41. 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

42. Tabela Translate this page 1985. 3,(17 milhões casas decimais). Yasumasa Kanada. 1987. 3,(134 milhões decasas decimais). Yasumasa Kanada. 1988. 3,(201 casas decimais). D. e G. Chudnovsky. http://www.educ.fc.ul.pt/icm/icm98/icm36/tabela.htm

O p AO LONGO DO TEMPO Para este número foram dadas várias aproximações ao longo da história. Estes são alguns valores importantes na longa procura de um valor de p Descobridor Data Valor Aproximado Egípcios cerca de 1650 a.C. 3,16(aprox.) Babilónios cerca de 1600 a.C. Baudhayana cerca de 500 a.C. 3,09(aprox.) Bíblia cerca de 500 a.C. Arquimedes cerca de 250 a.C. entre 3+1/71 e 3+1/7 Umasvati (India) cerca de 150 a.C. 3,16 (aprox.) Ptolomeu cerca de 150 d.C. Tsu Chung Chih cerca de 480 Aryabhata (India) cerca de 500 Bhaskara (India) cerca de 1150 Madhava (India) cerca de 1400 3,(11 casas decimais exactas) Al-Kashi (Pérsia) 3,(16 casas decimais) Viète 3,(9 casas decimais) Abraham Sharp 3,(16 casas decimais) Dahse 3,(200 casa decimais) Shanks 3,(707 casas decimais) Smith e Wrench 3,(1120 casas decimais) Genyus 3,(10000 casas decimais) Guiloud e Bouyer 3,(1 milhão casas decimais) Bill Gosper 3,(17 milhões casas decimais) Yasumasa Kanada 3,(134 milhões de casas decimais)

43. 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

DIGRESSIONS 2 calcul de pi le nombre d'or retour L'alphabet grec alpha gamma delta epsilon a b g d e z h q A B G D E Z H Q iota kappa lambda mu nu xi omicron pi i k l m n x o p I K L M N X O P ro sigma tau upsilon phi khi psi r s t u j c y w R S T U F C Y W Le calcul de Pi du grec (periphereia, pherein porter, peri autour) Pi = 3,141 592 953 589 793 238 462 643 383 279 Qui de ton jugement peut priser la valeur ? O quadrature ! Vieux tourment du philosophe ! Insoluble rondeur, trop longtemps vous avez Fonction du rayon. Pas trop ne s'y tiendra : calcul de pi date Babylone ( 16 / 9 ) x 2 = 3.555555556 Chine Bible Hon Han Shu Chung Hing Wang Fau Liu Hui Siddhanta Tsu Chung Chih Aryabhata Brahmagupta Al-Khowarizmi Fibonacci Al-Kashi Otho Viete Romanus Van Ceulen Grienberger Newton Sharp Seki John Machin Machin 16 ATAN(1/5) - 4 ATAN(1/239) = 3.141592654 De Lagny Euler 4 ATAN(1/2) + 4 ATAN(1/3) = 3.141592654 Takebe Katahiro Matsunaga Vega Euler 1755 20 ATAN(1/7) + 8 ATAN(3/79) = 3.141592654 Riemann Bernhard Pi ^4 / 90 = 1 + 1 / 2^4 + 1 / 3^4 + 1 / 4^4 + 1 / 5^4 + 1 / n ^4 Rutherford Euler 1764 16 ATAN(1/5) - 4 ATAN(1/70) + 4 ATAN(1/99) = 3.141592654 152 sur 208 Strassnitsky, Dahse

44. ATHENA: Literature, Books; Pierre Perroud Kanada, Yasumasa · One Divided by pi (in English, at PG); http://un2sg4.unige.ch/athena/html/author_k.html

