21. PI, FOURIER TRANSFORM AND LUDOLPH VAN CEULEN A replica of the original tombstone of ludolph van ceulen was placed into the Church ludolph van ceulen (born 28 January 1540 in Hildesheim and died 31 http://wwwhome.math.utwente.nl/~vajtam/publications/pub2000-3/temp00-pi.htm

PI, FOURIER TRANSFORM AND LUDOLPH VAN CEULEN M.Vajta Department of Mathematical Sciences University of Twente P.O.Box 217, 7500 AE Enschede The Netherlands e-mail m.vajta@math.utwente.nl ABSTRACT The paper describes an interesting (and unexpected) application of the Fast Fourier transform in number theory. Calculating more and more decimals of (first by hand and then from the mid-20 th century, by digital computers) not only fascinated mathematicians from ancient times but kept them busy as well. They invented and applied hundreds of methods in the process but the known number of decimals remained only a couple of hundred as of the late 19 th century. All that changed with the advent of the digital computers. And although digital computers made possible to calculate thousands of decimals, the underlying methods hardly changed and their convergence remained slow ( linear ). Until the 1970's. Then, in 1976, an innovative quadratic convergent formula (based on the method of algebraic-geometric mean) for the calculation of was published independently by Brent [10] and Salamin [14]. After their breakthrough, the Borwein brothers soon developed

22. Historia Matematica Mailing List Archive: [HM] Ludolph Van Ceul Subject HM ludolph van ceulen From Dick Klingens (dklingens@pandd.demon.nl)Date Thu Jun 08 2000 003743 EDT. Next message Jeremy Gray HM http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jun00/0036.html

[HM] Ludolph van Ceulen Subject: [HM] Ludolph van Ceulen From: Dick Klingens ( dklingens@pandd.demon.nl Date: Thu Jun 08 2000 - 00:37:43 EDT Next message: Jeremy Gray: "[HM] Cayley" Previous message: Ivan Van Laningham: "Re: [HM] The Universal History of Numbers" Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] On the July 5th, 2000 a memorial stone will be unveiled, honering Ludolph van Ceulen. The stone will be placed in the Pieterskerk (St. Pieter's Church) in Leiden (Netherlands) at the some spot as his lost gravestone. On the memorial stone Ludolph's 35 decimal digits of Pi will be engraved. In the afternoon and in the evening Pieter Borwein will give the Beeger lecture 2000 at the Leiden University (it's on Pi). The reveiling of the memory stone is an activity of the Wiskundig Genootschap (Dutch Mathematic Society) in connection with WMY2000. More information (in Dutch): http://www.math.rug.nl/~top/pi-dag/6juli.html Dick Klingens [][] De werkelijkheid is zoals je 'em voelt [][] Reality is just as you feel it dklingens@pandd.demon.nl

23. Seminarium Geschiedenis Van De Wiskunde (Leiden) ludolph van ceulen en zijn ruzies, oa over de cirkelkwadratuur. Zie oa ceulen,ludolph van, Solutie ende werckingghe op twee geometrische vraghen by Willem http://www.math.uu.nl/people/hogend/seml.html

Seminarium Geschiedenis van de Wiskunde (Leiden) De volgende informatie betreft het Seminarium Geschiedenis van de wiskunde, voor studenten van de Universiteit Leiden, voorjaar 2005. Docent: Jan Hogendijk, Mathematisch Instituut, Universiteit Leiden, email hogend@math.leidenuniv.nl , tel. 071-5277135 (woensdag), 030-2533697 (overige dagen) De bijeenkomsten zijn op woensdagochtenden, 11:15-13:00, in zaal 402 in het Snelliusgebouw, tenzij anders aangegeven in het rooster hieronder. De grootte van de cursus is 10 ECTS studiepunten. Het thema van het seminarium is wiskunde in Nederland in de late 16e en de 17e eeuw. In deze periode speelde Nederland een toonaangevende rol in de ontwikkeling van de wiskunde, met Leiden als belangrijk centrum. Dit seminarium is deel van een initiatief, deze Nederlandstalige literatuur zoveel mogelijk uiteindelijk via webpresentaties toegankelijk te maken, o.a. voor middelbare scholieren en hun leraren, en voor wetenschapshistorici. Om dit te kunnen doen moet er een boel werk gedaan worden. In dit seminarium zullen we een klein deel van dit werk gaan doen. Het is dus speciaal in de zin dat we niet alleen voor onszelf werken, maar ook voor de maatschappij. Vorm: we zullen een aantal in onderling overleg te kiezen (meestal in het Nederlands geschreven) wiskundeboeken uit deze periode uit het bezit van de Leidse universiteitsbibliotheek bestuderen. De Leidse bibliotheek heeft een unieke collectie van deze werken, die kunnen worden ingezien op de

