Pi Through The Ages Various people did, including Ptolemy (c. 150 AD) 3.1416 tsu ch'ung chi (430501AD) 355/113 al'Khwarizmi (c. 800 ) 3.1416 Al'Kashi (c. 1430) 14 places Viète http://www.veling.nl/anne/templars/Pi_through_the_ages.html
Extractions: A little known verse of the Bible reads And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23) The same verse can be found in II Chronicles 4, 2. It occurs in a list of specifications for the great temple of Solomon, built around 950 BC and its interest here is that it gives pi = 3. Not a very accurate value of course and not even very accurate in its day, for the Egyptian and Mesopotamian values of 25/8 = 3.125 and sqrt10 = 3.162 have been traced to much earlier dates: though in defence of Solomon's craftsmen it should be noted that the item being described seems to have been a very large brass casting, where a high degree of geometrical precision is neither possible nor necessary. There are some interpretations of this which lead to a much better value. The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite untraceable. The earliest values of pi including the 'Biblical' value of 3, were almost certainly found by measurement. In the Egyptian Rhind Papyrus, which is dated about 1650 BC, there is good evidence for 4(8/9)^2 = 3.16 as a value for pi. The first theoretical calculation seems to have been carried out by Archimedes of Syracuse (287-212 BC). He obtained the approximation
Chinese Astronomers moon. tsu ch'ung chi (430501) - astronomer and mathematician. Hecalculated pi and devised at new calendar which never was used. http://www.pa.msu.edu/people/horvatin/Astronomers/astronomerschinese.htm
- Great Books - Tabari (al), Ali Ibn Rabban (838-870), Medieval Science 17. Trotula of Salerno (c.1097-), Medieval Science 18. tsu ch'ung chi (430-501), Medieval Science 19. http://www.mala.bc.ca/~mcneil/s2.htm
New Page 1 tsu ch'ung chi, (430501 AD), 355/113. Al-Kashi lived still further east,in Samarkand, while tsu ch'ung chi, one need hardly add, lived in China. http://www.lawrence.org/edlinks/pi/pi_history.htm
Extractions: And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about. (I Kings 7, 23) The same verse can be found in II Chronicles 4, 2. It occurs in a list of specifications for the great temple of Solomon, built around 950 BC and its interest here is that it gives = 3. Not a very accurate value of course and not even very accurate in its day, for the Egyptian and Mesopotamian values of 25/8 = 3.125 and 10 = 3.162 have been traced to much earlier dates: though in defence of Solomon's craftsmen it should be noted that the item being described seems to have been a very large brass casting, where a high degree of geometrical precision is neither possible nor necessary. There are some interpretations of this which lead to a much better value. The fact that the ratio of the circumference to the diameter of a circle is constant has been known for so long that it is quite untraceable. The earliest values of including the 'Biblical' value of 3, were almost certainly found by measurement. In the Egyptian
New Page 1 Ptolemy, 150, 3, 3.14166. Wang Fan, 250, 1, 3.155555 (=142/45). Liu Hui, 263, 5,3.14159. tsu ch'ung chi, 480, 7, 3.141592920 (= 355/113). Aryabhata, 499, 4, 3.1416(=62832/2000). http://www.lawrence.org/edlinks/pi/pi_chronology.htm
Extractions: back A Chronology of Pi Pre Computer Calculations of Mathematician Date Places Comments Rhind papyrus 2000 BC Archimedes 250 BC 3.1418 (average of the bounds) Vitruvius 20 BC Chang Hong Ptolemy Wang Fan Liu Hui Tsu Ch'ung Chi Aryabhata Brahmagupta Al-Khwarizmi ... Al-Kashi Otho Viète Romanus Van Ceulen Van Ceulen ... Newton Sharp Seki Kowa Kamata Machin De Lagny Only 112 correct Takebe Matsunaga von Vega Only 136 correct Rutherford Only 152 correct Strassnitzky, Dase Clausen Lehmann Rutherford Shanks Only 527 correct Ferguson Computer Calculations of Mathematician Date Places Type of computer Ferguson Jan 1947 Desk calculator Ferguson, Wrench Sept 1947 Desk calculator Smith, Wrench Desk calculator Reitwiesner et al. ENIAC Nicholson, Jeenel NORAC Felton PEGASUS Genuys Jan 1958 IBM 704 Felton May 1958 PEGASUS Guilloud IBM 704 Shanks, Wrench IBM 7090 Guilloud, Filliatre IBM 7030 Guilloud, Dichampt CDC 6600 Guilloud, Bouyer CDC 7600 Miyoshi, Kanada FACOM M-200 Guilloud Tamura MELCOM 900II Tamura, Kanada HITACHI M-280H Tamura, Kanada HITACHI M-280H Kanada, Yoshino, Tamura
