21. Chinese And China Resources. China And Mathematics chu shihchieh chu shih-chieh wrote two important mathematical texts in 1299and 1303. Considered by many to represent the peak in Chinese mathematics. http://www.the-gallery-of-china.com/chinese-math.html

Chinese Paintings The Galleries Link to this page The Gallery of China First-time Visitor? Visit our Chinese Art Homepage Chinese Mathematics Add your site Tsinghua University, Applied Mathematics Department Information about the department and courses, plus links. In Chinese and English History of Chinese Mathematics An outline of the history of Chinese mathematics, including a chronology of mathematicians and mathematical works Mathematics and Mathematicians in Ancient China Includes information about Chung Ch'i, Yang Hui, Shen Kua, Ch'in Chiu Shao, Zhang Heng, Hsien Chung Wang and Chu Shih-Chien Development of Mathematics in Ancient China Shang numerals, Chinese mathematics texts, the discovery of zero. The art of calculation (suan chu) was both a practical and spiritual one, and covered a wide range of subjects from religion and astronomy to water control and administration Chinese Committees and Societies of Mathematics Includes the National Cheng Kung University, Tainan, Taiwan; Academia Sinica, Institute of Mathematics, Beijing, People's Republic of China; Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan Matteo Ricci Matteo Ricci, the Jesuit Priest, arrived in China in 1582 and was perhaps responsible for the first interaction between European and Chinese mathematics. Information and relevant links

22. TIMELINE 14th CENTURY Page Of ULTIMATE SCIENCE FICTION WEB GUIDE 1303 chu shihchieh of CHINA publishes the first known representationof what we call Pascal s Triangle. Arab mathematicans probably http://www.magicdragon.com/UltimateSF/timeline14.html

TIMELINE 14th CENTURY Return to Timeline Table of Contents Return to Ultimate Science Fiction Table of Contents TIMELINE 14th CENTURY May be posted electronically provided that it is transmitted unaltered, in its entirety, and without charge. We examine both works of fiction and important contemporaneous works on non-fiction which set the context for early Science Fiction and Fantasy. There are hotlinks here to authors, magazines, films, or television items elsewhere in the Ultimate Science Fiction Web Guide or beyond. Most recently updated: 24 December 2003 (to 36 Kilobytes). The single most enjoyable book about the 14th Century is: A Distant Mirror: The Calamitous 14th Century 14th Century Executive Summary of the Century Major Books of the Decade 1300-1310 Major Books of the Decade 1310-1320 Major Books of the Decade 1320-1330 ... Where to Go for More : 51 Useful Reference Books Executive Summary of the Century This Century marks an accelerating growth of Art Science , and Statecraft as if in preparation for the later Renaissance . By late in this Century

23. Cho Chrétien, Jean. Chu Hsi. chu shihchieh. Chu Ta. Chu Teh. Chrysorrhoas. Chrysostom.Chrétien de Troyes. Chrétien, Jean. Chu Hsi. chu shih-chieh. Chu Ta. Chu Teh. Chu-hai. http://www.slider.com/Enc/C/Cho.htm

The Web Encyclopaedia Shopping Ah‑ha ... Index The Web Encyclopaedia Shopping Ah-ha Kanoodle Findwhat Summary Top Encyclopaedia C Cho ... Rope Ladders Cho Still searching the hard way? Try the Free Slider Search Toolbar and spend less time searching!! www.trellian.com Sponsored Link -butenedioic acid C.I.A.M. CIO CISC processor ... city-state Slider in: Espa±ol Deutsch Dansk Nederlands ... Download the FREE Slider.com Search Toolbar!

