21. Kanada's Home Page Yasumasa Kanada. Picture taken by the Hokkaidoshinbun newspaper company. E-mail address. Kanada@pi.cc.u-tokyo.ac.jp http://www.hints.org/~kanada/

Yasumasa KANADA Picture taken by the Hokkaido-shinbun newspaper company. You are the -th visitor. Introduction of myself Curriculum vitae Licence Hobby Research interests Overview Papers Links Kanada family home page Kanada Lab. private room CCUT Home Page Kanada Lab. Japanese Home page ... Dept. of Information Science, Fac. of Science Home Page E-mail address: kanada@pi.cc.u-tokyo.ac.jp Last update: 4th of June, 2000

22. PROJECT GUTENBERG - Catalog By Author - Index - Kanada, Yasumasa - Kanada, Yasumasa K Index Main Index One Divided by pi Opera TheWorld s FASTER Browser! WordCruncher Promo.Net. Top http://www.informika.ru/text/books/gutenb/gutind/TEMP/i-_kanada_yasumasa.html

Etexts by Author Kanada, Yasumasa "K" Index... Main Index... One Divided by pi Web Site Designed and Administered by Pietro Di Miceli , webmaster of PROMO.NET The Original URL of Project Gutenberg Web site is: http://promo.net/pg/

23. Facts About Pi 1988 Yasumasa Kanada of the University of Tokyo computed pi to 201326000 1999, Pi is computed to 206158430000 decimal places by Yasumasa Kanada and http://www.pen.k12.va.us/Div/Winchester/jhhs/math/facts/pifacts.html

Some Facts about Pi Pi is the first letter of the Greek word perimeter meaning distance around. In 1737, Euler used the symbol for pi to be equal to the ratio of the circumference to the diameter in a circle. A brief history of pi: Biblical References: I Kings 7:23 II Chronicles 4:2 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

24. 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

Pi Computed to over 1.24 Trillion Places 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.

25. WON TOPIC 40 by Yasumasa Kanada and Daisuke Takahashi by Yasumasa Kanada (Kanada Laboratoryhome page). Some Background on Kanada s Recent Pi Calculation (in PDF) http://www.worldofnumbers.com/won40.htm

W orld O f N umbers WON plate July 1997 Sequences in the expansion of A NEW RECORD is set in the calculation of PI Declared record : 51.539.600.000 decimal digits The Brouwer-Heyting Sequence Here are some interesting pandigital sequences : : from 17.387.594.880-th of pi : from 21.981.157.633-th of pi A sequence of twelve 9's is detected in the value of 1/pi : from 12.479.021.132-th of 1/pi Source : Record for pi : 51.5 billion decimal digits Update October 11, 2002 Dr Francis Podmore (Senior Lecturer), Department of Physics, University of Zimbabwe, Mount Pleasant, Harare, Zimbabwe ( email told me that the current record for the length of the number of digits of pi is 206 billion, by Kanada in 1999. A NEW RECORD was set in the calculation of PI Declared record : 206.158.430.000 decimal digits by Yasumasa Kanada and Daisuke Takahashi Computing Pi to 206 billion digits Update January 14, 2003 1.241 TRILLION DIGITS of (Dec. 2002) Again a NEW RECORD is set in the calculation of PI Declared record : 1.241.100.000.000 decimal digits by Yasumasa Kanada ( Kanada Laboratory home page Some Background on Kanada's Recent Pi Calculation (in PDF) by David Bailey Has this been beaten yet :-) Prime Curios!