24. Lexikon Ludolph Van Ceulen ludolph van ceulen aus der freien http://lexikon.freenet.de/Ludolph_van_Ceulen

E-Mail Mitglieder Community Suche ... Hilfe document.write(''); im Web in freenet.de in Shopping Branchen Lexikon Artikel nach Themen alphabetischer Index Artikel in Kategorien Weitere Themen Doris gegen Angie: Neue Attacke im Krieg ums Kanzleramt Sex mit 50 Cent: Islands Frauen stehen Schlange Die Zukunft von Filesharing: Das kommt auf Sie zu Neuer Alfa im Test: Herrlich b¶se und aufregend maskulin ... "Mensch ¤rgere dich nicht:" Jetzt gratis mitspielen! Sie sind hier: Startseite Lexikon Ludolph van Ceulen Ludolph van Ceulen Ludolph van Ceulen 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 π ber¼hmt. Bis ins 19. Jahrhundert bezeichnete man π auch als Ludolphsche Zahl. Sie wurde zu einem eigenst¤ndigen mathematischen Untersuchungsobjekt: die Jagd nach immer mehr Stellen. Er war so stolz auf seine Berechnung, so dass er diese auf seinen Grabstein verewigte. Bearbeiten Van Ceulens Berechnungen Archimedes ging bei seinen Forschungen zur Kreiszahl von regelm¤Ÿigen Vielecken aus, die einem Kreis mit dem Durchmesser d=1 einbeschrieben bzw. umschrieben sind. Je h¶her die Eckenzahl dieser Vielecke ist, umso mehr n¤hern sie sich von innen und auŸen dem

25. Ludolph Van Ceulen. Holandský matematik ludolph van ceulen se narodil 28. ledna 1540 v Hildesheimuv Nemecku. Zrejme nemel univerzitní vzdelání, protože jeho rodice si nemohli http://www.quido.cz/osobnosti/ceulen.htm

Ludolph van Ceulen Holandský matematik Ludolph van Ceulen se narodil 28. ledna 1540 v Hildesheimu v Nìmecku. Zøejmì nemìl univerzitní vzdìlání, protože jeho rodièe si nemohli dovolit mu je zaplatit. Vyuèoval šerm a matematiku v Delftu. V roce 1594 si otevøel šermíøskou školu v Leidenu. V roce 1600 se dostal na technickou školu tamtéž. V posledních 10 letech svého života vyuèoval na této škole aritmetiku a pevnost. Napsal øadu prací, z nichž jedna z nejdùležitìjších byla O kružnici. Van Ceulen je proslulý svým výpoètem p (pí) , jednoho z nejstarších èísel (konstant) v matematice. Toto èíslo urèuje, kolikrát se prùmìr kružnice vejde do jejího obvodu. Van Ceulen spoèítal toto èíslo na 35 desetinných míst. Použil k tomu mnohostìn, který mìl 2 stran. Strávil nad tím vìtšinu svého života. Toto 35místné p má vyryto na svém náhrobku. íslo se po nìm v Nìmecku, u nás a v nìkterých jiných zemích nazývá "Ludolfo vo èíslo". Van Ceulen zemøel 31. prosince 1610 v nizozemském Leidenu.