Athena getting ready to write (amphora from Nola). ATHENA Alphabetical List Authors whose name begin with "K" KAFKA, Franz: Aphorismen (auf Deutsch, in GUTENBERG-DE) (auf Deutsch, in GUTENBERG-DE) Brief an den Vater (auf Deutsch, in GUTENBERG-DE) Das Urteil (auf Deutsch, in ABC) Das Urteil (auf Deutsch, in GUTENBERG-DE) (auf Deutsch, in GUTENBERG-DE) Die Verwandlung (auf Deutsch, in GUTENBERG-DE) Die Verwandlung (auf Deutsch, in GUTENBERG-DE) Ein Landarzt (auf Deutsch, in GUTENBERG-DE) (auf Deutsch, in GUTENBERG-DE) In der Strafkolonie (auf Deutsch, in GUTENBERG-DE) The Metamorphosis (in English, at JOHNSTONIA) KALIDASA: Sakuntala (in English, translation G. Reddy, at GNREDDY) Sakuntala (in English, translation G. Reddy, at GEOCITIES) (magyarul, MEK) KANADA, Yasumasa: One Divided by pi (in English, at PG) KANT, Immanuel: Allgemeine Naturgeschichte und Theorie Des Himmels (in English, at MALASPINA) Fundamental Principles of the Metaphysic of Morals (in English, at ARACHNE) Fundamental Principles of the Metaphysic of Morals Introduction to the Metaphysic of Morals (in English, at UIDAHO) Introduction to the Metaphysics of Morals ( Kritik der praktischen Vernunft (auf Deutsch, in GUTENBERG-DE)

45. Professor Breaks Own Record -- For Thrill Of Pi TOKYO To most people, it's a funnylooking Greek letter that has something todo with circles. To Professor Yasumasa Kanada, however, pi is an obsession. http://seattlepi.nwsource.com/national/98912_pi07.shtml

Jump to Weather Traffic Mariners Seahawks ... Forums NEWS Local Neighborhoods Sports Nation/World ... Special Reports COMMENTARY Opinion Columnists Letters David Horsey ... Forums COFFEE BREAK Mike Mailway TV Listings SHOPPING Archives NWclassifieds Jobs Autos ... Online Shop P-I ANYWHERE E-mail Newsletters News Alerts PDA Cell Phones ... Desktop OUR AFFILIATES Saturday, December 7, 2002 Professor breaks own record for thrill of pi Calculation to 1.24 trillion places is 'enormous feat of computing' By AUDREY MCAVOY THE ASSOCIATED PRESS TOKYO 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. Kanada and a team of researchers set a new world record by calculating the value of pi to 1.24 trillion places, project team member Makoto Kudo said yesterday. The previous record, set by Kanada in 1999, was 206.158 billion places. Figuring out pi to much more than about 1,000 decimal places serves little purpose in math or engineering, but researchers say it helps push computing power to a new level and can test the accuracy of supercomputers. "It's an enormous feat of computing not only for the sheer volume, but it's an advance in the technique he's using," said David Bailey, the chief technologist at the National Energy Research Scientific Computing Center at the Lawrence Berkeley National Laboratory in California.

46. History one day calculate to over ten billion places. World Record Holder.Yasumasa Kanada. In September and October, 1995, using the HITAC 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

47. 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

Brief History of Pi Calculation with Computers From: ftp://pi.super-computing.org/windows/super_pi.zip History of pi calculation with computer Brief history of pi calculation with computers. Return to Computing Pi Return to Harry's Home Page This page accessed times since June 7, 1997.

48. Record For Pi : 51.5 Billion Decimal Digits From Kanada@pi.cc.utokyo.ac.jp (Yasumasa Kanada) Subject New world recordof pi 51.5 billion decimal digits Yasumasa Kanada and Daisuke TAKAHASHI http://pw1.netcom.com/~hjsmith/Pi/Record51.html

From: kanada@pi.cc.u-tokyo.ac.jp (Yasumasa KANADA) 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: Declared record: 51,539,600,000 decimal digits 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: 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 : Borweins' 4-th order convergent algorithm Run the algorithm.

49. 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/liczby/pi.html

Ludolfina 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 Zu Chongzi Chiny, 430-501 Fibonacci W³ochy, ok. 1220 pierwszy warto¶ciowy wynik otrzymany w Europie, zaokr±glenie wyniku dla 96-k±ta D¿emszid al-Kaszi Samarkanda, 1424 16 cyfr po przecinku ulepszona metoda Archimedesa dla -k±ta, wynik podany jako u³amek dziesiêtny

50. 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

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.