26. Kanada (disambiguation) - Wikipedia, The Free Encyclopedia Yasumasa Kanada, a Japanese mathematician Kanada, the original native indianname for a region near Ottawa,Canada Kanada is the spelling of Canada in http://en.wikipedia.org/wiki/Kanada_(disambiguation)

Kanada (disambiguation) From Wikipedia, the free encyclopedia. Kanada can mean Yasumasa Kanada , a Japanese mathematician Kanada , the original native indian name for a region near Ottawa Canada Kanada is the spelling of Canada in many world languages. Kanada , the Hindu sage who founded the philosophy of Vaisheshika This is a disambiguation page — a list of pages that otherwise might share the same title. If an article link referred you here, you might want to go back and fix it to point directly to the intended page. Retrieved from " http://en.wikipedia.org/wiki/Kanada_%28disambiguation%29 Categories Disambiguation Views Article Discussion Edit this page History Personal tools Create account / log in Navigation Main Page Community portal Current events Recent changes ... Donations Search Toolbox What links here Related changes Upload file Special pages ... Permanent link This page was last modified 21:25, 12 June 2005. All text is available under the terms of the GNU Free Documentation License (see for details). About Wikipedia

27. One Divided By Pi (to 1 Million Digits) By Yasumasa Kanada - Project Gutenberg E Start here to download the Project Gutenberg eBook of One Divided By pi (to 1million digits) by Yasumasa Kanada. http://pge.rastko.net/etext/745

Project Gutenberg Europe Online Book Catalog Author: Title Word(s): EText-No.: Advanced Search Recent Books Top 100 Offline Catalogs ... In Depth Information One Divided By pi (to 1 million digits) by Yasumasa Kanada New Search Help on this page Data Creator Kanada, Yasumasa Title One Divided By pi (to 1 million digits) Language English LoC Class QA: Science: Mathematics Subject Mathematics EText-No. Release Date No Read this eBook online (experimental feature) Download this eBook Edition Format Encoding Compression Size Download Links Plain text none 1006 KB rastko.net Plain text zip 477 KB rastko.net If you are located outside of the U.S. you may want to download from a mirror site located near you to improve performance. Select a mirror site. If you need a special character set, try our new recode facility (experimental) Most recently updated: 2004-12-19 17:39:39.

28. Browse By Author: K - Project Gutenberg Europe Kanada, Yasumasa. One Divided By pi (to 1 million digits) (English). Kandinsky,Wassily. Concerning the Spiritual in Art (English). Kane, William Terence http://pge.rastko.net/browse/authors/k

Project Gutenberg Europe Online Book Catalog Author: Title Word(s): EText-No.: Advanced Search Recent Books Top 100 Offline Catalogs ... In Depth Information Browse By Author: K Authors: A B C D ... other Titles: A B C D ... other Languages: Afrikaans Albanian Aleut Basque ... Yiddish Recent: last 24 hours last 7 days last 30 days Kafka, Franz Der Heizer Ein Fragment (German) Ein Hungerk¼nstler (German) Metamorphosis (English) Der ProzeŸ (German) The Trial (English) Kaila, Eino Valitut teokset 1910-1922 (Finnish) Kailas, Uuno Purjehtijat (Finnish) Tuuli ja t¤hk¤ ynn¤ muita runoja (Finnish) Uni ja kuolema (Finnish) Kalidasa Sakoontala or the Lost Ring An Indian Drama (English) Kamban, Gudmundur Hadda Pada (English) Kanada, Yasumasa One Divided By pi (to 1 million digits) (English) Kandinsky, Wassily Concerning the Spiritual in Art (English) Kane, William Terence For Greater Things; the story of Saint Stanislaus Kostka (English) Kann, Reginald Reizen en vechten in het Zuiden van de Philippijnen De Aarde en haar volken, Jaargang 1908 (Dutch) Kant, Immanuel The Critique of Practical Reason (English) The Critique of Pure Reason (English) Fundamental Principles of the Metaphysic of Morals (English) Kritik der reinen Vernunft (Erste Fassung 1781) (German) Kritik der reinen Vernunft Zweite hin und wieder verbesserte Auflage (1787) (German) The Metaphysical Elements of Ethics (English) Was ist Aufkl¤rung?

