41. AMOF: Info On Subsets In chu shihchieh s Precious Mirror of the Four Elements (1300) thereis a diagram that is clearly the first part of Pascal s triangle. http://www.schoolnet.ca/vp-pv/amof/e_subsI.htm

Information on Subsets of a Set Description Example History Applications ... Links Description of the Problem How did the concept of number arise? Imagine explaining the number "three" to a two year old. You would take collections of three oranges, three crayons, three blocks, and three cookies, and then try to get them to see the common feature of each of those collections of objects. Each of those collections is a set, a set containing three elements. Mathematicians also use sets to define the number concept. One of the most useful operations on sets is to take all of its subsets, each possible sub-collection of the original collection. AMOF can list all subsets of a finite set in a variety of ways. n element set is 2 n since each element is either included in the subset or it isn't. For n = 0,1,2,...,10, the value of 2 n is 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024. These, of course, are the powers of 2. Gray Codes In Gray code order successive subsets differ by exactly one element. There are many such Gray codes; the one we use is called The B inary R eflected G ray C ode (or BRGC). The

42. Amof:Info On Combinations Pascal s triangle first appeared in 1303three hundred years before Pascalin aChinese manuscript, Precious Mirror of the Four Elements, by chu shihchieh. http://theory.cs.uvic.ca/~cos/amof/e_combI.htm

Information on Combinations of a Set Description Example History Applications ... Links Description of the Problem What are the different ways that Alice, Bob, Carol, and David can pair up to ride on a roller coaster car that has two seats in the front and two in the back? Who sits on the left and who on the right doesn't matter. We can immediately simplify the problem by observing that after the two front seats are taken, there is no choice about who goes into the back. One way of solving the problem is to list all possible front pairs: Alice and Bob, or Alice and Carol, or Alice and David, or Bob and Carol, or Bob and David, or Carol and David; there are exactly six ways. What we have just done is to list all "combinations" of two persons chosen from four persons. Similarly we could form the combinations of any number of persons from a larger group of persons. Below we give a mathematical definition of what constitutes a combination. A set is a collection of objects, and a subset k -combination of an n -set is a subset with k elements chosen from a set with n In the Amazing Mathematical Object Factory (AMOF), the set from which subsets are made is always the set [

43. À§´ëÇѼöÇÐÀÚ ¸ñ·Ï Chu, chu shihchieh Born about 1270 in China Died about 1330 Chuquet, NicolasChuquet Born 1445 in Paris, France Died 1488 in Lyon, France Church, Alonzo http://www.mathnet.or.kr/API/?MIval=people_seek_great&init=C

44. Figure This Math Challenges For Families - Did You Know? solve the challenge. Pascal s triangle was in chu shihchieh s PreciousMirror of Four Elements, a fourteenth century book in China. http://www.figurethis.org/challenges/c06/did_you_know.htm

Blaise Pascal was a French mathematician in the 1600s. He worked with a pattern of numbers (Pascal's triangle) to solve many counting problems. Pascal's triangle is formed by putting 1's along two "sides" of a triangle, then adding the two numbers above to the right and left to get the next number in the pattern. Pascal's triangle can be used to solve the challenge. Pascal's triangle was in Chu Shih-chieh's Precious Mirror of Four Elements, a fourteenth century book in China. Home Back to the Challenge Answer Try These ... KnowNet Construction, Inc

45. Home - Search Chu Mei Feng Video Scientists church alonzo. Scientists chuquet nicolas. Scientists chu shihchieh. Scientists aristarchus of samos. Religion victory http://www.algebraic.net/cgi-bin/988.cgi?q=chu mei feng video&show_page=1

46. Example: Pascal's Triangle It was mentioned by an early Chinese mathematician chu shihchieh in1303, and was known to Omar Khayyam, who lived from 1043 to 1123. http://pages.cpsc.ucalgary.ca/~becker/231/Notes/Introduction/PascalTriangle.html