26. Top's Bookmarks ludolph van ceulen (15401610). van ceulen werd vooral bekend vanwege zijn grafsteen .Hij had met enorm veel rekenwerk onder- en bovengrenzen voor pi http://www.math.rug.nl/~top/pi-dag/ceulen.html

Ludolph van Ceulen (1540-1610) Van Ceulen werd vooral bekend vanwege zijn grafsteen . Hij had met enorm veel rekenwerk onder- en bovengrenzen voor pi bepaald die pas in het 35ste cijfer achter de komma een eenheid verschilden. Dit feit werd op zijn grafsteen in de Leidse Pieterskerk vermeld. Tijdens zijn leven waren wel publicaties verschenen die minder nauwkeurige door hem gevonden benaderingen gaven (zijn boek "Van den Circkel" uit 1596 geeft 20 cijfers achter de komma, en een in 1603 verschenen boek van Christoffer Dybvad zelfs 31. Maar voor 35 cijfers kennen we als eerste bron alleen deze grafsteen, een tamelijk unieke plek voor een wetenschappelijk resultaat! Van Ceulen werd op advies van Simon Stevin door Prins Maurits in 1600 tot hoogleraar in Leiden benoemd, samen met Symon Fransz. van der Merwen. Maurits voegde in dat jaar een genieschool toe aan de universiteit, waar door deze twee heren " in goeder duytsche taele " les mochten geven in " Telkonsten ende Landmeten ", om zo ingenieurs op te leiden. Daaraan was behoefte in de oorlog tegen Spanje, en het is derhalve niet vreemd dat de nieuwe studenten "

27. The Galileo Project ceulen, ludolph van. 1. Dates Born Hildesheim, Germany, 28 Jan. 1540 DiedLeiden, 31 December 1610 Dateinfo Dates Certain Lifespan 70; 2. http://galileo.rice.edu/Catalog/NewFiles/ceulen.html

Ceulen, Ludolph van 1. Dates Born: Hildesheim, Germany, 28 Jan. 1540 Died: Leiden, 31 December 1610 Dateinfo: Dates Certain Lifespan: 2. Father Occupation: A Merchant Bosmans says that his father was in very modest condition, so that Van Ceulen's education stopped with elementary. I interpret this as poor. 3. Nationality Birth: German Career: Dutch Death: Dutch 4. Education Schooling: No University No evidence of any university education. 5 Religion: Cal. Nothing whatever is said; he must have conformed to the Calvinist church of the Netherlands. 5. Religion Affiliation: 6. Scientific Disciplines Primary: Mathematics Van Ceulen computed pi to 20 decimal places, and later, using Archimedes method (to which he added devices to speed things up) to 33 and ultimately to 35 places. In this he made himself an expert in trigonometry. 7. Means of Support Primary: Schoolmaster, Academic 1580: in Delft he was a fencing master and a teacher of mathematics. 1594: he received permission to open a fencing school in Leiden. 1600-10: he was appointed a teacher of arithmetic, surveying, and fortification in the engineering school that Maurice established in Leiden (with a salary of f400, later raised somewhat). Willibrord Snel was his student, and Snel later translated at least two of his works into Latin.

28. Ludolph Van Ceulen Université Montpellier II Translate this page ludolph van ceulen (1540-1610). Cette image et la biographie complète en anglaisrésident sur le site de l’université de St Andrews Écosse http://ens.math.univ-montp2.fr/SPIP/article.php3?id_article=1928

29. Biografia De Van Ceulen, Ludolph Translate this page van ceulen, ludolph. (Hildesheim, 1540-Leiden, 1610) Matemático holandés.Profesor en Amsterdam y Leiden, es conocido principalmente por haber calculado el http://www.biografiasyvidas.com/biografia/v/van_ceulen.htm

Inicio Buscador Las figuras clave de la historia Reportajes Los protagonistas de la actualidad Van Ceulen, Ludolph (Hildesheim, 1540-Leiden, 1610) Matemático holandés. Profesor en Amsterdam y Leiden, es conocido principalmente por haber calculado el valor de con una aproximación de 35 cifras decimales por el método de los perímetros. Escribió Fundamentos aritméticos y geométricos Inicio Buscador Recomendar sitio

30. What Is Algorithmic Number Theory? ludolph van ceulen is known to mathematical history buffs as the 17thcenturyfencing instructor who long held the record for computing pi 35 digits, http://www.math.harvard.edu/~elkies/compnt:.html