29. New World Record: 4th October 1999 Yasumasa Kanada Information Technology Center, Computer Centre Division, Fax +813-3814-7231 (office, G3 Super G3) E-mail Yasumasa Kanada http://www.lupi.ch/PiSites/Pi-Rekord.html

PI news by 20th September 1999, Adding Info. 4th October 1999 Dear folks, our latest record was established as the followings: Declared record: decimal digits Two independent calculation based on two different algorithms generated 206,158,430,208 (=3*2^36) decimal digits of pi and comparison of two generated sequences matched up to 206,158,430,163 decimal digits, e.g., 45 decimal digits difference. Then we are declaring 206,158,430,000 decimal digits as the new world record. Optimized Main program run: Job start : 18th September 1999 19:00:52 (JST) Job end : 20th September 1999 08:21:56 (JST) Elapsed time : 37:21:04 Main memory : 865 GB (= 6.758 GB * 128) Algorithm : Gauss-Legendre algorithm Optimized Verification program run: Job start : 26th June 1999 01:22:50 (JST) Job end : 27th June 1999 23:30:40 (JST) Elapsed time : 46:07:10 Main memory : 817 GB (= 6.383 GB * 128)

30. New Records At 6th July '97 And 5th April '99 Yasumasa Kanada. Computer Centre, University of Tokyo. Bunkyoku Yayoi 2-11-16.Tokyo 113 Japan. Fax +81-3-3814-7231 (office). E-mail Yasumasa Kanada http://www.lupi.ch/PiSites/Pi-Rekordold.html

first message from 1 Aug 97 - second message from April 99 Posted-Date: Fri, 1 Aug 1997 15:20:22 -0200 (GMT) Mime-Version: 1.0 Date: Fri, 1 Aug 1997 15:32:00 +0200 lmueller@pop.agri.ch From: xpolakis@hol.gr (Antreas P. Hatzipolakis) Subject: Pi Dear Lukas, Greetings from Athens - Antreas Latest PI news by 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 Our latest record was established as follows: Declared record: decimal digits 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: Job start : 6th June 1997 22:29:06 Job end : 8th June 1997 03:32:17 Elapsed time : 29:03:11 Main memory : 212 GB Algorithm : Borwein's 4-th order convergent algorithm (Run the algorithm.)

31. Computation Of Pi Takahashi, Daisuke; Kanada, Yasumasa Trans. Inform. Process. Soc. Japan 39 (1998),no. 7, 20742083, MathSciNet. A Simple Formula for Pi http://math.fullerton.edu/mathews/n2003/picomputation/PiComputationBib/Links/PiC

Bibliography for Computation of Pi unabridged Blending two major techniques in order to compute Pi International Journal of Mathematical Education in Science and Technology, 15 Jan - 15 Feb 2005, vol. 36, no. 1, pp. 85-92(8), Ingenta. Pi at the limits of computation. Hwang, Chien-Lih Tamkang J. Math. 35 (2004), no. 4, 305312, MathSciNet. Calculation of Pi by mean of trigonometric functions. (Spanish) Divulg. Mat. 10 (2002), no. 2, 149159, MathSciNet. Ramanujan's elliptic functions to alternative bases and approximations to Pi. Chan, Heng Huat Number theory for the millennium, I (Urbana, IL, 2000), 197213, A K Peters, Natick, MA, 2002, MathSciNet. Extrapolation: from calculation of Pi to finite element method of partial differential equations. Shen, Xiaoping Applied mathematics reviews, Vol. 1, 537558, World Sci. Publishing, River Edge, NJ, 2000, MathSciNet. New formulas for approximation of Pi and other transcendental numbers. Kalantari, Bahman

32. Research Experience For Undergraduates Takahashi, Daisuke; Kanada, Yasumasa Trans. Inform. Process. Soc. Japan 39(1998),no. 3, 519528, Math. Sci. Net. FFT algorithms and their adaptation to http://math.fullerton.edu/mathews/n2003/fourierseries/FourierSeriesBib/Links/Fou

