61. Probleme - π Translate this page Dieser Rekord wurde 1610 vom Deutschen ludolph van ceulen weiter verbessert,er verwendete nämlich das regelmäßige -Eck für seine Approximation. http://members.tripod.com/sfabel/mathematik/probleme_pi.html

Startseite Zur Startseite Überblick 600 v. Chr. ... SCHLUSS Die drei klassischen Probleme der Antike [ Die Zahl Pi ] bzw. Aus und ergaben sich dann die angegebenen Schranken. Durch Archimedes wurde Pi also mit 3,14 auf zwei Dezimalen genau angegeben. Um 480 gelangte der Chinese Tsu Chung-Chih zum Wert als "ungenauen" Wert die Zahl Seiten Pi auf neun Dezimalen genau: -Eck. Kurz darauf, 1630, berechnete Grienberger Pi auf 39 Dezimalen genau. Er verwendete die von Snell verbesserte klassische Methode. im heutigen Sinn in allgemeinen Gebrauch. Dazu drei Beispiele: Wie o dies oder: Now I, even I, would celebrate In rhymes unapt, the great Immortal Syracusan, rivaled nevermore, Who in bis wondrous lore, Passed on before Left men bis guidance How to circles mensurate. oder: How I want a drink, alcoholic of course, after the heavy lectures involving quantum mechanics. habe. Jahre); Nach oben

62. O4R Underground Pi By diligent use of Archimedes’ method, in a 1596 paper entitled “On the Circle,”Dutch mathematician ludolph van ceulen singlehandedly delivered the http://home.teleport.com/~or4think/pf_v4n3/PiUnderground.htm

63. History Of Math: Author List Regiomontanus (14361476) François Viète (1544-1603) John Napier (1550-1617) HenryBriggs (1561-1630) Adriaan Vlacq (1600-1667) ludolph van ceulen (1539-1610 http://www.brown.edu/Facilities/University_Library/exhibits/math/authorfr.html

Euclid (ca. 326-265 BC) Archimedes (ca. 287-212 BC) Apollonius of Perga (ca. 260-200 BC) Nichomachus of Gerasa (ca. 100) Claudius Ptolemy (ca. 85-165) Diophantus of Alexandria (ca. 200-284) Pappus of Alexandria (ca. 300-350) Proclus (ca. 410-485) Boethius (ca. 480-524) Thomas Bradwardine (ca. 1290-1349) Girolamo Cardano Robert Recorde Johann MŸller of Kšnigsberg called Regiomontanus Franois Vite John Napier Henry Briggs Adriaan Vlacq ... Bonaventura Cavalieri (ca. 1598-1647) Christiaan Huygens RenŽ Descartes Gottfried Wilhem Leibniz Sir Isaac Newton ... Guillaume Franois Antoine l'Hospital, Marquis de Sainte-Mesme

64. NRC Handelsblad - Pi-muziek Ouderwets was de aanpak van ludolph van ceulen, die veelhoeken met miljarden zijdenop Griekse wijze aanpakte om na jarenlange rekenarbeid in 1620 op 35 http://www.nrc.nl/W2/Lab/Pi/geschiedenis.html

N IEUWS T EGENSPRAAK ... ERVICE Zie ook: Aan decimalen geen gebrek De uitslag van de pi-compositieprijsvraag Een kleine geschiedenis van p DIRK VAN DELFT, 30 mei - De oudste vindplaats van p is de Rhind Papyrus, daterend van circa 1650 v.Chr. 'Kort in met deel en construeer op het restant een vierkant', schreef de Egyptische klerk Ahmes, 'deze heeft hetzelfde oppervlak als de cirkel.' Uitgaande van als formule voor de oppervlakte van een cirkel (d is de diameter), leidt dit tot , of p , een waarde die later ook de Romeinen zou aanspreken omdat er zo handig mee te werken was. Pas duizend jaar na Ahmes, toen de Grieken zich met p gingen bemoeien, werd de Egyptische waarde verbeterd. Intussen kwamen de Chinezen niet verder dan p =3, een waarde die ook in het Oude Testament opduikt. In 1 Koningen 7:23 lezen we over het metaalwerk van Salomo's paleis: 'Voorts maakte hij de zee, van gietwerk, tien el van rand tot rand, geheel rond, vijf el hoog, terwijl een meetsnoer van dertig el haar rondom kon omspannen.' Dus: p =3. Van de Grieken is het idee

