Timeline Yasumasa Kanada from the Computer Centre at the University of Tokyo has now computedpi to 6.4 billion places, and in six months hopes to increase the new http://www.mste.uiuc.edu/mathed/HumanResources/daleleibforth/timeline
Bibliography Kanada, Yasumasa. Lecture on Pi Calculationpushing the limits of number crunchingmachines. University of Illinois Champaign/Urbana. 27 November 1995. http://www.mste.uiuc.edu/mathed/HumanResources/daleleibforth/bib
Philippe B. De L'Arc - Digressions Translate this page 250. Miyoshi et Yasumasa Kanada, 1981, -, 2 000 036. Tamura, 1982, -,8 388 576. Yasumasa Kanada, Yoshino et Tamura, 1982, -, 16 777 206.Gosper, http://perso.club-internet.fr/pboursin/bonus2.htm
Extractions: PostgreSQL ... englischen Lexikon Google News zum Stichwort Ludolph van Ceulen 28. Januar in Hildesheim 31. Dezember in Leiden ) war ein niederl¤ndischer Mathematiker . Ludolph van Ceulen wurde durch die auf 35 Dezimalstellen genaue Berechnung der Kreiszahl Archimedes Vielecken Kreis n des n-Ecks neu zu berechnen. Archimedes fand mit Hilfe von Strahlensatz und Satz des Pythagoras und s n n n n Mathematiker Jahr Dezimalstellen al-Khwarizmi ca. 800 Fran§ois Vi¨te Ludolph van Ceulen Georg Freiherr von Vega Daniel Shanks Levi B. Smith, John W. Wrench Daniel Shanks, John W. Wrench Yasumasa Kanada, Sayaka Yoshino, Yoshiaki Tamura Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo Chudnovskys Yasumasa Kanada, Daisuke Takahashi Yasumasa Kanada, Daisuke Takahashi B¼cher bei Amazon.de zum Stichwort: Ludolph van Ceulen Info: Dieser Artikel aus Wikipedia wird durch die GNU FDL lizenziert.
Ludolfina Yoshiaki Tamura, 1982, 2097144, Yoshiaki Tamura i Yasumasa Kanada, 1982, 4194288,metody AGM. Yasumasa Kanada i Yoshiaki Tamura, 1986, 33554414, metody AGM. http://pi.home.staszic.waw.pl/~pi/liczby/pi.html
Extractions: L niewymierna i przestêpna Autor Czas i miejsce Metoda, komentarz Babiloñczycy i inne ludy staro¿ytne warto¶æ najpowszechniej stosowana w staro¿ytno¶ci do celów praktycznych (ocena obwodu lub pola ko³a, np. w Biblii: 1 Król. 7:23) Egipcjanie pocz. II tys. p.n.e. przybli¿enie otrzymane przy próbie oceny pola ko³a przez pole o¶miok±ta foremnego Archimedes Syrakuzy, III w. p.n.e. metoda wprowadzona przez Archimedesa i zastosowana do 96-k±ta foremnego Ptolemeusz Aleksandria, ok. 150 n.e. wynik otrzymany po rozwa¿eniu 360-k±ta (metoda nieco inna ni¿ Archimedesa) ró¿ni autorzy ¶redniowieczni ocena powszechnie przyjmowana w nauce przez ponad 1000 lat (np. Czung Hing ok. 250 n.e., Brahmagupta, ok. 640, Al-Chwarizmi, ok. 800) Liu Hui Chiny, III w. n.e. metoda Archimedesa dla 3072-k±ta Ariabhata Indie, ok. 500 n.e. metoda Archimedesa
Untitled Document In 1999, Yasumasa Kanada and his colleagues at the University of Tokyo computedpi to a record 206 billion decimal digits. Kanada, Yasumasa. 1999. http://www.sssgrp.com/Menu/readmepi.html
Extractions: I would like to acknowledge Mr. Aoki Mitsuru, High Energy Physics Laboratory, Nagoya University, http://www.hepl.phys.nagoya-u.ac.jp/~mitsuru/pi-e.html , for posting 400 million digits of Pi (excluding the first digit, 3) in manageable groups of 10 million digits. This computation of Pi was made around May 1998. 2. Source of Artwork
List Of Mathematical Topics (J-L) Kfold perfect number Kac Kac, Mark K?ler, Erich K?ler manifold Kaiser window Kalman filter Kanada, Yasumasa Kantorovich, Leonid http://www.fact-index.com/l/li/list_of_mathematical_topics__j_l_.html