Katrin Becker 1998-2001 Last Modified July 19, 2001 04:54 PM Course Notes - Pascal's Triangle EXAMPLE ALGORITHM: Pascal's Triangle (for a different link, click here Given any positive integer , the expression (1 + x) n can be written in the form (1 + x) n = b n,0 + b n,2 x + ... + b n,n x n for suitable numbers b n,m . This can be obtained by multiplying (1 + x) n times with itself and adding up equal powers of x As an example, (1 + x) + x and thus b = 1, b = 3, b = 3, b The numbers b n,m are called "binomial coefficients." Collecting the binomial coefficients into a table of the form: b b b b b b b b b b one obtains "Pascal's Triangle." Pascal's Triangle has a very long history. It was mentioned by an early Chinese mathematician Chu Shih-chieh in 1303, and was known to Omar Khayyam, who lived from 1043 to 1123. It obtained its name because it appeared in Blaise Pascal's Traite du Triangle Arithmetique , which was published in 1653. The first 6 lines of the "triangle" are: Each number in Pascal's triangle is the sum of the two numbers in the previous line that are above the desired number.

47. Thirteen Ed Online - Tracing Math's Evolution 5. George Washington Carver, inventor 6. al Khawarizmi, mathematician 7. Raman,physicist, mathematician 8. chu shihchieh, mathematician 9. Erastosthenes http://www.thirteen.org/edonline/lessons/mathevolution/b.html

Tracing Math's Evolution Procedures for Teachers is divided into four sections: Prep Preparing for the Lesson. Steps Conducting the Lesson. Extensions Additional Activities. Tips Managing Resources and Student Activities. Student Prerequisites: Students need to know how to connect to a Web site and follow links. Computer Resources: You will need at least one computer with Internet access to complete this lesson. While many configurations will work, we recommend: Modem: 28.8 Kbps or faster. Macintosh computer: System 7.5 or above and at least 16 MB of RAM. IBM-compatible computer: 386 or higher processor with at least 16 MB of RAM, running Windows 3.1. Or, a 486/66 or Pentium with at least 16 MB of RAM, running Windows 95. For more information, visit What You Need to Get Connected in wNetSchool's Internet Primer. Bookmarks: The following sites should be bookmarked: The Faces of Science: African Americans in the Sciences http://www.lib.lsu.edu/lib/chem/display/faces.html Compilation of African-American scientists and mathematicians, grouped by content area, and linked to biographical sites. Mathematicians/Scientists http://www.rialto.k12.ca.us/frisbie/mathematicians.html

48. History Of Mathematics: Chronology Of Mathematicians Zhu Shijie (Hanqing, Songting) chu shihchieh (fl. c. 1280-1303) *SB; Francisof Meyronnes (c. 1285-c. 1330) *SB; William of Ockham (c. 1285-c. 1349) *SB *MT; http://aleph0.clarku.edu/~djoyce/mathhist/chronology.html

Chronological List of Mathematicians Note: there are also a chronological lists of mathematical works and mathematics for China , and chronological lists of mathematicians for the Arabic sphere Europe Greece India , and Japan Table of Contents 1700 B.C.E. 100 B.C.E. 1 C.E. To return to this table of contents from below, just click on the years that appear in the headers. Footnotes (*MT, *MT, *RB, *W, *SB) are explained below List of Mathematicians 1700 B.C.E. Ahmes (c. 1650 B.C.E.) *MT 700 B.C.E. Baudhayana (c. 700) 600 B.C.E. Thales of Miletus (c. 630-c 550) *MT Apastamba (c. 600) Anaximander of Miletus (c. 610-c. 547) *SB Pythagoras of Samos (c. 570-c. 490) *SB *MT Anaximenes of Miletus (fl. 546) *SB Cleostratus of Tenedos (c. 520) 500 B.C.E. Katyayana (c. 500) Nabu-rimanni (c. 490) Kidinu (c. 480) Anaxagoras of Clazomenae (c. 500-c. 428) *SB *MT Zeno of Elea (c. 490-c. 430) *MT Antiphon of Rhamnos (the Sophist) (c. 480-411) *SB *MT Oenopides of Chios (c. 450?) *SB Leucippus (c. 450) *SB *MT Hippocrates of Chios (fl. c. 440) *SB Meton (c. 430) *SB