65. Selectie Televisie Verder het slot van de serie over de val van de moslimenclave Srebrenica en het monumentvoor de Nederlandse wiskundige ludolph van ceulen die in de 16de eeuw http://www.nrc.nl/W2/Nieuws/2000/06/30/Rtv/seltv.html

N IEUWS T EGENSPRAAK ... EDIA S e l e c t i e Televisie Radio S E L E C T I E T E L E V I S I E : ACTUALITEITEN 2 Vandaag. Naar aanleiding van de ontcijfering van de menselijke genenkaart aandacht voor eventueel misbruik en winstbejag. Verder het slot van de serie over de val van de moslimenclave Srebrenica en het monument voor de Nederlandse wiskundige Ludolph van Ceulen die in de 16de eeuw als eerste de waarde van het getal pi berekende. TV2, 17.35-18.43u. Netwerk. Nova. Orfeo aqua van Gluck die morgennacht in het Friese Borkum van vier uur tot half zes wordt opgevoerd. De toeschouwers volgen van donker naar licht zanger en citerspeler Orpheus op zijn reis naar het dodenrijk om daar zijn vrouw Euridice weg te halen. Ned.3, 22.56-23.16u. DOCUMENTAIRES De eetfabriek. Hoera, een kind. In deze tweede aflevering onder meer een echtpaar dat de Poolse jongen Yorick adopteerde. Toen deze bij hen thuis kwam bleek hij ernstige stoornissen te hebben. Ned.1, 21.55-22.26u. Well-Founded Fear. Portret van asielzoekers in de Verenigde Staten met o.a. de vraag wie een erkend asielzoekers is en wie niet. CNN, 22.00-23.00u. Stardust.

66. List Of Mathematical Topics - Wikipedia automata Cellular automation Center of a group Central limit theorem Centralizer and normalizer Cesaro, Ernesto ceulen, ludolph van Ch'ung http://www.wikipedia.org/wiki/List_of_mathematical_topics

Main Page Recent changes Edit this page Older versions Special pages Set my user preferences My watchlist Recently updated pages Upload image files Image list Registered users Site statistics Random article Orphaned articles Orphaned images Popular articles Most wanted articles Short articles Long articles Newly created articles Interlanguage links All pages by title Blocked IP addresses Maintenance page External book sources Printable version Talk Log in Help List of mathematical topics From Wikipedia, the free encyclopedia. This page aims to list all Wikipedia articles that are related to Mathematics . This is so that those interested in the subject can monitor changes to the pages by clicking on Related Changes in the sidebar. Everything remotely connected to mathematics, including articles about mathematicians, should be listed here. For a much nicer list of mathematicians, see list of mathematicians The list is not necessary complete or up to date - if you see an article that should be here but isn't (or one that shouldn't be here but is), please do update the page accordingly. A WikiProject is being developed at Wikipedia:WikiProject Mathematics regarding issues of form, structure and notation for mathematics articles. Check it out!

67. Pythagoras' Links: Pi Literatuur Pi Literature. Geschiedenis Pi through the ages; ludolph van ceulen.Pi-ezelsbruggetjes Rijmpjes, verhaaltjes, liedjes, versjes, geheugensteuntjes om http://www.science.uva.nl/misc/pythagoras/links/links.php3?section=pi

68. Ca 2000 F.Kr Babylonierna Använder Pi = 3 1/8. Egyptierna av pi. 1596, ludolph van ceulen beräknar 32 decimaler av pi. 1610,van ceulen utvidgar beräkningen till 35 decimaler. 1621, Willebrod http://www.stefa.se/matsa/matematik/pi/historik.html

