81. Calcul De Pi Translate this page 51 539 600 000. en 29 heures, avec 212Go, par Yasumasa Kanada. 6/12/2002. HITACHI.1 240 000 000 000. Yasumasa Kanada, en 400 heures de calcul (1). http://www.mines.inpl-nancy.fr/~tisseran/cours/pi/

connues ENIAC 70 heures NORC 13 minutes Pegasus IBM 704 1 h 40 mn IBM 704 IBM 7090 8 h 43 mn IBM 7030 CDC 6600 CDC 7600 23 h 18 mn Facom M200 HITACHI M280H HITACHI M280H HITACHI M280H CRAY 2 28 h HITACHI S810/20 NEC SX2 CRAY 2 IBM 3090 HITACHI S3800/480 HITACHI SR2201 1024 processeurs en 29 heures, avec 212Go, par Yasumasa KANADA HITACHI Yasumasa KANADA, en 400 heures de calcul ( source http://www.jcanu.hpg.ig.com.br/history/h4dec/h4dec06.html ) = 1 - x + x - x Suite : Ecole des Mines de Nancy Document : http://www.mines.u-nancy.fr/~tisseran/cours/pi/ Remarques, suggestions, questions, ... : e-mail tisseran@mines.u-nancy.fr

82. Online Books, Ebooks, E-books By Rproject.org Kafka, Franz Metamorphosis Read the ebook Kamban, Gudmundur Hadda Pada Read thee-book Kanada, Yasumasa One Divided By pi (to 1 million digits) Read the e http://www.rproject.org/list.php?i=1&sv=K

83. Calculate Pi 1) The easy to run Super_Pi (for MSWindows™) by Yasumasa Kanada Download Super_Pinow (in a 72 kb .zip file) and Calculate up to 32 Million digits of Pi. http://thestarman.pcministry.com/math/pi/piprogs.html

Programs for Calculating On Your Own Computer by Yasumasa Kanada. [ Windows binary available. ] Pi-AGM by Carey Bloodworth by Takuya Ooura. by Xavier Gourdon. Quick Pi by Steve Pagliarulo. [ Win 32 binary available. ] The following programs are generally listed according to the speed at which they compute values of Pi. (The last one listed here being the fastest program!) Since I'm running Windows 95/DOS 7 on a PC, each program listed here is at least available in an x86 (PC) DOS (or Win32) binary form. Executables for a particular program on another platform may exist, since some of them come with their own open source code! (Consult the program homepages and links listed below.) 1) The easy to run Super_Pi by Yasumasa Kanada Download Super_Pi now (in a 72 kb .zip file) and Calculate up to 32 Million digits of Pi. There are twelve different digit-lengths to choose from (see below). Simply extract the files ( Super_pi.exe, Super_pi.hlp and Super_pi.txt ) into any directory and run the program. The program creates the file pi_rec.txt

84. Forumy RZh Okolo poloviny vseh rekordov v etoi oblasti (a vsego ih 35 ili okolo togo) sobralyaponec Yasumasa Kanada (Yasumasa Kanada), matematik iz Komp yuternogo Centra http://www.russ.ru:8085/forums/msg/941/941.html

Soderzhanie Russkogo Zhurnala -Rubriki KRUG ChTENIYa Kniga na zavtra Novinki nedeli Vse knizhnye recenzii Elektronnye biblioteki Chtenie bez razboru Kondensator POLITIKA Novosti dnya Stat'i NOVOSTI KUL'TURY Kul'turnyi gid (arhiv) Afisha NET-KUL'TURA Bessrochnaya ssylka Nevod ISTORIYa SOVREMENNOSTI -Poisk Spisok rubrik Spisok avtorov Poisk po date publikacii Poisk po klyuchevomu slovu Avtory. Dos'e -FORUMY Novoe za den' Uchastniki Pravila DSP DAL'NYaYa SVYaZ' Vse vypuski Poslednii vypusk Avtory -Informaciya O nas Novosti servera Karta servera Podpiska RZh v Seti Arhiv zhurnala "Pushkin" Kniga otzyvov -Na servere Gumanitarnye resursy Antologii Russkii universitet Stranica M.Ya. Geftera Obrazovanie Forumy RZh : Obrazovanie Sovremennye obrazovatel'nye koncepcii i strategii vnutri bazovoi sistemy - shkola-vuz. Deyatel'nost' akademicheskogo soobshestva, razlichnye aspekty problemy Novogo Uchebnika. Kommentarii ekspertov i mneniya ryadovyh pol'zovatelei. Vse eto na forume rubriki – Vedushii - Il'ya Ovchinnikov Registraciya neobyazatel'na, Vy mozhete prosto ukazat' imya ili vystupit' anonimno.