49. February 25, 2003 One study, for example, has shown how the Chinese chu shihchieh triangle anticipatedby more than three centuries the highly similar arrangement of numerals http://commonsensewonder.com/mtarchives/000872.shtml

Main February 25, 2003 The multiculturalist crowd has set The multiculturalist crowd has set it's sights on another target, mathematics. There are calls to teach " Ethnomathematics To redress their pedagogical grievances, these ethnomathematicians want math curriculums that place greater emphasis on the systems of previous civilizations and certain traditional cultures. Studies of state civilizations might focus on Chinese or Arabic math concepts. One study, for example, has shown how the Chinese Chu Shih-chieh triangle anticipated by more than three centuries the highly similar arrangement of numerals by Pascal that holds sway in many Western teachings of probability theory. Now this may all be well and good in a "History of Mathematics" course, but I fail to see what advantage HS and JHS students of mathematics will gain from learning about "quipu, bundles of cotton cord knotted by Incans according to a sophisticated base-10 numeration system". Firstly, the basic premise that math "is absolutely integrated with Western civilization, which conquered and dominated the entire world" is incorrect. A good part of the foundation for modern algebra, number theory etc came to Europe from India and the Arabs. And while "African kinship numerics or Peruvian bead counting" may be interesting historical studies they will not help students learn how to solve Diophantine equations or master the mathematics, such as calculus or statistics or algebra, required for any study of modern science. As David Klein is quoted in the article:

50. Introduction The solution method is contained in chu shihchieh’s Precious Mirror ofthe Four Elements or, as it has become known, Pascal’s Triangle. http://jrieditor.bus.utexas.edu/macminn/keynote.htm

Risk and Choice By Richard MacMinn Keynote Speech Presentation at The International Risk Management and Insurance Conference Taipei July Introduction Risks are commodities that may be exchanged. The corporation, long viewed as a nexus of contracts, may also be viewed as a nexus of risks. The corporation may be described as a composite commodity or bundle of risks that may be separated. (Kohn 1999) An economy may achieve an efficient allocation of risks as well as resources through separation and trading, i.e., see (Arrow 1963) or (Debreu 1959) Risks have traditionally been categorized as speculative or pure. The speculative risk may yield a gain or a loss. Aristotle provides an early example of a speculative risk in Book I of Politics. He tells a story about the philosopher T h a les of Miletus. According to the story, Thales was chided because he was poor and that was taken to be evidence that philosophy is of no practical value. Thales demonstrated the foolishness of the reproach. Thales had exceptional skill in reading the stars. One winter he foresaw that the autumn olive harvest would be much larger than normal.

51. Pergunta Agora Precious Mirror of the Four Elements, pelo matemático chinês chu shih-chieh. http://www.apm.pt/pa/index.asp?accao=showtext&id=2572

52. Full Alphabetical Index Translate this page in (62) Chisholm Young, Grace (583*) Chowla, Sarvadaman (819*) Christoffel, Elwin(1580*) Chrysippus (831) Chrystal, George (2763*) chu shih-chieh (80) Chuquet 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)

53. Mathematicians Benjamin Banneker Lewis Latimer George Washington Carver Erastosthenes KatherineG. Johnson Annie Easley Raman Margarita Colmenares chu shihchieh Ada Hypatia http://www.stmarybashacatholic.org/mathematiciansp1.htm

Mathematicians/Scientists The answer key includes more names than the numbered worksheet. Johann Carl Friedrich Gauss Evelyn Boyd Granville George Polya Pedro Nunez Galileo Granville T. Woods al'Khawarizmi Jane Cooke Wright Benjamin Banneker Lewis Latimer George Washington Carver Erastosthenes Katherine G. Johnson Annie Easley Raman Margarita Colmenares Chu Shih-Chieh Ada Hypatia Blaise Pascal Zhu-Shijie Nina Karlovna Bari Albert Einstein GOOD LUCK!

