61. Table2 Translate this page 51 milliards de décimales. par Yasumasa Kanada de l'université de Tokyo. (L'écriture de cette approximations nécessite 100 000 livres de 200 pages. http://www.math.uha.fr/Pi/Table2.html

Les meilleures approximations de p au 20 NOM DATE NOMBRE DE DECIMALES EXACTES Ferguson Ferguson Ferguson et Wrench Smith et Wrench Reitwiesner et al. ( ENIAC) Nicholson et Jeenel Felton Genuys Felton Guilloud Shanks et Wrench Guilloud et Filliatre Guilloud et Dichampt Guilloud et Bouyer Miyoshi et Kanada Guilloud Tamura Tamura et Kanada Kanada, Yoshino et Tamura Ushiro et Kanada Gosper Bailey Kanada et Tamura Kanada, Tamura, Kobo et al. Kanada et Tamura Chudnovsky Chudnovsky Kanada et Tamura Chunovsky Kanada et Tamura Chudnovsky Chudnovsky Takahashi et Kanada Kanada Kanada RECORD ACTUEL

62. The Mad Cybrarian's Library: Free Online E-texts - Authors K-Kz Kanada, Yasumasa One Divided by pi (SUBJECT Mathematics Math 21 to a milliondigits ) Gutenberg FTP UITXT 996 Kb ZIP477 Kb SLTXT - ZIP ENTXT - ZIP. http://www.fortunecity.com/victorian/richmond/88/1libk.htm

web hosting domain names email addresses related sites The Mad Cybrarian's Library Authors: K-Kz Kanada, Yasumasa One Divided by pi (SUBJECT: Mathematics Math #21 to a million digits ) TXT 996 Kb - ZIP 477 Kb SL: TXT ZIP EN: TXT ZIP Kane, Eliza: Letter inviting Mrs. Brown and Miss Linn to tea, n.d.(UVa) 18(5 KB) Kant, Immanuel : Kane, Mr.: Letter inviting Miss Linn for a ride, n.d. (UVa) 18(5 KB) Kay Ross: Keary, Eliza Little Seal-skin and Other Poems (1874)(HTML at Victorian Women Writers) (size: 213K, 1 gif) Keary, Maud Enchanted Tulips and Other Verses for Children (1914)(HTML at Victorian Women Writers) [includes poems by Annie Keary and Eliza Keary] (size: 95K, 1 gif) Keats, John Keene translation: Brazell, Karen : Sekidera Komachi (UVa) 1970(30 KB) Keene, H. G.: The Fall of the Moghul Empire of Hindustan (1887 edition) Matisoff, Susan : Semimaru (UVa) 1970(35 KB) Kehoe, Brendan P. TXT 167 Kb - ZIP 70 Kb SL: TXT ZIP EN: TXT ZIP Keith, Marian: The Black Bearded Barbarian: The Life of George Leslie Mackay of Formosa Keller, Helen:

63. 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

Voltar Outra vez pi? Susana Diego (com base num artigo da Associated Press que pode encontrar-se em http://www.sfgate.com/cgi-bin/article.cgi?file=/news/archive/2002/12/06/international0835EST0499.DTL adaptada da obra de David Blatner 'The Joy of pi', 1997 20 de fevereiro de 2003 Projecto "Matemática é de todos"

64. Inverseur De Plouffe Translate this page Machine Hitachi SR8000. Qui Yasumasa Kanada et Daisuke Takahashi (Universitéde Tokyo). Qui Yasumasa Kanada et Daisuke Takahashi (Université de Tokyo). http://pi.lacim.uqam.ca/fra/records_fr.html