Bibliography for the Fast Fourier Transform unabridged Description of dental arch form using the Fourier series Valenzuela A, P.; Pardo, M. A.; Yezioro, S. International Journal of Adult Orthodontics and Orthognathic Surgery, 2002, vol. 17, no. 1, pp. 59-65 , Ingenta. Efficient implementation of quaternion Fourier transform, convolution, and correlation by 2-D complex FFT. Pei, Soo-Chang; Ding, Jian-Jiun; Chang, Ja-Han IEEE Trans. Signal Process. 49 (2001), no. 11, 27832797, Math. Sci. Net. The Cooley-Tukey FFT and group theory. Maslen, David K.; Rockmore, Daniel N. Notices Amer. Math. Soc. 48 (2001), no. 10, 11511160, Math. Sci. Net. Hou, Xiang Qian J. Ningxia Univ. Nat. Sci. Ed. 22 (2001), no. 3, 282283, Math. Sci. Net. Fast Fourier transforms for nonequispaced data: a tutorial. Potts, Daniel; Steidl, Gabriele; Tasche, Manfred The fast Fourier transform method and ill-conditioned matrices. Soon, Boon Yi; Eloe, Paul W.; Kammler, David Appl. Math. Comput. 117 (2001), no. 2-3, 117129.

33. History Yasumasa Kanada. In September and October, 1995, using the HITAC S3800/480,Professor Yasumasa Kanada of the University of Tokyo calculated 6442450000 http://archive.ncsa.uiuc.edu/Edu/RSE/RSEorange/kanada.html

Computer Calculation Scientists today are using algorithms developed by mathematicians in the past to program high speed computers, yielding larger and larger calculations of . The advent of the computer has allowed to be calculated to over 6 billion digits. The first computer calculation of was made in September, 1949 on ENIAC (Electronic Numerical Integrator and Computer), using the Machin formula. It took 70 hours to calculate to 2,037 places. During the years that followed, it became a challenge to calculate the largest number of digits of , just as it had been in earlier times. In the years between 1980 and 1990, the calculation went from a number in the millions to one in the billions. The current record for the calculation of is over 6 billion digits and the current record holder is Yasumasa Kanada, who hopes to one day calculate to over ten billion places. World Record Holder Yasumasa Kanada In September and October, 1995, using the HITAC S-3800/480, Professor Yasumasa Kanada of the University of Tokyo calculated decimal digits of . He used the Borwein formula, a 4 th order convergent algorithm. For verification of the results the

34. K-12 Math And Computer Science Colloquium Dr. Yasumasa Kanada. Computer Centre, The University of Tokyo Department ofInformation Science, Graduate School of the University of Tokyo 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

35. Kanada Translate this page Yasumasa Kanada. Pi. Voltar à história. http://www.educ.fc.ul.pt/icm/icm2001/icm34/kanada.htm

YASUMASA KANADA Voltar à história

36. Science & Technology > Mathematics > All Formats > Page 5 By Yasumasa Kanada Format Adobe Reader Availability Email Delivery 12 BusinessDays Platforms Windows Computers, Mac, Linux, more Learn more http://www.ebookmall.com/all-ebooks/group-206-all-ebooks-page5.htm

Mathematics All Formats eBooks Pages: Modern Algebra with Applications, 2nd Edition By: William J. Gilbert Format: Adobe Reader Availability: Download Now Platforms: Windows, Mac, Palm Price: $89.95 The Mountain Pass Theorem By: Youssef Jabri Format: Adobe Reader Availability: Download Now Platforms: Windows Computers, Mac, Linux, more... Price: $76.00 Numbers and Functions By: R. P. Burn Format: Adobe Reader Availability: Download Now Platforms: Windows Computers, Mac, Linux, more... Price: $36.00 Numerical Methods for Ordinary Differential Equations By: J. C. Butcher Format: Adobe Reader Availability: Download Now Platforms: Windows, Mac, Palm Price: $115.00 Number Theory and the Avta Foundation for Primes By: Theodore Ellis Hahn Format: Adobe Reader Availability: Download Now Platforms: Windows Computers, Mac, Linux, more... Price: $15.00 The Number By: Robert Nemiroff Format: Adobe Reader Availability: Email Delivery 1-2 Business Days Platforms: Windows Computers, Mac, Linux, more... Price: $7.95 The Number By: Robert Nemiroff Format: Gemstar/Rocket eBook Availability: Email Delivery 1-2 Business Days Platforms: Gemstar eBook RCA REB 1100, Rocket eBook