85. Daily Times - Site Edition Professor Yasumasa Kanada and nine other researchers at the Information TechnologyCentre at Tokyo University calculated the value of pi with a Hitachi http://www.dailytimes.com.pk/default.asp?page=story_10-12-2002_pg3_8

86. 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). . See the program for the 2004 celebration , and the S. Francisco Exploratorium PI Page Ideas for activities that can be used for Pi Day celebration on March 14 (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)

87. Homepage Or Ronald Benedik 1999. Pi computed for 206 billion digits, Yasumasa Kanada, Takahashi.2002. Pi computed for 1.241 trillion digits, Yasumasa Kanada. 2002. http://fsmat.htu.tuwien.ac.at/~rbenedik/mhistory.html

Homepage of Ronald Benedik Visit my projects page. History of Mathematics Math is the queen of sciences, number theory the queen of math. Year Discovery, theorem or event Name 2000 bc. Theorem of Pythagoras invented Babylonians 1600 bc. Number of Pi in papyrus Rhind Babylonians 600 bc. as number Indians 430 bc. Doubling a cubic volumina. To avoid plague an athen delegation had brought the problem home. Greek 400 bc. Algorithm for solving quadratic eqations Babylonians 375 bc. The method of exhaustion for the calculation of areas and volumes is invented Eudoxos 300 bc. Euclidian algorithm invented Euclid 300 bc. Golden ration of a line is constructed Euclid 300 bc. Pentagon is constructed Euclid 20 bc. Agrippa educates ordnance surveyors to survey the roman empire. Agrippa Diophant researches number theory Diophant Fall of Konstantinopel, bringing more greek knowledge to western europe Ottomans Cardanos formula for solving cubic equations discovered Cardano, Tartaglia Main theorem of Calculus proved Leibniz, Newton

88. 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

89. MachineDesign.com: Do You Know What Pi Is? Yasumasa Kanada at Tokyo University set a world s record for the number of decimalplaces to which p has been calculated, establishing it to 1.24 trillion http://www.machinedesign.com/ASP/strArticleID/55732/strSite/MDSite/viewSelectedA

Do you know what is? by Ronald Khol, Editor No, the headline is not a question asking whether or not you know to more decimal places than 3.14159. My query concerns whether you know how is used in a mathematical sense. Of what utility is it? My reason for asking is that a team of academics led by Prof. Yasumasa Kanada at Tokyo University set a world's record for the number of decimal places to which has been calculated, establishing it to 1.24 trillion places. Now let's look at the opening paragraph of an article about the event written for the Associated Press. The article begins with: "To most people, it's a funny-looking Greek letter that has something to do with circles. To Professor Yasumasa Kanada, however, pi is an obsession." Good grief! So the Associated Press feels that most people think is just a funny-looking Greek letter having something to do with circles. I couldn't believe the general public is so uninformed about math, and I thought the comment was just another example of dumb-and-dumber reporting in the mass media. So I did an informal survey, asking several people if they knew how is used in mathematics.

90. 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

91. 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)

92. Sci.math 139994 (18 + 1065 More) [1] From Xpolakis@prometheus. 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

93. 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/

@import url(../../../newinclude/plus_copy.css); @import url(../../../newinclude/print.css); @import url(../../../newinclude/plus.css); about Plus support Plus ... Plus search plus with google home latest issue explore the archive ... news Permission is granted to print and copy this page on paper for non-commercial use. For other uses, including electronic redistribution, please contact us. Latest news Cat count Using mathematics to do a head count, researchers have discovered the world's biggest jaguar population in a protected area. Let there be light... (but not too much!) Aquire the skills of a professional photographer thanks to some mathematical manipulation of your digital photos. A rare view of Venus The Venus transit on June 8 gives us the chance to measure the scale of the Solar System. Count-abel even if not solve-abel The 2004 Abel Prize celebrates one of the great landmarks of 20th century mathematics. Mathematically fluent A new online maths thesaurus puts maths at your fingertips. Post-14 post-Smith A UK government inquiry into maths education has the statistics community worried.