Table des records de calcul de constantes Simon Plouffe Notes Constantes classiques Pi = 3.141592653589... Temps de calcul : 33 et 40 heures pour chaque calcul. Machine: Hitachi SR8000. Quand : du 26 juin au 20 septembre 1999. 1/Pi = 0.3183098661... Temps de calcul : 33 et 40 heures. Machine: Hitachi SR8000. Quand : du 26 juin au 20 septembre 1999. E = 2.71828182845... Gros Fichiers Who : Xavier Gourdon When : Le 14 novembre 1999 (verification : 21 novembre 1999) Temps de calcul : 39h et 52 minutes sur un IBM ThinkPad Constante de Catalan = 0.915965594... Gros Fichiers Temps de calcul: 18 hours, 1 min. Qui : Xavier Gourdon Xavier.Gourdon@inria.fr Precision Temps de calcul: Machines :IBM S/390 G5 CMOS (9672-RX6) et IBM Power2 SC 135 MHz, 2 GB RAM, GNU C++ 2.8.0, AIX 4.1.5. et IBM PowerPC 604e 233 MHz, 1 GB RAM, GNU C++ 2.8.0, AIX 4.1.5. Qui : Sebastian Wedeniwski ( wedeniws@de.ibm.com Constante d'Euler-Mascheroni ou gamma = 0.577215664901... Qui : Patrick Demichel et Xavier Gourdon. Quand : entre le 23 et 26 septembre 1999.

65. Plouffe's Inverter Machine HITACHI SR8000. Who Yasumasa Kanada and Daisuke Takahashi (Universityof Tokyo). Who Yasumasa Kanada and Daisuke Takahashi . http://pi.lacim.uqam.ca/eng/records_en.html

Table of current records for the computation of constants last update was June 8, 2000 by Simon Plouffe N'th binary digit computations Other records Notes Classical constants Pi = 3.141592653589... Precision : decimal digits (almost 3*2^36). Time of computation : about 37 and 46 hours for each computation. Machine: HITACHI SR8000 Who : Yasumasa Kanada and Daisuke Takahashi (University of Tokyo). When : From June 26 to September 20 1999 (2 independant runs). Algorithms : Gauss-Legendre and Borwein's 4'th order iteration. 1/Pi = 0.3183098661... Precision digits which is almost 3*2^36. Time of computation: Same as above When : From June 26 to September 20 1999 (2 independant runs). Algorithm : Gauss-Legendre and Borwein's 4'th order iteration. E = 2.71828182845... Precision : digits. (for downloads see The Big files directory) Time of computation: real time: 79 hours and 30 minutes. Who : Xavier Gourdon When : 1999, Nov, 14 (verification : 1999, Nov 21) Timing : The computation took 39h and 52 minutes on a IBM ThinkPad (PII 350 Mhz, 320 Mo of memory). The verification took 40 hours 25

66. U. Of Western Ontario /All Locations Sorted by Title. Author, Kanada, Yasumasa. Title, 1/pi to 1.000.000 digits electronicresource / calculated by Yasumasa Kanada. Publisher, Champaign, Ill. http://alpha.lib.uwo.ca:5701/search/XEbooks -- UWO.&SORT=A&searchscope=13/XEbook

67. U. Of Western Ontario /All Locations Record 2 of 88006 Author, Kanada, Yasumasa. Title, 1/pi to 1.000.000 digits electronicresource / calculated by Yasumasa Kanada. Publisher, Champaign, Ill. http://alpha.lib.uwo.ca:5701/search/dEbooks -- UWO./debooks uwo/-5,-1,0,B/frames

AUTHOR TITLE SUBJECT MEDICAL SUBJECT WORD KEYWORD CALL NO Brescia University College Library Business Library Education Library Huron University College Library Music Library Law Library The D. B. Weldon Library Information and Media Studies Int'l Centre for Olympic Studies Electronic Resources Journals View Entire Collection Record 2 of 88006 Corporate au WHO Task Group on Environmental Health Criteria for 1,1,1-Trichloroethane. Title 1,1,1-trichloroethane. Publisher Geneva : World Health Organization, 1992. Click on the following to: Connect to Internet resource LOCATION CALL # STATUS TAY stack WA730.E615 no.136 1992 IN LIBRARY Description Series Note Summaries in French and Spanish. Bibliography Includes bibliographical references (p. 93-112). Note Also available via the Internet. Med subject Trichloroethanes adverse effects. Environmental Exposure. Subject Trichloroethane. Ebooks UWO. Alternate au Dobson, S. (Stuart) Jensen, Allan A. United Nations Environment Programme. International Labour Organisation. ... International Program on Chemical Safety. ISBN OCLC #