37. Math Trek: A Trillion Pieces Of Pi, Science News Online, Dec. 14, 2002 Computer scientist Yasumasa Kanada and his coworkers at the University of TokyoInformation Technology Center have now succeeded in computing 1241100000000 http://www.sciencenews.org/articles/20021214/mathtrek.asp

Science News Books. Subscribe to Science News ... Science News for Kids Math Trek A Trillion Pieces of Pi Food for Thought Science Safari Grossology TimeLine 70 Years Ago in Science News Science News e-LETTER. ... Week of Dec. 14, 2002; Vol. 162, No. 24 A Trillion Pieces of Pi Ivars Peterson The number pi ( p ) represents the ratio of a circle's circumference to its diameter. Starting with 3.1415926535897932384. . ., its digits run on forever. That hasn't stopped researchers from trying to calculate as many of those digits as computer technology and mathematical methods allow. Computer scientist Yasumasa Kanada and his coworkers at the University of Tokyo Information Technology Center have now succeeded in computing 1,241,100,000,000 decimal digits of pi, smashing their own previous world record of 206,158,430,000 digits, set in 1999. The calculation required about 602 hours on a Hitachi SR8000 computer, with access to a memory of about 1 terabyte. To calculate the digits of pi, Kanada and his team used formulas involving arctangent relations of pi. For instance, you can use the following expression to work out the value of the arctangent of x to any desired number of decimal places just by evaluating the series to a sufficiently large number of terms: arctangent( x x x x x x The value of pi can then be obtained from the following equation: p = 16 arctangent(1/5) – 4 arctangent(1/239).

38. Pi By The Billions - References And Sources, Science News Online (10/16/99) Yasumasa Kanada and his colleagues have computed 206.2 billion decimal digits ofpi, besting their previous record of 51.5 billion digits. http://www.sciencenews.org/pages/sn_arc99/10_16_99/note6ref.htm

Pi by the billions Yasumasa Kanada and his colleagues have computed 206.2 billion decimal digits of pi, besting their previous record of 51.5 billion digits. References: Kanada’s announcement of his computation of 206.2 billion digits of pi can be found at http://www.cecm.sfu.ca/personal/jborwein/Kanada_200b.html , with additional details at ftp://www.cc.u-tokyo.ac.jp/README.our_latest_record Further Readings: Peterson, I. 1998. Picking off more pieces of pi. Science News 154(Oct. 17):255. . 1997. An enormous chunk of pi. Science News 152(Aug. 9):92. . 1995. A new formula for picking off pieces of pi. Science News 148(Oct. 28):279. Additional information about pi can be found at http://www.cecm.sfu.ca/personal/jborwein/pi_cover.html Sources: Yasumasa Kanada University of Tokyo Information Technology Center Computer Centre Division Bunkyo-ku Yayoi 2-11-16 Tokyo 113-8658 Japan Web site: http://pi2.cc.u-tokyo.ac.jp/index.html From Science News

39. MachineDesign.com: Do You Know What Pi Is? Yasumasa Kanada at Tokyo University set a world s record for the number of decimalplaces to To Professor Yasumasa Kanada, however, pi is an obsession. 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.

40. Pi Charts Chudnovsky brothers, 1991, 2160000000. Yasumasa Kanada, 1995, 3221220000.Yasumasa Kanada, at the University of Tokyo, found the new record number of digits http://www.geocities.com/SiliconValley/Pines/5945/charts.html

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  B  C  D  E  F  G  H  I  J  K  L  M  N  O  P  Q  R  S  T  U  V  W  X  Y  Z

Page 2     21-40 of 97    Back | 1  | 2  | 3  | 4  | 5  | Next 20