Extractions: Main Page See live article Alphabetical index A-C D-F G-I - J-L - M-O P-R S-U V-Z Jacobi, Carl Gustav Jakob Jacobi identity Jacobian Jacobian matrix ... Johnson solid Jones, Vaughan Frederick Randal Jordan, Camille Jordan curve theorem Jordan normal form Josephus permutation ... Julia set K-Hyperperfect number K-fold perfect number Kac Kac, Mark Kähler, Erich Kähler manifold Kaiser window ... Kalman filter Kanada, Yasumasa Kantorovich, Leonid Vitalyevich Karnaugh map Kastner, Abraham Gotthelf KdV equation Kêng-Chih, Tsu Kepler, Johannes Kepler's laws of planetary motion Kepler solid Kernel (algebra) ... Koch snowflake Kodaira, Kunihiko Kolmogorov, Andrey Nikolaevich Kolmogorov-Arnold-Moser theorem Kolmogorov Smirnov test Kolmogorov space ... Kontsevich, Maxim Korteweg, Diederik Kovalevskaya, Sofia Kovalevskaya, Sofia Vasilyevna Kowa, Seki Kramp, Christian Kronecker, Leopold Krull dimension Kruskal, Martin Kruskal's algorithm K-theory Kummer Kummer, Ernst ... Kurtosis Kutta, Martin Wilhelm L-function L-system La Géometrie Lafforgue Lafforgue, Laurent
Wiswijzer 6600 (1967) 500.000 Guilloud and Bouyer (1973) 1.000.000 Tamura Kanada (1983) 16.777.216Chudnovsky brothers (1989) 1.011.196.691 Yasumasa Kanada (1989) 1.073 http://www.wiswijzer.nl/pagina.asp?nummer=314
Brief History Of Pi Calculation With Computers Computer Centre, U. of Tokyo, 128 CPUs Yasumasa Kanada 9 man team 2002/09 1.24trillion HITACHI supercompute, Information Technology Center, U. of Tokyo http://pw1.netcom.com/~hjsmith/Pi/Records.html
Record For Pi : 68.7 Billion Decimal Digits Yasumasa Kanada Computer Centre, University of Tokyo Bunkyoku Yayoi 2-11-16 Tokyo113-8658 Japan Fax +81-3-3814-7231 (office) E-mail Kanada@pi.cc.u-tokyo.ac http://pw1.netcom.com/~hjsmith/Pi/Record68.html
Extractions: Our latest record was established as follows: (More details soon at http://pi2.cc.u-tokyo.ac.jp/index.html Yasumasa KANADA and Daisuke TAKAHASHI Declared record: Two independent calculations based on two different algorithms generated 68,719,476,736 (=2^36) decimal digits of pi and comparison of two generated sequences matched 68,719,476,693 decimal digits, e.g., 43 decimal digits difference. Then we are declaring 68,719,470,000 decimal digits as the new world record. Main program run: Programs were written by Mr. Daisuke TAKAHASHI, a Research Associate at our Computer Centre. CPU used was HITACHI SR8000 at the Computer Centre, University of Tokyo. Half of total CPU, e.g. 64PE's, were definitely used through single job parallel processing for both of programs run. Yasumasa KANADA Computer Centre, University of Tokyo Bunkyo-ku Yayoi 2-11-16 Tokyo 113-8658 Japan Fax : +81-3-3814-7231 (office) E-mail: email@example.com
Pi Charts Chudnovsky brothers, 1989, 1,011,196,691. Yasumasa Kanada, 1989, 1,073,740,000. Chudnovskybrothers, 1991, 2,160,000,000. Yasumasa Kanada, 1995, 3,221,220,000. http://www.geocities.com/SiliconValley/Pines/5945/charts.html
Extractions: Pi charts Here are some of the records in the calculation of pi over the centuries: NAME YEAR NUMBER OF DECIMAL PLACES Al-Kashi Ludolph van Ceulen Sharp Machin Johann Dase Ferguson and Wrench ENIAC Guilloud and Bouyer Chudnovsky brothers Yasumasa Kanada Chudnovsky brothers Yasumasa Kanada Yasumasa Kanada, at the University of Tokyo, found the new record number of digits between 16 and 26 June 1995. He used two methods to check himself: Borwein's quartic convergent algorithm and the Gauss-Legendre algorithm. Chudnovsky brothers over 8 billion!!! Find out more about the Chudnovsky brothers here Comparison of "Time Per Digit" in certain calculations of pi! Year Computer Time # of digits Time per digit Wm. Shanks (by hand) Shanks calculated those decimals by the Machin's formula (1706): pi/4 = 4artg(1/5) - artg(1/239) and used the artg power-serie of Gregory-Leibniz. ca. 22 yrs. 707 (only 527 were correct-(Proceedings of The Royal Society of London, Vol. XXI., p.319) 1 week! Johann Dase (by hand) < 2 months 7 hrs. D. F. Ferguson, desk calculator ca. 1 yrs.