68. 404 Not Found Kanada, Yasumasa • One Divided By pi (to 1 million digits) Kane, William Terence• For Greater Things; the story of Saint Stanislaus Kostka Kay, Ross http://www.globusz.com/authors_k.html

Not Found The requested URL was not found on this server. Apache Server at globusz.com

69. Www.math.ucl.ac.be/~magnus/num1a/pinews.txt Yasumasa Kanada Computer Centre, University of Tokyo Bunkyoku Yayoi 2-11-16 Tokyo113 Japan Fax +81-3-3814-7231 (office) E-mail Kanada@pi.cc.u-tokyo.ac.jp http://www.math.ucl.ac.be/~magnus/num1a/pinews.txt

sci.math #139994 (18 + 1065 more) [1] From: xpolakis@prometheus.hol.gr (Antreas P. Hatzipolakis) Newsgroups: sci.math [1] Pi to 6+ billions places (was: Pi to a million places) Date: Sat, 01 Jun 1996 00:04:28 +0200 Organization: Hellas On Line Lines: 89 Message-ID: NNTP-Posting-Host: cronos.hol.gr On Wed, 29 May 1996

70. Só Páginas Sobre O Número PI Pi through the ages; Yasumasa Kanada's FTP site Computer Centre, University of Tokyo Latest Record of Yasumasa Kanada; 6.4 Billion 6,400,000,000,000 digits! http://www.mat.uc.pt/~jaimecs/pipag.html

A Trillion Pieces of Pi in Ivars Peterson's MathTrek POETIC LICENCE: Pi calculated to 1.24 trillion digits by Kaleem Omar, Daily Times (Pakistan) Boffins find 1.2 trillion pieces of pi (news.com.au) A Much Bigger Piece Of Pi (slashdot.org) Researchers calculate pi to more than 1 trillion places for world record (SFGate.com) A very precise slice of pi (The Japan Times) - Mathematicians tackle the seeming randomness of pi's digits (Science News) Current publisized world record of pi calculation Frequency distribution of digits up to 1,200,000,000,000-th digit of decimal digit of pi , from Kanada Laboratory (Tokyo, Japan). O dia do PI aproxima-se // PI Day is approaching... National Pi Day is March 14th (3.14). PI APPROXIMATION DAY "This Pungenday (the 57th of Confusion) is Pi Approximation Day, being on the Aneristic Calendar 22/7" - Pi Approximation Day is on the 22/7 - that is, July 22. For the past few years, people at Chalmers University have celebrated it. Pi Approximation Day (March 14) e-cards Pi Approximation Day (March 14) is a day to recognise the importance of our favorite number, Pi [3.1428..]. So, let's lay back and try to memorise the value of Pi giving thought to the marvellous mysteries behind this number. While you are at it, why not celebrate by eating pies [Pi's] and send some Pi greeting cards to your friends? (123Greetings) Tudo sobre o PI // All about PI Conhecendo melhor PI Segredos de PI Valor de PI PI, o filme

71. Books And Reading - Queens Borough Public Library Kendall F.; Clark, Donna. 1/pi to 1.000.000 digits, Kanada, Yasumasa.The online world, De Presno, Odd. Organic syntheses, . The origin of http://www.queenslibrary.org/books/ebook/ebook.asp?category=Science