51. 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

A Treatise on Pi 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

52. Einführung In Die Berechnung Von Pi: Record For Pi - 51.5 Billion Decimal Digit From Kanada@pi.cc.utokyo.ac.jp (Yasumasa Kanada) Subject New world recordof pi 51.5 billion decimal digits. Yasumasa Kanada and Daisuke TAKAHASHI. http://www.uni-leipzig.de/~sma/pi_einfuehrung/record51.html

From: kanada@pi.cc.u-tokyo.ac.jp (Yasumasa KANADA) 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: Declared record: 51,539,600,000 decimal digits 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: 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 : Borweins' 4-th order convergent algorithm Verification program run Job start : 4th July 1997 22:11:42 Job end : 6th July 1997 11:19:58 Elapsed time : 37:08:16 Main memory : 188 GB Algorithm : Gauss-Legendre algorithm (Brent-Salamin) Optimized main program run Job start : 1st Augst 1997 23:04:15 Job end : 3rd Augst 1997 00:18:47

53. 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

A Chronology of Pi *2000 Babylonians use pi=25/8 and Egyptians use pi=256/81 *900 Bible, I Kings 7:23 implies pi=3 *434 Anaxagoras attempts to square the circle *414 Aristophanes refers to squaring the circle in his comedy The Birds *480 Tsu Chung-chih approximates pi by 355/113 *1429 Al-Kashi calculates pi to 16 decimal places *1610 Ludolph van Ceulen calculates pi to 35 decimal places *1621 Snell refines Archimedes' clasical method *1630 Grienberger uses Snell's refinement to calculate pi to 39 decimal places *1655 Wallis shows that pi/2=2/1*2/3*4/3*4/5*6/5*6/7*8/7*8/9. . *1674 Leibniz shows that pi/4=1-1/3+1/5-. . . *1699 Sharp uses Gregory's series with x=sq. rt. 3 to calculate pi to 71 decimal places *1706 Machin finds pi to 100 decimal places *1706 William Jones first uses pi for the circle ratio *1736 Euler proves that 1/1^2+1/2^2+1/3^2+. . . =(pi)^2/6 *1737 Euler uses the symbol pi, thus establishing it as standard notation *1761 Lambert shows that pi is irrational *1777 Buffon devises his needle problem *1794 Legendre shows that (pi)^2 is irrational *1844 Johann Dase, a lightning calculator, finds pi to 200 decimal places

54. 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

Works Cited Books/Papers: Beckmann, Petr. A History of Pi. New York: St. Martin's Press, 1971. Cajori, Florian. A History of Mathematical Notations. New York: Dover Publications, Inc., 1993. Kanada, Yasumasa. Lecture on Pi Calculationpushing the limits of number crunching machines. University of Illinois Champaign/Urbana. 27 November 1995. Katz, Victor J. A History of Mathematics: An Introduction. New York: HarperCollins College Publishers, 1993. Posamentier, Alfred S., and Jay Stepelman. Teaching Secondary School Mathematics: Techniques and Enrichment Units. New York: Macmillan Publishing Company, 1990. Scott, Heather, and Charles Snape. Puzzles, Mazes, and Numbers. Cambridge: Cambridge University Press, 1995. Swetz, Frank J. Learning Activities from the History of Mathematics. Maine: J. Weston Walch, Publisher, 1994. Williams, Becky, et al. The Evolution of Pi: How the Advancement of Civilization Has Affected the Calculating of Pi. 1995. U. R. L. Addresses: All of the Web pages that I have used, I made links to.

55. 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

S OCIAL S YSTEMS S IMULATION G ROUP E-mail: rwerner@sssgrp.com Readme Pi 400 M Digits of Pi Readme.txt Roland Werner, Ph.D. Master Model Maker Social Systems Simulation Group http://www.sssgrp.com Contents 1. Source of Digits 2. Source of Artwork 3. Organization of the CD 4. Some Observations 5. References 6. Other Interesting Links 1. Source of Digits 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 I would like to acknowledge Ms. Eve A. Andersson, cofounder of ArsDigita an open-source enterprise software company, http://www.arsdigita.com , for providing the inspiration to the artwork for the jewel case and the CD. 3. Organization of the CD Files on this beta version CD: (Java programs are currently under development; 02/2002.) Readme.txt

56. 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

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

57. Search Result For Yasumasa Kanada Search Result for Yasumasa Kanada. Status Associate Member, Professor Lycos Yasumasa Kanada What Yasumasa has to say about himself http://hpsearch.uni-trier.de/hp/a-tree/k/Kanada:Yasumasa.html

Search Result for Yasumasa Kanada Personpage in DBLP Search Computer Science Bibliography ResearchIndex Cora Google(pdf) ... Kanada's Home Page http://www.hints.org/~kanada/ 212 Points (Preselect:126) Source: Google(3); Lycos(6); FAST(8); MS Search(2); Yahoo(2) UP:/papers-j.html Google: Yasumasa KANADA . Picture taken by the Hokkaido-shinbun newspaper company. You are the -th visitor. Introduction of myself. Curriculum vitae Licence Hobby ... Lycos: 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 ... FAST: 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... MS Search: 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 Yahoo: Yasumasa KANADA . Picture taken by the Hokkaido-shinbun newspaper company. You are the -th visitor. Introduction of myself. Curriculum vitae Licence Hobby ...