24. CHANGES TO VOLUME 1 OF THE ART OF COMPUTER PROGRAMMING % della Scienze\/ \bf3} (1939), 721757. \endchange \amendpage 1.53 near the bottom(00.11.30) line $5$ Shih-Chieh Chu \becomes chu shih-chieh\nlh line $-4 http://www-cs-faculty.stanford.edu/~knuth/err1.textxt

25. Triangle De Pascal - Historique miroir des quatre éléments de Yang Hui s et chu shih-chieh. http://membres.lycos.fr/villemingerard/Iteration/TrgPasc2.htm

NOMBRES - Curiosités, théorie et usages Accueil Dictionnaire Rubriques Index ... M'écrire Édition du: Rubrique: ITÉRATIONS , CYCLES Suite de Fibonacci Triangle de Pascal Triangle de Leibniz Procédé de Kaprekar ... Suite de Steinhaus Sommaire de cette page LE TAXI EN VILLE TRIANGLE DE PASCAL - Introduction PROPRIÉTÉS HISTORIQUE TRIANGLE DE PASCAL dans sa présentation classique du triangle isocèle Pages voisines Combinaisons Petit théorème de Fermat Formule du binôme Autres Récurrence Théorie des nombres Calcul mental Géométrie ... Boucle infernale HISTORIQUE On trouve sa trace en Chine vers 1100. Il est décrit par Omar Khayyàm qui meurt en 1123. Un livre, écrit en 1303, le montre de toute évidence: " Précieux miroir des quatre éléments " de Yang Hui's et Chu Shih-chieh. En fait, il s'agissait de la loi binomiale, montrant la construction jusqu'à l'ordre 8. On le retrouve chez les Perses au XI ème siècle: Omar Khayyam écrit un livre intitulé: " Algèbre ". Le livre " Rechnung " (1527) de Peter Apian montre le triangle en page de couverture.

26. Mathematicians Sequence). chu shihchieh, Chinese, 1270-1330, Szu-yuen yu-chien ( ThePrecious Mirror of the Four Elements ), which deals with modern Al. http://members.fortunecity.com/kokhuitan/mathematicians.html

Great Mathematicians and Their Achievements Mathematics exist before 1900 BC, in great civilizations everywhere, including China, India, Babylon etc. However, the first record of Mathematical manuscripts is found in Egypt, namely, the Moscow Papyrus and the Rhind Papyrus. In the 'Achievement' column below, the notations are as follows: AG = Analytic Geometry Al = Algebra Ar = Arithmetic As = Astronomy C = Calculus DE = Differential Equation FM = Foundation of Mathematics G = Geometry GT = Group Theory L = Logic M = Mechanics N = Number Theory P = Probability RM = Recreational Mathematics S = Statistic ST = Set Theory T = Topology The list here is not exhaustive. The mathematicians listed here are either pioneers in various fields of Mathematics, or those who have contributed to almost all fields, or those who have settled unsolved problems. For a more complete list of mathematicians, click on index of mathematicians Name Nationality Year Achievements Egyptian 1900 BC Moscow Papyrus (25 problems on G Ahmes Egyptian 1700 BC Rhind Papyrus (84 problems on Ar, Al, G

27. Math History - Middle Ages chu shihchieh writes Szu-yuen Yu-chien (The Precious Mirror of the Four Elements),which contains a number of methods for solving equations up to degree 14. http://lahabra.seniorhigh.net/pages/teachers/pages/math/timeline/MmiddleAges.htm

28. DVD-vitriini - The Contract Hankkeeseen sotkeutuu myös Sam Huin näyttelemä yökerhotaikuri chu shihchieh,joka on korviaan myöten veloissa televisiossa esiintyvälle opettajalleen. http://koti.mbnet.fi/~vitriini/contract.html

The Contract (Maishen qi / Mr. Boo 3: The Contract) Universe (Region 0, NTSC) Kuvasuhde: Kanton DD 5.1, mandariini DD 5.1 Tekstitys: Englanti, kiina Kesto: 97 min Biografiat, trailereita ( The Contract Games Gamblers Play The Private Eyes The Last Message Ohjaus: Michael Hui, 1978 The Contract The Contractin The Contractissa The Contract The Contract The Private Eyesissa The Contract Ulkoisesti The Contract The Contract Elokuva: Kuva: Testilaitteisto: Toshiba DVD-ROM SD-M1212, HL-5870B 15", Philips-vahvistin ja kaiuttimet.