54. ExC 7.7 : Matris har delvis ortogonala kolonner ! b) , c) och d) Matlab program fortsättning tfin=190011990 ; u=A\y; %Polynom beräkning enligt chu shihchieh ! http://www.cs.umu.se/kurser/TDBA44/Heath/K7/KAP7/exc7.htm

ExC 7.7 : a b Rita polynom och indata . c) Interpolera indata med en kubisk splinefunktion . Rita approximation och indata. d e ) Uppgift med Langrange bas och tidtagning f g a) Matlabprogram t=[1900:10:1980]'; y=[76212168;92228496;106021537;123202624;132164569;151325798;179323175;203302031;226542199]; for i=1:4 if i==1, x=t; elseif i==2 , x=(t-1900); elseif i==3 , x=(t-1940); else , x=(t-1940)/40; end A=[x.^0,x.^1,x.^2,x.^3,x.^4,x.^5,x.^6,x.^7,x.^8]; disp([sprintf(`Nr=%g',i),sprintf(` konditionstal=%g',cond(A))]) disp([sprintf(` norm A = %g', norm(A)),sprintf(` norminvers A=%g',norm(inv(A)))]) disp(` `) end Utmatning Nr=1 konditionstal=Inf norm A = 6.08309e+26 norminvers A=6.81576e+14. Stora element i matris och invers Nr=2 konditionstal=6.33025e+15 norm A = 1.78252e+15 norminvers A=3.36284 Stora element i matris Nr=3 konditionstal=9.31554e+12 norm A = 9.31459e+12 norminvers A=1.0001 Stora element i matris Nr=4 konditionstal=1605.44 norm A = 3.81046 norminvers A=421.325 Matris har delvis ortogonala kolonner b) , c) och d) Matlab program tfin=[1900:1:1990]';

55. ENC Online: Curriculum Resources: Multiculturalism In Mathematics, Science, And Graphs to go George Washington Carver A soapy success story Plant doctor, soil doctorThe Celts The chemistry of butter chu shihchieh Pascal s triangle and http://www.enc.org/resources/records/full/0,1240,001354,00.shtm

Skip Navigation You Are Here ENC Home Curriculum Resources Search the Site More Options Classroom Calendar Digital Dozen ENC Focus ... Ask ENC Explore online lesson plans, student activities, and teacher learning tools. Search Browse About Curriculum Resources Read articles about inquiry, equity, and other key topics for educators and parents. Create your learning plan, read the standards, and find tips for getting grants. Multiculturalism in mathematics, science, and technology: readings and activities Grades: ENC#: ENC-001354 Publisher: Addison-Wesley Publishing Company Date: Ordering Information Similar Records Featured in ENC Focus Subjects: Mathematics Algebra. Applied mathematics. Arithmetic. Equations. Geometry. Graphing. Instructional issues. Multicultural instruction. Quadratic equations. Ratios. Science Agriculture. Astronomy. Biology. Botany. Chemistry. Ecology. Electricity. Engineering. Instructional issues. Life Science. Multicultural instruction. Physical Science. Physiology. Space sciences. Integrated/interdisciplinary approaches Resource Type: Lessons and activities.