[from a travel journal e-mailed to a number of friends and family members in mid-August 2000; ANTS = Algorithmic Number Theory Symposium. NDE] A Mathematician's Apology , 1940) that it has no ``practical'' use at all? Well, a lot has happened since 1940. I got this far in my travel report without saying anything to describe what algorithmic number theory is, but some explanation is needed now, not only to explain the NSA's presence but also to put my own talk and the pi celebration in context. Readers already conversant with number theory and its cryptological applications may want to skim through the next three paragraphs. To describe algorithmic number theory, I must first say something about number theory, and I could start with the dry definition: it's the study of whole numbers and related mathematical structures primes, solving equations in rational numbers, that sort of thing. But number theory is unique among modern mathematical disciplines in having a wealth of problems, some extremely hard, that can be stated in terms comprehensible to the non-specialist. So rather than give technical definitions I'll try to suggest the spirit of the subject by giving examples. The canonical example is the problem suggested by Fermat and known misleadingly as ``Fermat's Last Theorem'', in fact proved only a few years ago see this URL for one telling of the story.

31. Pi Facts, Page 3 You may remember than ludolph van ceulen spent many years in calculation, and bythe time he died in 1610 he had found 35 decimal digits of pi. http://www.joyofpi.com/pifacts4.html

The Pi Shawl The late, great Elizabeth Zimmerman, known by many as the guru of knitting, designed a circular shawl called the "Pi Shawl," knitted from the center to the outside edge. You can see pictures of the pi shawl here: One Two Three Pi Day Leiden You may remember than Ludolph Van Ceulen spent many years in calculation, and by the time he died in 1610 he had found 35 decimal digits of pi. Those digits were engraved on his headstone, which unfortunately has been lost. On July 5, 2000, a special service was held in the city of Leiden, the Netherlands, commemorating Ludolph Van Ceulen and his devotion. Maarten Willems was on hand, and wrote: "The event was very well organised and there was a surprisingly great interest, both in audience (an estimated 400 people in the afternoon; about 750 people that night) and in the press. There even was an item on pi on national television!" At left: A replica of the Van Ceulen tombstone, installed at the Leiden pi day. Pi Poetry Dena R. Bortman

32. Pi History Pi was then called the ludolphian number, after ludolph van ceulen, a Germanmathematician. The first person to use the Greek letter Pi for the number was http://www.geocities.com/SiliconValley/Pines/5945/his.html

History of Pi Pi was known by the Egyptians, who calculated it to be approximately (4/3)^4 which equals 3.1604. The earliest known reference to pi occurs in a Middle Kingdom papyrus scroll, written around 1650 BC by a scribe named Ahmes. He began the scroll with the words: "The Entrance Into the Knowledge of All Existing Things" and remarked in passing that he composed the scroll "in likeness to writings made of old." Towards the end of the scroll, which is composed of various mathematical problems and their solutions, the area of a circle is found using a rough sort of pi. Around 200 BC, Archimedes of Syracuse found that pi is somewhere about 3.14 (in fractions; Greeks did not have decimals). Pi (which is a letter in the Greek alphabet) was discovered by a Greek mathematician named Archimedes. Archimedes wrote a book called The Measurement of a Circle. In the book he states that Pi is a number between 3 10/71 and 3 1/7. He figured this out by taking a polygon with 96 sides and inscribing a circle inside the polygon. That was Archemedes' concept of Pi. New knowledge of Pi then bogged down until the 17th century. Pi was then called the Ludolphian number, after Ludolph van Ceulen, a German mathematician. The first person to use the Greek letter Pi for the number was William Jones, an English mathematician, who coined it in1706.