29. ThinkQuest : Library : Ancient Chinese Technology from China. This diagram comes from chu shihchieh s Precious Mirrorof the Four Elements, published in 1303. The caption refers http://library.thinkquest.org/23062/pastri2.html

Index Technology Inventions Ancient Chinese Technology According to this site, from AD 600 through 1500, China was the world's most technologically advanced society. Many innovations were developed in China, such as the mariner's compass, paper-making, gunpowder, paper money, wheelbarrows, umbrellas, and numerous other items. Click on topics such as "Physics," "Transportation," or "Mathematics" to learn about Chinese contributions to this field. Visit Site 1998 ThinkQuest Internet Challenge Languages English Students Ken Willly Michael Coaches Bruce Dover Bay Secondary School, Nanaimo, Canada 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

30. Pascalsches Dreieck Spiegel der vier Elemente des Chinesen chu shih-chieh abgebildet. http://www.madeasy.de/2/pascal.htm

Pascalsches Dreieck Links Orginaltexte Pascal und das Chinesische Dreieck Dasselbe in schiefer Darstellung: 1 etc .........etc 1 Daher stellt es auch kein Problem dar, das Schema beliebig zu erweitern. Doch trotz der Einfachheit der Regel ist es erstaunlich, wie viele verschiedene Muster das Dreieck zu bieten hat, wobei das mit den kombinatorischen (bzw. binominalen) Koeffizienten wahrscheinlich das wichtigste von allen ist. In der 4. Reihe des Dreiecks sind die Zahlen 1,4,6,4,1. In dem Dreieck stecken aber noch ganz andere Muster in den Diagonalen, z. B.: die ganzen Zahlen (1, 2, 3, 4...) die Trigonalzahlen (als trigonale Punktanordnungen schreibbar, wie z.B. 3, 6, 10 etc.) die Tetraederzahlen (als tetraedische Punktanordnungen schreibbar, wie z.B. 4, 10, 20 etc.) Text aus dem Buch von John Allen Paulos Von Algebra bis Zufall Campus Verlag Das Pascal'sches Dreieck ist ein Zahlenschema, welches aus den Koeffizienten besteht, die sich durch das Ausmultiplizieren der Terme (a + b) n (a + b) = a + 2 a b + b (a + b) = a + 3 a b + 3 a b + b (a + b) = a + 4 a b + 6 a b + 4 a b + b Das Pascal'sche Dreieck Das Pascal'sche Dreieck Es wird durch folgende einfache Regel konstruiert: Was das Pascal'sche Dreieck so erstaunlich macht: Die n a b n auftreten, wobei mit

31. Ethnicity Chinese. chu shihchieh. 1303 AD. The discovery of triangle; Influential contributionto Pascal’s Triangle and Horner method. Egyptian. The Ancient Egyptians. http://www.as.wvu.edu/~equity/science.html

Contributions to Mathematics and Science from Individuals with Broad Ethnic Backgrounds Equity has many facets. It also has a variety of "meaning" to different people. In Mathematics and Science, many different ethnicities have contributed to the disciplines we now call Mathematics or Science. Below are two Tables, of some of these individuals (and groups) have contributed over the span of many centuries. The first Table is about Mathematicians and the second Table about Scientists. Table of Mathematicians of Diverse Ethnicity and their Discoveries Ethnicity Name Time Achievement Italian Maria Agnesi Discovery of the bell-shaped curve, the "versiera of Agnesi" Arabian Al-Khowarizmi 850 AD Solving Quadratic Equations Aztec Aztec - Native Americans ~ 1325 AD Accounting in commerce: conceptual zero Highly accurate land records: use of number base 20 Babylonian Babylonians in area of Iraq 2000 BC Base 60 system which is still in use today (e.g. squares, angles, and degrees) African-American Benjamin Banneker Created calculations of astronomical tables Survey for the layout of Washington, D.C.