Pi´s historik Ca 2000 f.Kr Babylonierna använder pi = 3 1/8. Egyptierna använder pi=(256/81)=3.1605. Ca 1100 f.Kr Kineserna använder pi=3. Ca 550 f.Kr Gamla testamentet innebär underförstått pi=3. Ca 434 f.Kr Anaxagoras försöker finna cirkelns kvadratur. Ca 430 f.Kr Antifonos och Bryson formulerar exhaustionsprincipen Ca 335 f.Kr Dinostratos använder kvadratrisen för att "kvadrera cirkeln". 200-talet f.Kr Arkimedes använder en 96-sidig polygon för att fastställa att 3 10/71 < pi 100-talet f.Kr Klaudios Ptolemaios använder pi=3 grader 8 minuter 30 sekunder (3/1 + 8/60 + 30/3600) = 377/120 = 3.14166... 200-talet e.Kr Wang Fau använder pi=142/45 = 3.1555... Liu Hui använder pi=157/50 = 3.14. Ca 450 Tsu Ch´ung-chih fastställer att pi=355/113 = 3.1415929. Ca 530 Aryabhata använder pi=62 832/20 000 = 3.1416. Ca 650 Brahmagupta använder pi=kvadratroten ur 10 = 3.162... Leonardo de Pisa (Fibonacci) finner att pi=3.141818... Francois Viète finner den första oändliga produkten för att beskriva pi; Adriaen Romanus finner 15:e decimalen av pi. Ludolph van Ceulen beräknar 32 decimaler av pi.

69. APM - Educação E Matemática Translate this page casas decimais. 1596 ludolph van ceulen calcula pi com 32 casas.1610 van ceulen amplia o cálculo para 35 casas decimais. 1663 http://www.apm.pt/apm/curiosidades/curio3.htm

Voltar c. 1100 a. C. Os chineses empregam pi=3. c. 550 a. C. O Antigo Testamento afirma que pi=3. séc. II d. C. Cláudio Ptolomeu utiliza pi=3° 8' 30"=377/120=3,14166... 263 d. C. Liu Hui emprega pi=157/50=3,14. c. 450 Tsu Ch'ung-chih acha 355/113. c. 530 Aryabhata usa pi=62832/20000=3,1416. 1220 Leonardo de Pisa (Fibonacci) descobre pi=3,141818... 1593 Adriaen Romanus calcula pi com 15 casas decimais. 1596 Ludolph Van Ceulen calcula pi com 32 casas. 1665-66 Isaac Newton calcula pi com 16 casas decimais pelo menos; resultado apenas publicado postumamente em 1737. 1699 Abraham Sharp calcula pi com 72 casas decimais. 1713 A corte chinesa publica o Su-li Ching-yun, que tem pi representado com 1719 Thomas Fantet de Lagny calcula pi com 127 casas.

70. Welcome To The Wonderful World Of PI decimal places. 1596 ludolph van ceulen calculates pi to 32 places.1610 van ceulen expands calculation to 35 decimal places. 1621 http://www.thepi.isyummy.com/BIZCARD/

Welcome to the Wonderful World of "PI" Made specially for the mathematicians of Miss Hamilton's 5th period Trigonometry class! What is 'PI' day? The actual date of PI DAY can be debated. Some of our math fanatics (that like fractions) insist pi day is 22/7 (July 22). Other math fanatics declare pi is 3.14 (March 14)... the decimal value (also EINSTEIN'S BIRTHDAY! But deep down inside we all know that EVERYDAY IS PI DAY! This day may be celebrated in a variety of ways. Pause and give thought to the role that the number pi has played in your life. Imagine a world without pi. Attempt to memorise pi to as many decimal places as you can. If you're feeling creative, devise alternative values for pi. Go to a party and commemorate the glory that is "pi" What in BLAZES is PI Undoubtedly, pi is one of the most famous and most remarkable numbers you shall ever encounter. The number, which is the ratio of circumference of a circle to its diameter, has a long story about its value. Even nowadays super-computers are used to try and find its decimal expansion to as many places as possible. For pi is one of those numbers that cannot be evaluated exactly as a decimal - it is in that class of numbers called irrationals.