58. WON TOPIC 40 2002). Again a NEW RECORD is set in the calculation of PI. Declared record 1.241.100.000.000decimal digits by Yasumasa Kanada (Kanada Laboratory home page). 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!

59. Untitled of Tokyo , year = 1974, number = Technical Report 7405 } Implementation of HLISPand algebraic manipulation language REDUCE-2, Yasumasa Kanada @TechReport{is http://www.is.s.u-tokyo.ac.jp/~library/new-books/html/is.html

Estimation of errors in the numerical quadrature of analytic functions Hidetosi Takahasi and Masatake Mori Transformations of periodic sequences by cellular automata Masatosi Imori and Hisao Yamada Monocopy and associative algorithms in an extended LISP Eiichi Goto A new type of cathode ray tube suitable for bubble chamber film measurements Shinkichi Shibata et.al. Minimization of a sum of squares using the singular value decomposition Hajime Ohiwa Implementation of HLISP and algebraic manipulation language REDUCE-2 Yasumasa Kanada A proposal for virtual multihead multitape processor Lachezar Antonov Mateev Algorithms used in an implementation of HLISP Motoaki Terashima On backtrack programming and some results on combinatorial puzzles Satoru Kawai and Kohei Noshita and Ikuo Takeuchi LIP-40 reference manual, Version 1 Satoru Kawai PASCAL 8000 reference manual, Version 1.0 Teruo Hikita and Kiyoshi Ishihata Analysis of hash addressing methods Takao Gunji Bootstrapping PASCAL using a trunk Kiyoshi Ishihata and Teruo Hikita A portable LISP compiler on a hypothetical LISP machine Fumio Motoyoshi Development of an intelligent remote station based on a minicomputer network Yoshihiko Ono Elementary methods for formal language theory and matrix languages Hidetaka Tanaka Reference manual for STOP: structure oriented processor Kaoru Kotoh and Hisao M. Yamada

60. Untitled Furber , title = ARM system architecture , publisher = ADDISONWESLEY , year =1996 } HLISP and supplementary HLISP-REDUCE manual, Yasumasa Kanada @Manual{UT http://www.is.s.u-tokyo.ac.jp/~library/new-books/html/manual.html

A computer perspective : background to the computer age Charles Eames and Ray Eames Creating the computer : government,industry,and high technology Kenneth Flamm IBM's 360 and Early 370 systems Emerson W. Pugh and Lyle R. Johnson and Jhon H. Palmer Project whirlwind : the history of a pioneer computer Kent C. Redmond and Thomas M.Smith A history of computing technology Michael R. Williams ARM system architecture Steve Furber HLISP and supplementary HLISP-REDUCE manual Yasumasa Kanada SIGMA-1 K. Hiraki AMD-K6-III Processor data sheet Axil320 workstaiton user's guide ALTRAN user's manual Vol.1 ALTRAN Installation and maintenance Vol.2 Alpha architecture handbook Alpha 21264 microprocessor data sheet CRAY-1 S series site planning reference manual CRAY-1 S series hardware reference manual FCT logic products Timing technology products Cyrix M 11 data book Alpha architecture handbook DECChip 21064-AA RISC microprocessor preliminary data sheet Pdp11 processor handbook : pdp11/04/34a/44/60/70 PDP-11/44 system user's guide User's guide VT100 VAX11/780 Software handbook VAX11/780 Hardware handbook VAX technical summary VAX Hardware handbook Alpha architecture handbook Alpha 21164 microprocessor hardware reference manual VAX architecture handbook Introduction to designing a system with the DECchip 21064 microprocessor DECChip 21064-AA RISC microprocessor preliminary data sheet MB93501 LSI $B;EMM=q(B

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