33. Pi Page ludolph van ceulen was the first man to calculate 20 digits of pi back in the 1610s.After his death, another calculation credited to van ceulen was http://www.geocities.com/lkp42/pi.html

Back in my junior year of high school, our final six weeks precalculus project was to pair off and write a math research paper. Little did my friend Jessica and I know what random things we would uncover as we researched the number pi. Of course, there were methods upon methods of calculating pi, some so simple and inaccurate that even we could have done better, and others way above our heads. Yet, we did uncover some humor midst all the number calculating. Francois Viete, who found an approximation of pi accurate to nine decimal places way back in the day in the 1580s by using polygon approximations, was thought to be "in league with the devil" because he managed to break spaniard top secret code. (he's good with numbers and patterns, so he's evil? r i g h t...now tell me where the logic is in that...) Ludolph van Ceulen was the first man to calculate 20 digits of pi back in the 1610s. After his death, another calculation credited to van Ceulen was published by his wife containing 32 digits and even later a friend of his, Willebrord Snellius, famous for pi-related research himself, credited Ludolph with finding a 35 digit estimation of pi. Why do we care how many digits Ludolph calculated? Well, rumor has it he had his calculation for pi etched on his tombstone, however historians have debated for years whether digits 33-35 or all 35 digits were etched. The world will never know. Ludolph's gravestone has been lost. Another nifty fact, Leonhard Euler, credited as the greatest mathematician of all time discovered that

34. Ludolph Van Ceulen - Wikipedia Translate this page ludolph van ceulen wurde durch die auf 35 Dezimalstellen genaue Berechnung derKreiszahl p berühmt. Bis ins 19. Jahrhundert bezeichnete man p auch als http://de.wikipedia.org/wiki/Ludolph_van_Ceulen

Es ist geschafft - unser Spendenziel von 200.000$ ist erreicht . Herzlichen Dank an alle Spender. Ludolph van Ceulen aus Wikipedia, der freien Enzyklop¤die Ludolph van Ceulen 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 π ber¼hmt. Bis ins 19. Jahrhundert bezeichnete man π auch als Ludolphsche Zahl. Er war so stolz auf seine Berechnung, so dass er diese auf seinen Grabstein verewigte. Bearbeiten Van Ceulens Berechnungen Archimedes ging bei seinen Forschungen zur Kreiszahl von regelm¤Ÿigen Vielecken aus, die einem Kreis mit dem Durchmesser d=1 einbeschrieben bzw. umschrieben sind, die sogenannte Exhaustionsmethode . Je h¶her die Eckenzahl dieser Vielecke ist, umso mehr n¤hern sie sich von innen und auŸen dem Kreis an. Archimedes begann beim regelm¤Ÿigen Sechseck, setzte mit dem Zw¶lfeck fort, dann mit dem 24-, 48-, 96-Eck usw. Jedesmal ist die Seitenl¤nge s n des n-Ecks neu zu berechnen. Archimedes fand mit Hilfe des

35. Ludolph Van Ceulen - Wikipédia, L Encyclopédie Libre Et Gratuite Translate this page ludolph van ceulen passa la majeure partie de sa vie à calculer la valeur de laconstante Het grafschrift van ludolph van ceulen (en hollandais). http://fr.wikipedia.org/wiki/Ludolph_van_Ceulen

36. Lexikon: Ludolph Van Ceulen - Begriff Translate this page ludolph van ceulen (*28. Januar 1540 in Hildesheim, †31. ludolph van ceulenwurde durch die auf 35 Dezimalstellen genaue Berechnung der Kreiszahl π http://lexikon.donx.de/?action=details&show=Ludolph van Ceulen

37. Special Collections | The Dibner Library Of The History Of Science And Technolog ceulen, ludolph van. van den circkel, daer in gheleert werdt te winden de naeste ludolph van ceulen (15401610) is best known as a fencing master and a http://www.sil.si.edu/libraries/Dibner/newacq_2001.htm