94. Hashing LEMMAs On Time Complexities With Applications To Formula Manipulation 7 J. McCarthy, Page 151 of Symbol Manipulation Languages and Technique, D. Bobrow,ed., NorthHolland, 1971. 8 Y. Kanada, Tech. Rep. 75-01, ISD, 1975. http://portal.acm.org/citation.cfm?id=806334&dl=ACM&coll=portal&CFID=11111111&CF

95. Parallelism In Algebraic Computation And Parallel Algorithms For Symbolic Linear 13 Sasaki, T., Kanada, Y. and Watanabe, S., Calculation of Discriminantsof High Degree Equations, Tokyo J. Math., (to appear). INDEX TERMS http://portal.acm.org/citation.cfm?id=806388&dl=ACM&coll=portal&CFID=11111111&CF

96. Pi Statistics Kanada Laboratories The FTP server from the record calculation team ofYasumasa Kanada serves free available data up to 4.2 billion digits. http://www.piworld.de/pi-statistics/

p Statistics for 4.2 x 10 decimal digits by JVSchmidt (September 2003) Motivation for p mining p is a surprising number. Over hundreds of years mathematicians have found dozens of presentations and armies of formulas to compute the value of Ludolph's number. Regardless of this fact any new record in p calculation demonstrates the randomness of the digit series. Frequency analysis of these results didn't point out any order in these sequences. So, how do welldefinied formulas produce random output? David Bailey and Richard Crandall are working on a proof that the famous BBP-formula for the hexadecimal presentation of a certain PI-digit generates randomizes digits. The exact mathematical proof for p 's "randomness" ist not given yet. Thus any deeper statistical examination of known PI sequences could be helpful. The results of those tests so far are suprisingly poor. Most of them present even digit counts. Others are based on a small data material only. Nowadays an ordinary home pc can manage hugh raw material. And since I am p -minded for a long time (see also MAGIC PIWORLD ) the decision was made to set my computer on the trail. Results presented as follow are derived with a selfwritten statanalyzing program on a 4.2 billion

97. Www.cc.u-tokyo.ac.jp/kenkai/kanada-lab/ Table2 L écriture de cette approximations nécessite 100 000 livres de 200 pages. http://www.cc.u-tokyo.ac.jp/kenkai/kanada-lab/

98. K-12 Math And Computer Science Colloquium calculation pushing the limits of number crunching machines. Dr. YasumasaKANADA. Computer Centre, The University of Tokyo Department http://archive.ncsa.uiuc.edu/Edu/RSE/pirse.html

calculation pushing the limits of number crunching machines Dr. Yasumasa KANADA Computer Centre, The University of Tokyo Department of Information Science, Graduate School of the University of Tokyo 1:30 pm, Monday, November 27, 1995, 2269 Beckman Institute Special K-12 Math and Science Colloquium: 4:00 pm, Monday, November 27, 1995, 4169 Beckman Institute ABSTRACT: About five years ago I had calculated pi to 1 billion decimal places using the HITAC S-820/80 supercomputer. This year, I have calculated pi to 3.2 billion and 4.2 billion decimal places by late June and August, respectively, using the HITAC S-3800/480. The main algorithm used for the calculation was based on the AGM algorithm which was suggested by Salamin and Brent in 1976. For verification, I used a fourth order algorithm which was developed in the early 1980's by Jonathan and Peter Borwein. In order to generate more than 1 billion decimal places of pi, supercomputers, fast Fourier transforms for "big-number arithmetic" and the challenge of competition were all crucial. In my talk, I will include a discussion of how I successfully implemented the algorithms, and my future plans for a new record. Please explore a related K-12 project: Mathematics Sponsored by NCSA Education and Outreach Division For further information, please contact: Lisa A. Bievenue, 244-1993

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