Untitled in class) Pythagoras of Samos (?, 569475 BC) Euclid of Alexandria(, 325-265 BC) tsu ch'ung chi (?, 430-501 AD) Leonardo da http://www.csie.ntu.edu.tw/~kmchao/math.html
Did You Know? Bits And Pieces From The NR Trivia Collection 14 Using Archimede's works, Ptolemy of Alexandria (Egypt, 150 AD) gave the value as377/120 (3.14166667 ), and tsu ch'ung chi of China (500 AD) set it to 355/133 http://www.geocities.com/SunsetStrip/Basement/9666/trqv6n2/article5.html
Extractions: with support by Nils Kreutzer Though it is the only card with the keyword "DecKrash" in the base set (v1.0) of Netrunner , PI in the 'Face is somewhat of a staple among sentry ice: If all you want is an end-the-run subroutine on a sentry ice to complement your mix of code gates and walls, PI in the 'Face is the natural candidate. It's a simple but effective little piece of code, and always a good choice in Sealed-deck tournaments. First of all, the name of this card is a pun between pie (as in 'cake') and the Greek letter pi, which is of course the symbol for and the name of a mathematical constant. Further, 'face is a pun between face and interface . Like so many concepts of Netrunner , this card's design can be traced back to R. Talsorian's Cyberpunk 2.0.2.0. Roleplaying Game. Interestingly, in Cyberpunk , PI in the 'Face is not a defense program for data forts, but an attack program used by Runners to fry a data fort's CPU. Here is the description that can be found in Cyberpunk 's Chromebook 3 supplement, on page 73:
The Math Forum - Math Library - History/Biography Pi Through the Ages MacTutor Math History Archives A history of pi the Rhind papyrus(Egypt), Ptolemy, tsu ch'ung chi, al'Khwarizmi, Al'Kashi, Viet, Romanus http://mathforum.org/library/topics/history/?start_at=401
About "Pi Through The Ages" A history of pi the Rhind papyrus (Egypt), Ptolemy, tsu ch'ung chi,al'Khwarizmi, Al'Kashi, Viet, Romanus, Van Ceulen, Gregory, Shanks, Lambert http://mathforum.org/library/view/5241.html
Extractions: Visit this site: http://www-history.mcs.st-and.ac.uk/history/HistTopics/Pi_through_the_ages.html Author: MacTutor Math History Archives Description: A history of pi: the Rhind papyrus (Egypt), Ptolemy, Tsu Ch'ung Chi, al'Khwarizmi, Al'Kashi, Viet, Romanus, Van Ceulen, Gregory, Shanks, Lambert, Euler, Buffon, and many more, with other Web sites and 30 references (books/articles). Levels: Middle School (6-8) High School (9-12) College Languages: English Resource Types: Articles Bibliographies Math Topics: Pi History and Biography
Sci-Philately - A History Of Science On Stamps tsu ch'ung chi (430501) was a Chinese mathematician and astronomer. His approximationof pi was 355/113, which is correct to six decimal places. http://ublib.buffalo.edu/libraries/units/sel/exhibits/stamps/math1a.htm
Extractions: The beginning of mathematics was primitive man's discovery of counting; adding one and one to make two is pictured on this stamp. Upon seeing two birds, an Egyptian makes the cerebral leap to count them on his fingers. ( Detail ) This stamp is the first in a set of ten issued by Nicaragua in 1970 which features important mathematical formulas that changed the face of the earth. Besides showing the law, equation, or formula, the name of its originator, and an application, the reverse of each stamp is printed with a brief paragraph in Spanish explaining the significance of the formula and its far-reaching applications in modern life. Presumably the user can ponder this educational message while licking the stamp; whether the recipient would appreciate it or be aware of it is another matter. The illustrations contain a wealth of interesting detail, and the sci-philatelic sleuth can enjoy identifying the many clues and their relationship to the original formula. The Inca civilization of the 15th century, centered in Peru, did not have a written language, but kept records (and count) of items on an array of colored, knotted cords called quipu. Color, type of knot, spacing and placement of the cords were all meaningful and part of a code that was used to send information on production, census, resources, and taxes owed or collected to distant parts of the empire. Runners carried the quipi which were then decoded at their destination.