72. Book_id Full_title Author Publisher 2009052 Come Unto Me All Ye BiblioBytes,. 2009498, 1/pi to 1.000.000 digits, Kanada, Yasumasa. ProjectGutenberg,. 2011141, 100% the story of a patriot, Sinclair, Upton. http://library.usask.ca/dbs/docs/publicly_accessible_collection_title.htm

author publisher "Come unto Me all ye that labour" Boston, Thomas. Mount Zion, "Compel them to come in" Spurgeon, C. H. Mount Zion, "Hell fer Sartain" and other stories Fox, John. University of Virginia Library, "House divided" speech Lincoln, Abraham. Project Gutenberg, "Mr. Charles W. Chesnutt's stories" Howells, William Dean. University of Virginia Library, "My escape from slavery" Douglass, Frederick. Project Gutenberg, "She stoops to conquer" or, The mistakes of a night, a comedy Goldsmith, Oliver. Project Gutenberg, "Speaking of operations" Cobb, Irvin, S. Project Gutenberg, "Till he come" communion meditations and addresses Spurgeon, C. H. Christian Classics Et hereal Library, "Undo" Hutsko, Joe. Project Gutenberg, (Of the) institution and education of children Montaigne, Michel de. BiblioBytes, (Of the) standard of taste Hume, David. BiblioBytes, (Of) agriculture Cowley, Abraham. BiblioBytes

73. 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

Next: Euler's formula: Up: Special Numbers and Functions Previous: Special Numbers and Functions How to compute digits of ? 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.

74. 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

Next: Euler's formula: e^(i pi) Up: Special Numbers and Functions Previous: Special Numbers and Functions How to compute digits of pi ? 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.

75. 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

Portada Mapa Buscar La pregunta ... PMF CienciaNet Busca en CIENCIAnet cómo buscar Curiosidades Elementos Experimentos ... Más ... Algunas curiosidades sobre el número Pi ( Pi es la razón de la circunferencia de un circulo a su diámetro En distintas culturas, china, egipcia, europea, india, etc., se trato de obtener mejores aproximaciones de Pi por ser de aplicación en campos tan distintos como la astronomía o la construcción. Muchos de los intentos de evaluar Pi en la antigüedad utilizaban el método de calcular el perímetro de polígonos inscritos y circunscritos a circunferencias. Modernamente para evaluar Pi se utiliza una serie infinita convergente. Este método fue utilizado por primera vez en Kerala (India) en el Siglo XV La probabilidad de que dos enteros positivos escogidos al azar sean primos entre si es 6/Pi Si se eligen al azar dos números positivos menores que 1, la probabilidad de que junto con el número 1 puedan ser los lados de un triángulo obtusángulo es (Pi-2)/4 En 1706, el inglés

76. Pushing Back Pi So just how accurately do we know what it is? To find out you might like totalk to Yasumasa Kanada and his colleagues at the University of Tokyo. http://plus.maths.org/issue3/news/pi/

PRIME NRICH PLUS Current Issue ... Subject index Issue 23: Jan 03 Issue 22: Nov 02 Issue 21: Sep 02 Issue 20: May 02 Issue 19: Mar 02 Issue 18: Jan 02 Issue 17: Nov 01 Issue 16: Sep 01 Issue 15: Jun 01 Issue 14: Mar 01 Issue 13: Jan 01 Issue 12: Sep 00 Issue 11: Jun 00 Issue 10: Jan 00 Issue 9: Sep 99 Issue 8: May 99 Issue 7: Jan 99 Issue 6: Sep 98 Issue 5: May 98 Issue 4: Jan 98 Issue 3: Sep 97 Issue 2: May 97 Issue 1: Jan 97 Pushing back Pi The decimal number system was introduced to Europe nearly 800 years ago and is a vast improvement on the previous system of Roman numerals (see " The life and numbers of Fibonacci " elsewhere in this issue). But good though it is, the decimal number system cannot represent all numbers exactly. Although sums like 4 divided by 33 result in values with an infinite number of digits to the right of the decimal point, they always have repeating patterns. We can use special dots placed above the digits to show this. Numbers like Pi, on the other hand, have no repeating pattern. So just how accurately do we know what it is? To find out you might like to talk to Yasumasa Kanada and his colleagues at the University of Tokyo. They have recently broken the world record for calculating the most accurate approximation using a Hitachi supercomputer. The Japanese researches have calculated 50 billion decimal digits of Pi, that's about 10 digits for every person in the world today. So if this sequence of digits contains no repeating pattern does that mean it's completely random? It depends who you ask. Mathematicians have been grappling with the idea of just what makes a random sequence for decades. A simple way of measuring randomness could have applications in a wide range of fields from the analysis of the stock market to the prevention of sudden infant death syndrome.