71. Resources For Pi Resources for Pi. ludolph van ceulen and Pi; History of Calculating Pi; Pithrough the ages; the Pi Pages. Class Page Wright Page Math West SCCC. http://www2.sunysuffolk.edu/wrightj/MA28/Pi/

Resources for Pi Ludolph van Ceulen and Pi History of Calculating Pi Pi through the ages the Pi Pages ... SCCC LastM = document.lastModified; document.write(" Last Modified " + LastM + "");

72. Pi2 ludolph van ceulen (15401610) holland matematikus 35 tizedesjegyig számítottaki p értékét. Ezért szokás a p-t ludolph-féle számnak nevezni. http://www.jgytf.u-szeged.hu/tanszek/matematika/speckoll/2001/pi/

avagy amit már az Ókorban is ismertek és akik ismerték (Ludolph-féle szám) A jelölés a periféria (kerület) görög szó kezdõbetûje. A kör kerülete és átmérõje közötti arányt jelenti. 1739-ben Euler javasolta, hogy ezt az arányszámot betûvel jelöljék. Az egyiptomi Rhind-papiruszon (i.e. 2000-1700) a d átmérõjû kör kerületére a képlet szerinti utasítás található. Ha ezt összehasonlítjuk a mai képletünkkel: akkor láthatjuk, hogy p helyett a =3,1065 számot használták. Ugyanakkor Mezopotámiában a p =3 vagy a p =3,125 lényegesen durvább közelítõ értékeket használták. Az indiai "Szulvaszutrák" kb. i. e. 500-ból p értékére két érdekes kifejezést adtak. Ezek a és Árjabhatta (476-550?), neves indiai matematikus és csillagász, 499-ben íródott könyvecskéjét, az Árjabhatiját, sokak Eukleidész Sztoikheiájához szokták hasonlítani, melyben Árjabhatta a hatványfogalom, a négyzetgyök- és köbgyökvonás mellett terület- és térfogatszámítással is foglalkozott. Ebben az "összefoglaló" mûben a legnagyobb érdekesség az, hogy az író a háromszög területét helyesen számolja ki, de a piramis térfogatát a háromszögtõl vett helytelen analógiával úgy határozta meg, hogy az alapterületet megszorozta a magasság felével. A kör területéhez úgy jutott el, hogy a kerületet szorozta a fél sugárral, ami jó, de már a gömb térfogatát úgy számította ki, hogy a gömbi fõkör területét megszorozta a négyzetgyökével, ami pedig egyáltalán nem jó. (A jó és rossz eredmények e párhuzamát találhatjuk a négyszögek területszámításánál is.)

73. "Cijfers Liegen Niet!" - 3,141 592 653 589 793 238 462 643 383 279 502 884 197 1 Zo rekende de Leidse hoogleraar ludolph van ceulen (15401610) in1596 pi tot op 20 decimalen uit. Enkele jaren daarna verbeterde http://www.cijfers.net/pi.html

Hoofdpagina Terug Reacties FAQ ... Mail Als je de middellijn van een cirkel weet, laat de omtrek van die cirkel zich gemakkelijk uitrekenen. Op school heb je namelijk geleerd dat de omtrek van een cirkel gelijk is aan de diameter maal pi. De aarde bijvoorbeeld, heeft bij de evenaar een middellijn van 12 756 340 meter. Vermenigvuldig dat getal met pi en je hebt de omtrek van onze planeet. Rest de vraag: "Hoe groot is pi?" Je kunt het ongetwijfeld zo ophoesten: pi is ongeveer 22/7 of 3,14. Een calculator is iets nauwkeuriger: die geeft bijvoorbeeld 3,141 592 654 aan. Toch zijn we er daarmee nog (lang) niet want pi telt een oneindig aantal cijfers achter de komma. Ontvang iedere dag een WEETJE VAN DE DAG Gratis! Abonneer je nu! Zo rekende de Leidse hoogleraar Ludolph van Ceulen (1540-1610) in 1596 pi tot op 20 decimalen uit. Enkele jaren daarna verbeterde hij zijn eigen wereldrecord met nog eens 15 decimalen. Het leverde hem een gedenksteen in de Leidse Pieterskerk op. Aan het begin van de 18e eeuw gingen wiskundigen ruim over de 100 decimalen en rond 1875 over de 500. Vanaf 1945 worden computers ingezet en sindsdien is het hek van de dam. Ook deze site stortte zich in het feestgewoel en rekende pi tot 49 980 cijfers achter de komma uit. Het resultaat vind je hieronder. Het wereldrecord staat echter op naam van Japanse wiskundigen: zij hebben pi tot 1,24