ENC: Curriculum Resources: Pi Mathematics (ENC-004496, Full Record) Contents Activities Introduction History Calculations over time Old Testament Archimedes,Syracuse tsu ch'ung chi, China al'Khwarizimi, Baghdad Ludolph Van http://www.enc.org/resources/records/full/0,1240,004496,00.shtm
Extractions: Search ... 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. URL: http://www.ncsa.uiuc.edu:80/edu/RSE/RSEorange/buttons.html
The Contest Center - Pi 5, v(227/23), pi .00000 624, Rubin. 6, 355/113, pi + .00000 0266,tsu ch'ung chi 450AD. 7, v527 - v354 - 1, pi - .00000 0190, Rubin. http://www.contestcen.com/pi.htm
Extractions: This is an open-ended competition to find the best possible approximations to pi (about 3.14159 26535 89793 23846 26433). A good approximation would be an expression which matches pi to more significant digits than the number of digits contained in that expression. For example, the most common approximation to pi is 22/7 which is about 3.14286. This contains 3 digits, and matches the first 3 digits of pi, so it is a fair approximation. We will consider 4 types of approximations. The first type uses only the mathematical operations of addition, subtraction, multiplication, division, and square root. It may not use other operations such as decimal fractions, exponentiation, logarithms, or any trig functions. For example, 355/113 (approximately pi+0.00000 0266) would be a valid expression, but 2 arcsin(1) would not. These approximations can be constructed with ruler and compass.
Www.math.niu.edu/~rusin/known-math/96/buffon result was that of Lazzerini (1901), who made 34080 tosses and got pi = 355/113= 3.1415929 which, incidentally, is the value found by tsu ch'ung chi. http://www.math.niu.edu/~rusin/known-math/96/buffon
Calcul De Pi Par Archimède Translate this page Autres résultats 150 Ptolémée 3.1416 500 tsu ch'ung chi 355 / 113 800 al'Khwarizmi 3.1416 1430 Al'Kashi 14 décimales 1570 Viète 9 http://www.sfrs.fr/e-doc/pi.htm
Math Trivia Quiz 1 4. Who estimated Pi ( ) to be around 355/113? A. tsu ch'ung chi B. PythagorasC. Euclid D. Euler E. Archimedes. 5. What is Pi ( ), exactly? http://www.ktb.net/~cct/geom/trivia1.html
FullChess SMIRF / Mathematik - (Pi-Berechnung - Im 24-Eck) Translate this page Außen-96-Eck) = 3,1415928338 , die sich leicht als Kettenbruch 3+ 1 /(7+ 1 /16)approximieren lässt, welcher mit der von tsu ch'ung chi bekannten Näherung http://www.rescon.de/Wissen/mathepiberech7.html
Extractions: Folgendes Script bezweckt eine Befreiung aus fremden Frames. Start-Seite Antikes Wissen Mathematik Sumerer ... Davidstern 2:1-Methode gemittelt haben. Betrachten wir also das 12-Eck 24-Eck sexagesimal ( aber auch Vieta Archimedes 96-Ecken einzugrenzen, hat er diese effektive, 2:1 gewichtende Mittelwertbildung leider nicht verwendet. Er erhielt zuletzt etwa 2,7 dezimale Nachkommastellen mit: 3 , die sich leicht als Kettenbruch 3+ Tsu Ch'ung Chi sexagesimal. SMIRF Impressum Site-Map