Highlights from Recent Acquisitions The Dibner Library acquires a Herald of Science: Joseph Lister's classic work of 1867, "On the antiseptic principle in the practice of surgery." Lister, Joseph (1827-1912). "On a new method of treating compound fracture, abscess, etc., with observations on the conditions of suppuration," in Lancet (1867): 95-96. WITH: "On the antiseptic principle in the practice of surgery," in Lancet (1867): 353-356, 668-669. Together two volumes of the Lancet, 4to. [2], 818; [2], 826 pp. The Dibner Library obtains another Herald of Science: A set of Acts of Parliament relating to the longitude problem. Recently the Dibner Library acquired a collection of Acts of the British Parliament and two period newspaper articles relating to the longitude problem and calendar reform. The purchase of the set was made possible with the Special Collections Endowment Fund. The importance of solving the problems of longitude and calendar reform were critical to the history of science and technology and this collection will enhance the research and exhibition values of the Dibner Library's holdings. "An Act for rendering more effectual an Act made in the twelfth year of the reign of her late majesty Queen Anne, intituled, 'An Act for providing a publick reward for such person or persons as shall discover the longitude at sea', with regard to the making experiments of proposals made for discovering the longitude" (1762)

38. Library And Archival Exhibitions On The Web Title, ludolph van ceulen en de Berekening van het Getal Pi. Institution,Universiteit Leiden / Universiteitsbibliotheek Leiden http://www.sil.si.edu/SILPublications/Online-Exhibitions/CF/oe_display_instituti

39. Pi: Facts And Figures 58) ludolph van ceulen (1540 1610) spent most of his life working out Pi to 35decimal places. Pi is sometimes known as ludolph s Constant http://thestarman.dan123.com/math/pi/pifacts.html

(Pi): Facts and Figures Edited by The Starman The Basics 100 Decimal Places of Pi. The Circle Definition of Pi, Diameter and Circumference. Area of a Circle. The Sphere Area and Volume. Pi ( ) to decimal places is: A Circle of (Pi) diameter 1 unit , then its (see links below for proof *) . If a circle has a diameter of 2 units , then its For various proofs that , try these pages: I'm still researching this! is the 16th letter of the Greek alphabet (it also denoted the number 80 in ancient Greece). Note that the pronunciation of this letter in Greek is like the English word 'Pea' (the same way they say the name of the letter 'P') or perhaps like the p and i in the word 'Pit.' But it's NEVER pronounced like the English word 'Pie' in Greece! To create that type of sound, Greek could use the diphthong 'ai' (it means two vowels together; like the 'oi' in the English word 'oil'); so, 'pai' in Greek would sound like 'pie' in English. So, how did this Greek letter become the Mathematical symbol it's known for today? In the mid to late 1600's, some mathematicians were using

40. Ludolph Van Ceulen - Wikipedia, Wolna Encyklopedia ludolph van ceulen. Z Wikipedii, wolnej encyklopedii. ludolph van ceulen (28stycznia 1540 31 grudnia 1610) to matematyk holenderski pochodzenia http://pl.wikipedia.org/wiki/Ludolph_van_Ceulen

Zebraliśmy już ponad $200 000! Więcej informacji o dotacjach znajdziecie na stronie Fundacji Wikimedia Ludolph van Ceulen Z Wikipedii, wolnej encyklopedii. Ludolph van Ceulen 28 stycznia 31 grudnia ) to matematyk holenderski pochodzenia niemieckiego Urodzony w Hildesheim (Niemcy). Był profesorem matematyki na Uniwesytecie w Lejdzie Znany jest z tego, że w podał wartość liczby z dokładnościÄ do 20 miejsc po przecinku. Potem rozszerzył sw³j wynik do 35 miejsc podajÄ c wartośc liczby jako: Liczba ta została wyryta na jego nagrobku po śmierci. Na cześć jego dokonań liczba ta została nazwana ludolfinÄ Å¹r³dło: " http://pl.wikipedia.org/wiki/Ludolph_van_Ceulen Kategorie Matematycy Holendrzy Views artykuł dyskusja edytuj historia osobiste Logowanie nawigacja Strona gł³wna Portal wikipedyst³w BieÅ¼Ä ce wydarzenia Ostatnie zmiany ... Dary pieniężne Szukaj narzędzia LinkujÄ ce Zmiany w dolinkowanych Prześlij plik Strony specjalne ... Link do tej wersji W innych językach Deutsch English Espa±ol Fran§ais ... Svenska Tę stronę ostatnio zmodyfikowano o 21:42, 11 cze 2005 Treść udostępniana na licencji GNU Free Documentation License O Wikipedii Informacje prawne

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