74. Nova Página 2 Translate this page 1583. 2. Anthoniszoon. ~1590. 5. Adriaen van Roomen. 1593. 17. ludolph van ceulen.1596. 20. ludolph van ceulen. 1610. 35. Snell. 1621. 7. Grienberger. 1630. 39. Newton.1665. 16. http://web.rcts.pt/~pr1181/trabalunos.htm

Trabalho realizado pela aluna Mónica do 6ºano turma F Nesta página pode ser consultada parte de um trabalho, efectuado por Aline de Sousa Alves e Pedro Barroso Magalhães, no âmbito da disciplina de História da Matemática, da Licenciatura em Matemática (Ensino de) da U.T.A.D. O trabalho realizado é constituído por 18 capítulos (em cerca de 243 páginas) onde é apresentada: a evolução cronológica do p (pi) até à actualidade; a relação existente entre o p e os computadores; além de inúmeras curiosidades envolvendo p (uma parte é aqui apresentada); algumas mnemónicas para as casas decimais do p ; para além dos tópicos apresentados de seguida. Quem estiver interessado em consultar a totalidade da obra, assim como para enviar comentários ou outros dados importantes é favor contactar para um dos seguintes endereços electrónicos: Aline_Alves@Portugalmail.pt ou P.Barroso.Magalhaes@Portugalmail.pt Índice Índice Introdução Tabela Cronológica Porquê Calcular ... Bibliografia Introdução A matemática é uma grande aventura no mundo das ideias; a sua história reflecte alguns dos mais nobres pensamentos de inúmeras gerações. Muitas das mais fantásticas descobertas matemáticas surgiram como resultado do estudo do desconhecido, da necessidade inerente ao Homem de ultrapassar os seus limites. De facto, os limites são detentores de um poder misterioso que fascina o Homem e o leva a querer ultrapassá-los criando e caracterizando novas quantidades e novos objectos.

75. IRRACIONAIS Translate this page O matemático mais bem sucedido e mais obsessivo foi ludolph van ceulen, que passoua maior parte da sua vida a calcular o valor de p. Primeiro determinou o http://www.educ.fc.ul.pt/icm/icm98/icm36/irracionais.htm

IRRACIONAIS Voltando um pouco atrás na história da matemática, falemos um pouco da Escola Pitagórica. Nesta, surge a Teoria da Ordenação Matemática do Universo, e a ela é atribuída a celebre frase "Tudo é número" . Embora bastante polémica, ela traduz a forma como os pitagóricos entendiam o Universo. Usavam números inteiros ou fraccionários para explicar as questões práticas e teóricas da vida do Homem. Como consequência do Teorema de Pitágoras, descobriram que existiam segmentos, como a diagonal de um quadrado de lado 1, para os quais não havia números que representassem os seus comprimentos. Atribuíram tal facto a uma falha de Deus, e entre eles decidiram não divulgar o problema. Só um século mais tarde é que os intelectuais da época tiveram conhecimento de tal falha, e a filosofia dos pitagóricos começou a cair em descrédito. Como era possível existir um segmento e não existir um número que representasse o seu comprimento? A demonstração clássica de que Não se pode dizer que os números irracionais foram descobertos pelos gregos; aliás passaram séculos até que fosse elaborada uma teoria geral destes números. A sua formalização deve-se ao matemático Dedekind. Alguns números irracionais conhecidos: p e F p p é o único número irracional e transcendental que ocorre na natureza, ele é o quociente do perímetro de uma circunferência pelo seu diâmetro e a área de um círculo unitário.