A Treatise On Pi The current world record is held by Yasumasa Kanada of the University of Tokyo,who in 1999 calculated to 206,158,430,000 decimal places using a computer http://www.geocities.com/pi_is_my_favourite_number/Pi/Pi.html
Extractions: The number has always been my favourite number because of its unparalleled aesthetic beauty. On this page, I shall provide an overview of this extraordinary number: its history, properties, and its interesting facts. History of Pi Ancient History is perhaps the most famous ratio in mathematics. It is defined as the ratio between the circumference of a circle and its diameter. Throughout the ages, mathematicians have strived to find the value of . One of the earliest reference to was recorded in the Rhind Papyrus during the Egyptian Middle Kingdom, and was written by a scribe named Ahmes around 1650 BC. Ahmes began the scroll with the words: "The Entrance Into the Knowledge of All Existing Things", and made passing remarks that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which comprises of various mathematical problems and their solutions, the area of a circle is found using a rough sort of It is interesting to note that the number is also indrectly quoted in the Bible. There is a little-known verse that reads
Facts About Pi arithmetic operations); 1988 Yasumasa Kanada of the University of Tokyocomputed pi to 201,326,000 decimal places. 1990 The Chudnovsky http://www.pen.k12.va.us/Div/Winchester/jhhs/math/facts/pifacts.html
Extractions: In Kings, it states, "And he made a molten sea, ten cubits from one brim to the other: it was round all about, and a line of thirty cubits did compass it about." 240 B.C. Archimedes found pi to be between 223/71 and 22/7 150 A.D. Ptolemy found pi to be approximately 377/120 (or 3.1416) 480 A.D. In China, pi was found to be approximately equal to 355/113 or 3.1415929 ... 1150 Bhaskara (a Hindu) gave 3927/1250 as an accurate value of pi 1579 Viete used polygons having 393,216 sides to evaluate pi correct to 9 places
Facts About Pi Professor Yasumasa Kanada and nine other researchers at the Information TechnologyCenter at Tokyo University calculated the value for pi with a Hitachi http://www.pen.k12.va.us/Div/Winchester/jhhs/math/facts/pifacts3.html
Extractions: TOKYO (Dec. 6) - A team of researchers at a leading national university have set a world record by calculating the value of pi to 1.24 trillion places, one of the researchers said Friday. Professor Yasumasa Kanada and nine other researchers at the Information Technology Center at Tokyo University calculated the value for pi with a Hitachi supercomputer over 400 hours in September, project team member Makoto Kudo said. The new calculation is more than six times the number of places in the record currently recognized by Guinness World Records - 206.158 billion places - which Kanada also helped calculate in 1999. ``We would need to verify it, but it sounds like Professor Kanada has broken his own record,'' Guinness World Records spokesman Neil Hayes said. He said a Guinness math expert would need to verify the data. Kanada's team spent five years designing the program used in the September experiment, Kudo said. The Hitachi supercomputer is capable of 2 trillion calculations per second, or twice as fast as the one used for the current Guinness record calculation. Pi, usually given as 3.14, is the ratio of the circumference to the diameter of a circle and has an infinite number of decimal places.