77. THE SIZE OF PI Professor Yasumasa Kanada of the University of Tokyo and Dr Daisuke Takahashimade the calculation by running two different programs in 1999. http://www.il-st-acad-sci.org/kingdom/math1001.html

THE SIZE OF PI The most decimal places to which Pi has been calculated is 206,158,430,000. Professor Yasumasa Kanada of the University of Tokyo and Dr Daisuke Takahashi made the calculation by running two different programs in 1999. The number Pi (22/7) is one of the most important numbers in mathematics. Whenever circles are involved in any calculation, Pi is a critical number. Pi is what mathematicians call an irrational number, it has an infinite number of digits after its decimal point, which follow no repeating pattern. Because of this lack of a pattern, many people have become fascinated by calculating Pi to more and more accurate values. The latest value, by Yasumasa Kanada is 3.141 followed by 206,158,430,000 more digits! The fact that Pi is a constant has been known since prehistory. In the Bible, it is stated approximately as being equal to 3. Pi is always equal to half the circumference of a circle, divided by its radius. The main program used by the mathematicians ran for 37 h 21 min. Mathematics databases Kingdoms Project ISAS homepage Armando G. Amador

78. 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

79. Programme UK), Performance of Automatically Tuned Parallel GMRES(m) Method on DistributedMemory Machines Hisayasu Kuroda, Takahiro Katagiri and Yasumasa Kanada (Japan). http://vecpar.fe.up.pt/2000/Prog.html

Final Programme The final programme consists in 66 papers, 11 posters, 6 invited talks and 3 tutorials. All papers and posters will be included in the proceedings to be distributed during the conference; however, only the 67 papers will be eligible for publication by Springer. The conference will open on Wednesday (21 June) and close on Friday evening (23 June) with a banquet, after which you are invited to participate in the annual celebration of São João (Saint John), the city patron saint. The day before the conference (20 June, Tuesday) has been allocated to 3 tutorials (one full day and two half day) on the following subjects: June tuesday Linear Algebra Algorithms and Software for Large Scientific Problems (Full day) by Jack Dongarra (University of Tennessee and ORNL, USA), Iain Duff (CERFACS, France, and RAL, United Kingdom) and Danny Sorensen (Rice University, USA) Benchmarking High Performance Computers: Fundamentals and Practice (Half day) by Aad J. Van der Steen (Utrecht University, The Netherlands) The Globus Grid Programming Toolkit (Half day) by Ian Foster (Argonne National Lab. and the University of Chicago, USA)

80. Stu's Pi Page by Steve Pagliarulo, Xavier Gourdon, Takuya Ooura, Carey Bloodworth, Mikko Tommila,Sebastian Wedeniwski, Alan Pittman, Gio Ciampa, and Yasumasa Kanada. http://home.istar.ca/~lyster/chart.html

B Program Speed Records F astest program C hart of programs ... isclaimer B Size Records S uper computer H ome computer Links A uthors's links E -mail to Stu ... i-Hacks e-mail discussion group THE FASTEST PI PROGRAMS that will run on your PC Consult the chart below for the programs by Steve Pagliarulo, Xavier Gourdon, Takuya Ooura, Carey Bloodworth, Mikko Tommila, Sebastian Wedeniwski, Alan Pittman, Gio Ciampa, and Yasumasa Kanada. A recent pi program running on Linux, named Schnell-pi and written by Dominique Delande is potentially faster than all these. No windows version of this program exists for the moment. The programs below were run in Windows 98 in 'Safe Mode' so that no other programs conflicted Please see Dara's page for another comparison of ALL these programs and more, run on Linux..... Stu's world ranking Program Author digits digits Effic- iency 16-meg digits Maximum digits Programming Comments QuickPi v. 2.01 Steve Pagliarulo 0.67 secs 8.76 secs. 250 million Based on Chudnovskys' algorithm, with other algorithms included, also calculates sqrt-2 and e PiFast.EXE ver 4.2

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