76. Scavenger Hunt Links The Four Color Problem. Ivar Peterson's MathLand. ludolph van ceulen. MathematicalQuotation Server. Mathematician Biographies. Calculation Tips and Tricks. Logic. http://www.littletonps.org/schools/high/Library/Resource.Links/Math/MathScav.htm

Scavenger Hunt Links The Abacus Ask Dr. Math The Four Color Problem Ivar Peterson's MathLand ... Return to Littleton Jr-Sr High School Home Page This page produced by Kathryn Blair, Library Media Specialist and Miss Lordan with the help of faculty, LM_Net Listserve, Blue Web 'N' Update, The Scout Report and many others who have sent their links. Updated 11/20/98

77. Pi -- From MathWorld Castellanos (1988). is sometimes known as ludolph's constant afterludolph van ceulen (15391610), a Dutch calculator. The symbol http://mathworld.wolfram.com/Pi.html

Number Theory Constants Pi Recreational Mathematics ... Mathematics in Literature Pi A real number denoted which is defined as the ratio of a circle 's circumference C to its diameter It is equal to (Sloane's Pi's digits have many interesting properties, although not very much is known about their analytic properties. Pi's continued fraction is given by [3, 7, 15, 1, 292, 1, 1, 1, ...] (Sloane's is known to be irrational Legendre also proved that is irrational (Wells 1986, p. 76). is also transcendental (Lindemann 1882). An immediate consequence of Lindemann's proof of the transcendence of also proved that the geometric problem of antiquity known as circle squaring is impossible. A simplified, but still difficult, version of Lindemann's proof is given by Klein (1955). It is also known that is not a Liouville number (Mahler 1953), but it is not known if is normal to any base (Stoneham 1970). The following table summarizes progress in computing upper bounds on the irrationality measure for . It is likely that the exponent can be reduced to , where is an infinitesimally small number (Borwein et al.

78. Historic People Of Science Links van ceulen, ludolph site dedicated to this longignored mathematician, who spenthis entire life approximating pi to 35 places. Bohr, Niels (1885-1962) http://www.pipcom.com/~tempus/links/links/si_peop.html

Historic People of Science Links Hilbert, David his influential address at the 1900 International Congress of Mathematicians outlined 23 research problems to be investigated in the coming century. Hinton, Charles H. a selection of his Fourth Dimension writings. Mersenne, Marin French philosopher, mathematician, Jesuit theologian, and scientist. Van Ceulen, Ludolph site dedicated to this long-ignored mathematician, who spent his entire life approximating pi to 35 places. Bohr, Niels (1885-1962) Niels Bohr [st-and.ac.uk] Niels Bohr [umd.edu] Physicists:Feynman, Richard Caltech's Photo Archive collection includes photos of Feynman juggling, lecturing, dancing and playing the drums. Cargo Cult Science adapted from a Caltech commencement address given in 1974; HTML'ed from the book "Surely You're Joking, Mr. Feynman!". Feynman, Richard from the Enola Gay Perspectives site that was initiated as a group project at the University of Maryland, College Park. Richard Feynman on Teaching "The Dignified Professor." Richard Feynman Online a page all about the witty and brilliant physicist.

79. Wiswijzer Les 2 Archimedes, Ptolemeus, Zu Chongzhi, AlKhasji, ludolph van Ceulenen Metius. Les 3 Leibniz, Graaf Georges Buffon en de rekenmachine. http://www.wiswijzer.nl/pagina.asp?nummer=311

80. Pi Page righ t now tell me where the logic is in that ) ludolph van Ceulenwas the first man to calculate 20 digits of pi back in the 1610s. 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

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