Extractions: Subject: New world record of pi : 51.5 billion decimal digits Dear pi people; Now is the time for the announcement of new world record of pi. It took longer time than our expectation. Nearly two years has passed since we got new world record of 6.4 billion. Now, we got eight times more record than 6.4 billion as the following texts which you can get with anonymous ftp to 'www.cc.u-tokyo.ac.jp' Yasumasa KANADA , Computer Centre, University of Tokyo Our latest record was established as follows: Yasumasa KANADA and Daisuke TAKAHASHI Two independent calculations based on two different algorithms generated 51,539,607,552 (=3*2^34) decimal digits of pi and comparison of two generated sequences matched 51,539,607,510 decimal digits, e.g., a 42 decimal digits difference. Then we are declaring 51,539,600,000 decimal digits as the new world record. ( See related lecture on Pi Main program run:
CienciaNet : Pi Translate this page En 1983, Yoshiaki Tamura y Yasumasa Kanada, en menos de 30 h, en unHITAC M-280 H obtuvieron 16.777.206 (2 24 ) cifras. En Julio http://ciencianet.com/pi.html
How To Compute Digits Of Pi ? The current record is held by Yasumasa Kanada and Daisuke Takahashi from the Universityof Tokyo with 51 billion digits of pi (51,539,600,000 decimal digits to http://db.uwaterloo.ca/~alopez-o/math-faq/mathtext/node12.html
Extractions: Next: Euler's formula: e^(i pi) Up: Special Numbers and Functions Previous: Special Numbers and Functions Symbolic Computation software such as Maple or Mathematica can compute 10,000 digits of pi in a blink, and another 20,000-1,000,000 digits overnight (range depends on hardware platform). It is possible to retrieve 1.25+ million digits of pi via anonymous ftp from the site wuarchive.wustl.edu, in the files pi.doc.Z and pi.dat.Z which reside in subdirectory doc/misc/pi. New York's Chudnovsky brothers have computed 2 billion digits of pi on a homebrew computer. The current record is held by Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo with 51 billion digits of pi (51,539,600,000 decimal digits to be precise). Nick Johnson-Hill has an interesting page of pi trivia at: http://www.users.globalnet.co.uk/ nickjh/Pi.htm This computations were made by Yasumasa Kanada, at the University of Tokyo. There are essentially 3 different methods to calculate pi to many decimals.
How To Compute Digits Of ? The current record is held by Yasumasa Kanada and Daisuke Takahashi from the Universityof Tokyo with 51 billion digits of (51,539,600,000 decimal digits to be http://db.uwaterloo.ca/~alopez-o/math-faq/node38.html
Extractions: Next: Euler's formula: Up: Special Numbers and Functions Previous: Special Numbers and Functions Symbolic Computation software such as Maple or Mathematica can compute 10,000 digits of in a blink, and another 20,000-1,000,000 digits overnight (range depends on hardware platform). It is possible to retrieve 1.25+ million digits of via anonymous ftp from the site wuarchive.wustl.edu, in the files pi.doc.Z and pi.dat.Z which reside in subdirectory doc/misc/pi. New York's Chudnovsky brothers have computed 2 billion digits of on a homebrew computer. The current record is held by Yasumasa Kanada and Daisuke Takahashi from the University of Tokyo with 51 billion digits of (51,539,600,000 decimal digits to be precise). Nick Johnson-Hill has an interesting page of trivia at: http://www.users.globalnet.co.uk/ nickjh/Pi.htm The new record for the number of digits of is 4.29496 billion decimal digits of pi were calculated and verified by 28th August '95. Related documents are available with anonymous ftp to www.cc.u-tokyo.ac.jp.
APM - Educação E Matemática Translate this page Mas Yasumasa Kanada continuou a sua investigação e, em 1999 estabeleceuo recorde 206.158 milhares de milhão de casas decimais. http://www.apm.pt/apm/curiosidades/curio14.htm
- Organization Laboratories Limited; OSHIYAMA, Atsushi Professor, University of Tsukuba;Kanada, Yasumasa Professor, University of Tokyo; SAITO, Susumu http://www.tokyo.rist.or.jp/cnt/menu/org_e.html