32. Multcrit For example, Needham (1959; 137) shows how the Chinese chu shihchieh trianglecan be mapped onto Pascal s triangle by a rotation of ninety degrees. http://www.rpi.edu/~eglash/isgem.dir/texts.dir/multcrit.htm

Multicultural Mathematics: An Ethnomathematics Critique Ron Eglash (Mostly excerpts from Eglash, R. "When math worlds collide: intention and invention in ethnomathematics." Science, Technology and Human Values , vol 22, no 1, pp. 79-97, Winter 1997.) 0) Introduction Ethnomathematics is typically defined as the study of mathematical concepts in cohesive social groups, with an emphasis on small-scale or indigenous cultures. Working in many different areas of the world, Ascher (1990), Closs (1986), Crump (1990), D'Ambrosio (1990), Gerdes (1991), Njock (1979), Washburn and Crowe (1988), Zaslavsky (1973), and many others (see Fisher 1992, Shirley 1995 for reviews), have provided mathematical analyses of a variety of indigenous patterns and abstractions, while drawing attention to the role of conscious intent in these designs. 1) Five Subfields in ethnomathematics a Non-western mathematics consists primarily of historical studies (e.g. Cajori 1896), with a cultural focus (which has continued in contemporary works, such as Joseph 1991) on state empires such as the ancient Chinese, Hindu and Muslim civilizations. It is epistemologically based on the idea of direct, literal translations of nonwestern mathematics to the western tradition. For example, Needham (1959; 137) shows how the Chinese Chu Shih-chieh triangle can be mapped onto Pascal's triangle by a rotation of ninety degrees. b Mathematical anthropology uses mathematical modelling in ethnographic and archaeological studies to describe material and cognitive patterns, generally without attributing conscious intent to the population under study. The patterns are instead seen as the structural basis of underlying social forces, or as epiphenomena resulting unintentionally from the nature of the activity itself. Classificatory systems for kinship (e.g. Morgan 1871) were the first of these models. Later refinements of mathematical anthropology (e.g. Kay 1971) expanded this analysis to a variety of social phenomena, and increasingly complex mathematical tools.

33. Anthropology Of Science And Technology 2) Needham shows how the Chinese chu shihchieh triangle can be mappedonto Pascal’s triangle by a rotation of ninety degrees. http://www.rpi.edu/~eglash/eglash.dir/res_sem/day1/knowsys.htm

Local/Global Knowledge Systems: four categories Science and Technology in "The West" (professional mainstream) Science and Technology in non-western state societies (“ancient empire civilizations") Vernacular science and technology (“street smarts,” “just plain folks”) Indigenous science and technology (band and tribe societies) Examples from social studies of mathematics: Bloor's analysis of social choice in Euler's theorem of polyhedra Needham shows how the Chinese Chu Shih-chieh triangle can be mapped onto Pascal’s triangle by a rotation of ninety degrees. Jean Lave's Situated Cognition: knitting as algorithm Marcia Ascher on symmetry in Maori art

34. Chiffres Et écriture 1303 comme le triangle de chu shih-chieh . Là aussi il nous http://www.bib.ulb.ac.be/coursmath/chiffres.htm

35. Binomialkoeffizienten Translate this page älteren Datums ist. Eine Seite aus dem 1303 von dem chinesischenMathematiker chu shih-chieh veröffentlichten Werk Ssu Yuan Yu. http://www.mathe.tu-freiberg.de/~hebisch/cafe/binomial.html