Die Geschichte Der Berechnung Der Zahl Pi Translate this page In China gelang tsu ch'ung chi (430 - 510), der Archimedes' Arbeit vermutlichnicht kannte, eine wichtige Verbesserung pi = 355/113 = 3.141593. http://www.astro.univie.ac.at/~wasi/PI/vielseitig/geschichte_der_berechnung.html
Extractions: verwendete man um 1500 v. Chr. den Wert (16/9)^2 = 3.1605... Archimedes von Syrakus Tsu Ch'ung Chi (430 - 510), der Archimedes' Arbeit vermutlich nicht kannte, eine wichtige Verbesserung: pi = 355/113 = 3.141593. Danach herrschte ein Jahrtausend des Schweigens. Um 1430 errechnete Al'Kashi 14 Stellen; Vieta erlangte 1579 durch Betrachtung eines eingeschriebenen 2^16-Ecks neun, Ludolph van Ceulen 1610 durch ein 2^62-Eck 35 Dezimalen. Euler (1707 - 1783), der erstmals den griechischen Buchstaben pi verwendete (von perimetros, dt. Umfang), schaffte so mittels Bleistift und Papier in einer Stunde 20 Dezimalen von Pi. Johann Dase (1824 1861) verwendete zwei Monate seines Lebens darauf, 200 Stellen der Zahl Pi zu berechnen. William Shanks Yasumasa Kanada mit 51 539 600 000 Nachkommastellen (Rechendauer: 29 Stunden). Doch was bedeuten schon Milliarden angesichts der Unendlichkeit ... wasi@astro.univie.ac.at Freunde der Zahl Pi 3.14159@astro.univie.ac.at
Extractions: Accueil Dictionnaire Rubriques Index ... M'écrire Édition du: Jouer à raisonner: DATES Av. J.-C. Voir aussi Liste alphabétique Lien Date Nom Événement Nicomachus Nombres parfaits, abondants et déficients Ptolémée Diophante Équations Diophantiennes Tsu Ch'ung Chi Calcule p jusqu'à la 9e décimale Vers cette époque, le système de numération indien ressemble au système décimal actuel Al Khwarizmi i Surnom du mathématicien arabe (Ouzbekistan) Abu Ja'far Muhammad ibn Mûsâ al-Khowârizmi Son nom a donné le mot Algorithme Auteur du premier traité important d'algèbre Kitab al jabr w'al-muqabala Son ouvrage a donné le mot Algèbre (al jabr veut dire "accomplissement") Les Arabes adoptent les chiffres indiens, y compris le zéro Serment de Strasbourg Le roman devient le français Gerbert d'Aurillac Gerbert En Espagne, il s'initie à la culture arabe et aux chiffres arabes (qui viennent en réalité d'Inde) Ce sont nos chiffres dont l'usage est très pratique: ils simplifient les opérations Il introduit ces chiffres et les abaques pour compter et multiplier Il écrit des ouvrages d'arithmétique Il perfectionne l'astrolabe Gerbert Devient Pape sous le nom de Sylvestre II PTOLÉMÉE Claude vers 100 - vers 170 70 ans Grec Alexandrie Auteur de « Almageste » (le plus grand) constitué de 13 livres: ouvrage de référence dastronomie jusquà Copernic et Kepler Univers géocentrique: Terre centre de lUnivers. Les planètes tournent autour de la Terre et décrivent des petits cercles (épicycle)
Geschichte tsu ch'ung chi (430-510),der Archimedes' Arbeit vermutlich nicht kannte, eine wichtige Verbesserung p http://www.eag.aa.schule-bw.de/PROJEKTE/MUW/PI/gesch.htm
C Index 1364*) Cesàro, Ernesto (1069*) Ceulen, Ludolph van (223*) Ceva, Giovanni (296),Ceva, Tommaso (172*) Ch'in chiuShao (62) ch'ung chi tsu (127*) Chandrasekhar http://www-gap.dcs.st-and.ac.uk/~history/Indexes/C.html