56. Galerie H Translate this page Allerdings hatten einige Jahre zuvor der Italiener Ruffini und bereits im Jahre500 vor Christus der Chinese chu shih-chieh ähnliche Methoden verwendet. http://www.fh-rosenheim.de/~gki/gallery/gallery_h.php

Galerie der Computer-Pioniere A: Adleman Aiken Al Chwarizmi Allen ... Aristoteles B: Babagge Backus Baran Bauer ... Bush C: Cäsar Cerf Chaitin Chappe ... Cray D: Darwin d'Aurillac Diffie Dijkstra E: Eckert, J. Eckert, W. Edison Eratosthenes ... Euler F: Fanning Fechner Feynman Fermat ... Frege G: Gates Gauß Gödel Gosling H: Hahn Hamilton Hamming Harel ... Huffman I,J: Jacobsen Jacquard Jobs Joy K: Kant Kernighan Keynes Kildall ... Kuratowski L: Lai Landis Leibniz Lempel ... Lovelace (Ada) M: Mandelbrot Marconi Mauchly McCarthy ... Morse N: Nassi Naur von Neumann Newton ... Nyquist O,P: Papert Pascal Patterson Peano ... Prigogine Q,R: Radó Rechenberg Reis Ritchie ... Rutishauser S: Schickard Schroedinger Shamir Shannon ... Szilard T: Thompson Thue Tomlinson Torvalds ... Turing U: Ulam V: Venn Vernam Veuve-Clicquot Vigenére W: Warshall Watson Weizenbaum Welch ... Wozniak X,Y,Z: Zadeh Zimmermann Ziv Zuse Top Ten "Wegbereiter": Euklid Al Chwarizmi Babbage Gödel ... [Impressum und Quellenangaben] Hahn Philipp Matthäus Hahn Hamilton Hamilton Hamming Richard Wesley * 11. Februar 1915 Chicago (USA) + 7. Januar 1998 Monterey (USA) Ein neues Feld der Codierungstheorie: Fehlerkorrigierende Codes Hamming studierte bis 1939 an der University of Chicago und an der University of Nebraska Mathematik. 1942 promovierte er an der University of Illinois. Anschließend war er am Manhattan-Projekt in Los Alamos an der Entwicklung von Atomwaffen beteiligt. 1946 wechselte Hamming zu den Bell Telephone Laboratories und arbeitete dort mit

57. Untitled Document This is the case with chu shihchieh, which is considered the greatestamong the Sung-mathematicians; we know very little about him. http://www.stud.fim.ntnu.no/~sundsoy/kvantenytt/utenriks/brage.htm

The Chinese civilization is recognized by many as one of the oldest ones in the world, and it is definitely the one that we have the most knowledge of. The mythical Xia-dynasty is said to be founded by the Great Yu approximately 2500 bc, but of this we have no archeologically evidence. This is also the case with the succeeding Shang-dynasty, however there are so many references to it in ancient Chinese texts that we are certain of its existence. Of the Chou-dynasty, founded by the Duke of Chou in 1200 bc, we have much evidence. This dynasty, which lasted impressing eight hundred years, is also the one where we find traces of mathematical works. It is however difficult to determine its date of origin, because most of the works are lost, and many historians have tended to overestimate the age of the works that are preserved. The Chou Pei Suan Ching is generally considered to be the oldest of the mathematical classics, however estimates of its age differ by almost a thousand years, from 1200 b.c to the first century before our era. It is generally believed to be a product of the early Han dynasty (approximately 200 bc). Chou Pei contains astronomical calculations, which has always been of supreme importance to the ruling powers in ancient China. The Emperor was the only person on Earth with the power to communicate directly to the gods, and a good way of proving this to the people was to predict astronomical events such as solar and lunar eclipses. The beginning of the book, which is the oldest part of the text, contains the following discussion of right-angled triangles:

58. Historia Matematica Mailing List Archive: Re: [HM] Pascal's Triangle in 1265. In China, the triangle appears in the work of chu shihchieh(1303), but may have been very ancient by then. The triangle http://sunsite.utk.edu/math_archives/.http/hypermail/historia/may99/0073.html