Binomialkoeffizienten Unter einem Binom (oder binomischen Ausdruck ) versteht man einen Term der Form (a + b) n mit einem Exponenten n = 0, 1, 2, 3,... a und b Schreibt man (1) in der Form eines Produktes aus n Faktoren (a + b)*(a + b)*...*(a + b) a n-k * b k bzw. b n-k * a k k = 0,1,...,n) darstellen. Im Fall n = 2 (a + b)*(a + b) = a*(a + b) + b*(a + b) = a + a*b + b*a + b n = und n = 1 (a + b) = 1 = 1*a *b und (a + b) = a + b = 1*a *b + 1*a *b ein. a und b auch das Kommutativgesetz a*b = b*a , so bleiben nur n + 1 Produkte der Form a n-k * b k n = 3 (a + b) = 1*a + 3*a *b + 3*a*b + 1*b Diese Vielfachen der Produkte (3) in der Summendarstellung des Binoms (a + b) n Binomialkoeffizienten der Ordnung n n genau n + 1 Binomialkoeefizienten. Diese werden allgemein mit dem Symbol k = 0,1,...,n Blaise Pascal entdeckt. Er schrieb die Binomialkoeffizienten derselben Ordnung n jeweils zentriert in eine Zeile und ordnete die Zeilen mit wachsender Ordnung untereinander an. n = 0,1,2,3,4 also n - 1 berechnet. Dieses dreieckige Schema der Binomialkoeffizienten wird heute zu Ehren seines Entdeckers auch Pascalsches Dreieck Auszug aus der arabischen Handschrift Al-Bahir fi'ilm al hisab Ssu Yuan Yu

36. Lebensdaten Von Mathematikern Translate this page 1868 - 1944) Christoffel, Elwin Bruno (1829 - 1900) Chrysippus (280 - 206 v. Chr.)Chrystal, George (1851 - 1911) chu shih-chieh (1270 - 1330) Chuquet, Nicolas http://www.mathe.tu-freiberg.de/~hebisch/cafe/lebensdaten.html

Diese Seite ist dem Andenken meines Vaters Otto Hebisch (1917 - 1998) gewidmet. By our fathers and their fathers in some old and distant town from places no one here remembers come the things we've handed down. Marc Cohn Dies ist eine Sammlung, die aus verschiedenen Quellen stammt, u. a. aus Jean Dieudonne, Geschichte der Mathematik, 1700 - 1900, VEB Deutscher Verlag der Wissenschaften, Berlin 1985. Helmut Gericke, Mathematik in Antike und Orient - Mathematik im Abendland, Fourier Verlag, Wiesbaden 1992. Otto Toeplitz, Die Entwicklung der Infinitesimalrechnung, Springer, Berlin 1949. MacTutor History of Mathematics archive A B C ... Z Abbe, Ernst (1840 - 1909) Abel, Niels Henrik (5.8.1802 - 6.4.1829) Abraham bar Hiyya (1070 - 1130) Abraham, Max (1875 - 1922) Abu Kamil, Shuja (um 850 - um 930) Abu'l-Wafa al'Buzjani (940 - 998) Ackermann, Wilhelm (1896 - 1962) Adams, John Couch (5.6.1819 - 21.1.1892) Adams, John Frank (5.11.1930 - 7.1.1989) Adelard von Bath (1075 - 1160) Adler, August (1863 - 1923) Adrain, Robert (1775 - 1843)

37. Biografisk Register Translate this page 1598-1647) Cayley, Arthur (1821-95) Ceva, Giovanni (1647-1734) Chatelet, Gabrielle-Émiliede (1706-49) Chhin Chiu-Shao (1202-61) chu shih-chieh (ca. http://www.geocities.com/CapeCanaveral/Hangar/3736/biografi.htm

