. Translate this page Zur Modul-Startseite, Zahl Pi XXL (Archimedes-Methode Biographie ). BiographischeDaten. ludolph van ceulen geboren 28. Januar 1540 in Hildesheim gestorben 31. http://www.matheprisma.uni-wuppertal.de/Module/PIXXL/pages/node17.htm
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
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/
Extractions: 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.)
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
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
Extractions: 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
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
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
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
Extractions: 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.
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
Extractions: (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.
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/
Extractions: 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" 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.
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
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
Extractions: 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.
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/
Extractions: 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 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
Extractions: Ahmes ca. 1650 vC Pythagoras ca. 540 vC Hippocrates ca. 440 vC Plato ca. 430 vC - ca. 349 vC Hippias ca. 425 vC Theaethetus ca. 417 vC - ca. 369 vC Archytas ca. 400 vC Xenocrates 396 vC - 314 vC Theodorus ca. 390 vC Aristoteles 384 vC - 322 vC Menaechmus ca. 350 vC Euclides ca. 300 vC Archimedes ca. 287 vC - ca. 212 vC Nicomedes ca. 240 vC Eeratosthenes ca. 230 vC Diocles ca. 180 vC Hipparchus ca. 180 vC - ca. 125 vC Hero van Alexandrie ca. 75 Ptolemaeus ca. 85 - ca. 165 Nicomachus van Gerasa ca. 100 Theoon van Smyrna ca. 125 Diophantus 1ste of 3de eeuw Pappus ca. 320 Iamblichus ca. 325 Produs Zu Chongzhi Brahmagupta ca. 628 Al-Chwarizmi ca. 825 Thabit ibn Qurra Mahavira ca. 850 Bhaskara 1114 - ca. 1185 Leonardo van Pisa
Extractions: Mathematics Resources on the Web Up one level See also: Business Government , and Science Databases Databases Texts Association of Christians in the Mathematical Sciences Association for Computational Linguistics - ACL Association for Computing Machinery - ACM Australian Mathematical Society Australian Mathematics Sciences Council Canadian Mathematical Society - CMS, CAMEL European Mathematical Information Service Geometry Center - Minnesota Geometry Forum - Swarthmore Hewlett-Packard's Basic Research Institute in the Mathematical Sciences - BRIMS The Institute for Advanced Study - IAS The Institute for Advanced Study - IAS, School of Mathematics The Institute for Advanced Study - IAS, School of Natural Sciences
Slice Of Pi, Anyone? - About Pi Day And The Transcendental Number Pi Includes some history, facts and related links.Category Science Math Recreations Specific Numbers Pi ludolph van ceulen, who lived from 1540 to 1610, spent most of his days tediouslyperforming the calculations for the first 35 decimal places of pi. http://www.johnshepler.com/articles/piday.html
Extractions: About Pi Day and the Transcendental Number Pi "For a time I stood pondering on circle sizes. The large computer mainframe quietly processed all of its assembly code. Inside my entire hope lay for figuring out an elusive expansion. Value: pi." is a transcendental figment of mathematics. It is a number that has been chased by scholars for almost 4,000 years. Its precision has been calculated to over two billion decimal places without an end in sight. Examine those digits and the frequency of the numbers is no more than random. Yet, pi is everywhere around us. There is pi in pie. Cut a pie in half. Pi is the number of times the length of that cut will go around the outside of the pie. Pi pie? That would be one each for three of us with some left over. Ah, but how much left over? That is the very question that has agonized mathematicians throughout the centuries. The supercomputers crunch and crunch and crunch those numbers until somebody cries "enough" and moves on to something more pressing, like trying to predict next week's weather. Like that's a more likely problem to be solved. There may be issues seemingly more pressing to humankind, but the pursuit of pi has always had a romance that captivated mathematicians...sometimes to obsession. The Bible tells us that pi has a value of around 3. Oh, yes. It's there in the specifications for the great temple of Solomon, describing the pouring of what seems to be a large brass casting. "And he made a molten sea, ten cubits from the one brim to the other: it was round all about, and his height was five cubits: and a line of thirty cubits did compass it about." (I Kings 7, 23).
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
Extractions: 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 Introdução Tabela Cronológica Porquê Calcular ... Bibliografia 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.
Pi Sayýsýnýn Kronolojisi 1596, Hollandali ludolph van ceulen; 'yi 35 basamaga kadar hesapliyor.(Bunedenle Almanya'da ; ludolph Sayisi olarak bilinir.). http://matlab.s5.com/pi kronoloji.htm
Extractions: SAYISININ KRONOLOJÝSÝ PÝ'NÝN KRONOLOJÝSÝ M.Ö 20 yy Babilliler = 31/8 deðerini kullanýyorlar. M.Ö 20 yy Mýsýrlýlar = (16/9)*(16/9)= 3,1605 deðerini kullanýyorlar. M.Ö 12 yy Çinliler = 3 deðerini kullanýyorlar. M.Ö 550 Kutsal Kitapta I.Krallar = 3 deðerini kullanýyorlar. M.Ö 434 Anaksagoras ; daireyi kare yapmaya çalýþýyor. M.Ö 3 yy Arþimed = 211875/67441 kesrini de buluyor. 2. yy Batlamyos = 377/120 = 3,14166... deðerini kullanýyor. 3. yy Çung Hing Vang Fav Liu Hui = 471/150 = 3,14 deðerlerini kullanýyorlar. 5. yy Zu Çung Çi 6. yy Hintli Aryabhatta = 62832/2000 = 3,1416 deðerini, Brahmagupta = kök 10 deðerini kullanýyorlar. Fibonacci = 3,141818 deðerini kullanýyor. Semerkantlý El Kaþi 'yi 14 basamaðýna kadar hesaplýyor. Valentinus Otho = 355/113 = 3,1415929 olduðunu buluyor. Hollandalý Adriaen van Rooman 'yi 15 basamaðýna kadar hesaplýyor. Hollandalý Ludolph Van Ceulen 'yi 35 basamaða kadar hesaplýyor.(Bu nedenle Almanya'da Ludolph Sayýsý olarak bilinir.)
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
Extractions: 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