Re: [HM] Pascal's Triangle James A Landau JJJRLandau@aol.com Sat, 8 May 1999 16:14:33 EDT Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Dave Cohen: "[HM] Chinese history" Previous message: David Fowler: "Re: [HM] M.H.A. Newman" Maybe in reply to: Arthur B. Powell: "[HM] Pascal's Triangle" Next in thread: Prof. Dr. Ivo Schneider: "Re: [HM] Pascal's Triangle" Next in thread: David Fowler: "Re: [HM] M.H.A. Newman" In a message dated 99-05-08 09:50:25 EDT, Arthur B. Powell wrote: When looking for the first occurrence of a mathematical term, a good place to check is Jeff Miller's Web page at http://members.aol.com/jeff570/mathword.html (one reason to check there is that a number of members of this mailing list are contributors to Jeff's page) The entry for "Pascal's Triangle" reads used the term "arithmetical triangle" (triangle arithmetique). In Italy it is called Tartaglia's triangle and in China it is called Yang Hui's triangle. Who was Yang Hui? He was a Chinese mathematician who flourished from circa 1261 to 1275 and who may also have been known as "Qianguong".

59. Literature hsien chih by Chen Menglin ? (who arrived in Taiwan in 1716)and Hsiao-liu-chiu man-chih ? by chu shih-chieh ? (who http://www.gio.gov.tw/taiwan-website/5-gp/yearbook/2001/chpt24-1.htm

Taiwan 2001 Literature Early Taiwanese Literature Aboriginal Traditions Chinese Immigrant Literature Between 1612 and 1844, quite a few Chinese intellectuals visited or stayed in Taiwan, most notably the Ming poet Shen Kuang-wen ¨H¥ú¤å, who was forced to land on the island by a typhoon in 1662 and afterward played an important role in forming a Taiwanese poets society under the name of Tung-yin Chu-lo-hsien chih ½Ñ¹¿¤§Ó by Chen Meng-lin ³¯¹ÚªL (who arrived in Taiwan in 1716) and Hsiao-liu-chiu man-chih ¤p¯[²yº©»x by Chu Shih-chieh ¦¶¤hÍk (who stayed from June 1763 until August 1764). Early Colonial Literature Taiwan Wen-i Chiu-chih »OÆW¤åÀ»x; it was also instrumental in supporting nationalist movements. Lien's monumental work on Taiwan's history, A Comprehensive History of Taiwan »OÆW³q¥v, remains a classic in the field. In 1911, Liang Chi-chao ±ç±Ò¶W visited Taiwan and brought with him ideas of Western enlightenment and experimental literature. Even though Taiwanese writers of the time were versed in the classical Chinese tradition, they were forced to confront the colonial reality and to work in more realistic modes of literary expression. This made a shift toward modern literature inevitable. Government Information Office

60. Accidental Death Of An Anarchist clownface makeup on all the characters in Accidental Death of an Anarchist cannotbut make one think of Chin shihchieh-directed plays such as Ho-chu’s New http://www.pwshop.com/html/english/drama-eng-21.html

Accidental Death of an Anarchist Premiere: November 12, 1995, National Arts Hall, Taipei ABOUT THE PLAY: Dario Fo¡¦s mischievous yet haunting work is set in a police station, where outside a crowd has gathered to protest the ¡§accidental¡¨ death of an anarchist who supposedly fell from the precinct window. The play is dominated by a seeming madman who has been apprehended by the police, released, but keeps hanging around while changing identities, gradually forcing the political truth from the other characters. The play was directed by Chin Shih-chieh, one of Taiwan¡¦s foremost playwright/directors in his own right, who had performed in many Workshop productions, and he brought a surrealistic touch to the zany action. The play also served as a showcase for the talents of Zhao Ziqiang, who played the main role, constantly transforming into different personas on stage. It also featured the set of noted architect John Wei-jan Yang. The political overtones in the play fit well with Taiwan politics, and the play opened at a time of several mysterious deaths in the Taiwan military, all claimed to be ¡§accidental,¡¨ but later proved to be the result of foul play. CREDITS Script: Dario Fo Translation: Stan Lai Adaptation: Stan Lai and Chin Shih-chieh Director: Chin Shih-chieh Cast: Zhao Ziqiang as the Clown Li Jien-chang as Policeman, Drummer

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