Biografisk register Matematikerne er ordnet alfabetisk på bakgrunn av etternavn. Linker angir at personen har en egen artikkel her. Fødsels- og dødsår oppgis der dette har vært tilgjengelig. Abel, Niels Henrik Abu Kamil (ca. 850-930) Ackermann, Wilhelm (1896-1962) Adelard fra Bath (1075-1160) Agnesi, Maria G. (1718-99) al-Karaji (rundt 1000) al-Khwarizmi, Abu Abd-Allah Ibn Musa (ca. 790-850) Anaximander (610-547 f.Kr.) Apollonis fra Perga (ca. 262-190 f.Kr.) Appel, Kenneth Archytas fra Taras (ca. 428-350 f.Kr.) Argand, Jean Robert (1768-1822) Aristoteles (384-322 f.Kr.) Arkimedes (287-212 f.Kr.) Arnauld, Antoine (1612-94) Aryabhata (476-550) Aschbacher, Michael Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Ball, Walter W. R. (1892-1945) Banach, Stéfan (1892-1945) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Bharati Krsna Tirthaji, Sri (1884-1960)

38. Full Alphabetical Index (1580*) Crisippo (329) Chrystal, George (312*) chu shih-chieh (80) Chuquet http://www.geocities.com/Heartland/Plains/4142/matematici.html

39. Sir Isaac Newton Biography, Biografia, Picture, Gravity, Laws Of chu shihchieh (Han-ch ing) (fl. c.1280-1303) One of the greatest Chinese mathematiciansof all time. His major contribution was to the theory of equations. http://isaac-newton.info/isaac-newton/Sir-Isaac-Newton-biography-biografia-pictu

KEYNOTE TECHNOLOGY SPEAKER Are you ready to take your conference to the next level? Do you need a great speaker to inform, inspire and show your audience the future? We can provide a keynote speaker on information technology , offshore outsourcing , or a custom presentation. Visit emeagwali.com and book Emeagwali Or call 7 (US/Canada) and 443-850-0850 (Outside US). Refer this speaker Get $500! What's New! Can I patent an idea How to patent a product Where to get patent application Information on patent submission Where do I obtain patents Where do I obtain Links to help artists, authors and musicians Info on obtaining protections Scientific Measurements: Major Mathematicians Scientific Measurements: Major Mathematicians Archimedes (c. 287-212 b.c.) Greek mathematician who is considered to be the greatest mathematician and engineer of ancient times. He discovered the lever and the principle of buoyancy, and he came close to inventing calculus. Banach, Stefan (1892-1945) Russian mathematician who founded modern functional analysis. He also developed the theory of topological

40. Ny Side 1 Translate this page Viggo (1885-1978) Cayley, Arthur (1821-95) Ceva, Giovanni (1647-1734) Chatelet,Gabrielle-Émilie de (1706-49) Chhin Chiu-Shao (1202-61) chu shih-chieh (ca. http://www.matte.no/matematikere.htm

Kurs i Matematikkens kulturhistorie. Siden er under arbeid - sist oppdatert Indexes of Biographies Abel, Nils Henrik Abelsenteret Matematikkens verden Om NHA Mat. kulturhist. Arkimedes Matematikkens verden Ackermann, Wilhelm (1896-1962) Aristoteles (384-322 f.Kr.) Babbage, Charles (1792-1871) Bachmann, Paul Gustav (1837-1920) Bacon, Francis (1561-1626) Baker, Alan (1939-) Banneker, Benjamin Berkeley, George (1658-1753) Bernoulli, Jacques (1654-1705) Bernoulli, Jean (1667-1748) Bernstein, Felix (1878-1956) Bertrand, Joseph Louis Francois (1822-1900) Binet, Jacques Philippe Marie (1786-1856) Boole, George (1815-64) Brahe, Tyco (1546-1601) Brun, Viggo (1885-1978) Cayley, Arthur (1821-95) Ceva, Giovanni (1647-1734) Chatelet, Gabrielle-Émilie de (1706-49) Chhin Chiu-Shao (1202-61) Chu Shih-Chieh (ca. 1270-1330)) Chuquet, Nicolas (1445-88) Cohen, Paul J. (1934-) Cole, Frank Nelson (1861-1926) Comandino, Federigo (1506-1575)

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