundation for new breakthroughs to defend your enterprise against information security marauders or secure your applications from hackers. And it offers a distinguished roster of speakers, sessions and attendees. Mark the dates and register now. For questions regarding Conference Registration, please call or call from outside the US and Canada. For General Conference questions, please call 866-518-2076 or call 404-508-2884 from outside the US and Canada or email conferenceinfo@rsasecurity.com Home Contact Us RSA is a registered trademark or trademark of RSA Security Inc. in the United States and/or other countries. All other products and services mentioned are trademarks of their respective companies. The views expressed by a conference attendee, speaker, exhibitor or sponsor are not necessarily those of RSA Security Inc. All conference attendees, speaker, exhibitors and sponsors are solely responsible for the content of any and all individual or corporation presentation, marketing collateral, advertising and online web content.

18. 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://pt.slider.com/enc/11000/Ch'in_chiu-shao.htm

19. RSA Conference 2004 Japan During the 13th century, a patriotic poet, musician, archer, and student of calendricalcomputation and mathematics named Ch in chiushao joined the military http://www.medialive.jp/events/rsa2004/eng/default.html

The RSA Conference 2004 is the most prestigious information security event of the year. It is the must-attend event for organizations that deploy, develop or investigate data security or cryptography products. The RSA Conference brings together IT professionals, developers, policy makers, industry leaders and academics to share information and exchange ideas on technology trends and best practices in identity theft, hacking, cyber-terrorism, biometrics, network forensics, perimeter defense, secure web services, encryption and related topics. The 3rd annual RSA Conference Japan delivers more learning, networking, and product demonstrations than any other security gathering. You will meet the best and the brightest in the information security industry, both decision makers and technology luminaries. Don't miss this opportunity to learn fresh approaches and develop creative solutions. The Guardian of Treasures. An Imperial Emblem of Vigilance.

20. Chinese Remainder Theorem 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.fact-index.com/c/ch/chinese_remainder_theorem.html

Main Page See live article Alphabetical index Chinese remainder theorem The Chinese remainder theorem is the name applied to a number of related results in abstract algebra and number theory Table of contents 1 Simultaneous congruences of integers 2 Statement for principal ideal domains 3 Statement for general rings 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 x to this system are congruent modulo the product n n n k A solution x can be found as follows. For each i , the integers n i and n n i are coprime, and using the extended Euclidean algorithm we can find integers r and s such that r n i s n n i = 1. If we set e i s n n i , then we have e i mod n i ) and e i mod n j ) for j i The number x i k a i e i then solves the given system of simultaneous congruences.

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