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
Science -- Sign In Modern machines crank out digits of pi by the gigabyte, but 400 years ago Dutchmathematician ludolph van ceulen got the ball rolling with a hand computation http://intl.sciencemag.org/cgi/content/summary/289/5477/241e
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Ca 1100 F.Kr av pi. 1596, ludolph van ceulen beräknar 32 decimaler av pi. 1610,van ceulen utvidgar beräkningen till 35 decimaler. 1621, Willebrod http://www.mats-andersson.se/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.
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://www.o4r.org/pf_v4n3/PiUnderground.htm
Extractions: Underground Pi Digging Out from Under Pseudoscience By Mark Cowan I n the Washington Park Station of the Westside Light Rail Tunnel, in the 16-million year recitation of history that runs alongside a 260-foot core sample of Portlands West Hills, you will find, etched in granite, the first 107 digits of the transcendental constant pi (figure 1). Figure 1. Pi as it appears in the Washington Park Station of the Westside MAX Light Rail Pi, as every schoolchild knows, is the ratio of the circumference of a circle to its diameter - one of the fundamental ratios of the space that fills our universe. Its digits never repeat, and they follow no pattern. Other than its role in geometry, and the fact that it pops up in many diverse branches of mathematics, pi has no special significance. It does not mean anything...so far as we know. Yet pi has exerted a steady pull on the human imagination. The Babylonians and Egyptians knew its value to within a half a percent some 4000 years ago. By the 3rd century BC, Archimedes had rectified the circle, nearly invented the calculus, and established pis value to about one part in 100,000 by the use of regular polygons. And by the 5th century AD a Chinese father and son, using a variation of this method, pinned down eight digits-a precision unequaled in Europe until the 16th century. Their laborious extraction of square roots was aided by the early Chinese introduction of a blank for zero.
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
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Mathematics Resources On The Web 16231662); Ptolemy, Claudius (c 87 - 150); Pythagoras (c 580 - c520 BCE); van ceulen, ludolph (1540-1610). Software Computational http://www.eastern.edu/library/www/Subjects/Websites/math.html
Extractions: Previous Level Home Books Databases / Indexes ... Reference Mathematics Resources on the Web Reference 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
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
Extractions: 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.
Extractions: Quando em 1939 (ano que nosso v´ nasceu!) Einstein informou ao presidente americano, Franklin Roosevelt, que talvez fosse possvel construir uma bomba at´mica, o tiozinho genial n£o sabia na enrascada que tava se metendo... O cientista, que sempre foi um pacifista e pensador afudª, deixou de dormir bons sonos pensando naquilo... Pos bem, hoje dia 06 de Agosto de 2003, est¡ completando 58 anos que a bombinha at´mica foi lan§ada sobre algumas cabe§as em Hiroshima... A estupidez humana me d¡ ¢nsia!!
History 1596 A.D 1596 AD Rene DescartesThe Father of Analytical Geometry or LudolphVan ceulen and the history of pi. Rene Descartes was born on http://faculty.oxy.edu/jquinn/home/Math490/Timeline/1596AD.html
Extractions: Rene Descartes was born on March 31, 1596 in Touraine, France. His family lived in the estate of Les Cartes at La Haye, France and his father was a Councilor in the city of Rennes, France. The second child of a family of two sons and one daughter, Descartes was sent to the Jesuit School at La Fleche at the age of 8. There he studied classics, logic and traditional Aristotelian philosophy and math. While in school, Descartes suffered from poor health and was granted permission by his school to remain in bed until 11 o'clock in the morning. He continued this practice throughout his life. When he visited Pascal in 1647, he said "the only way to do good work in mathematics and preserve my health is to never allow anyone to make me get up in the morning before I feel inclined to do so"(Ball, p. 1) When he left school in 1612, he spent 2 years in Paris studying mathematics with his schoolboy friend Mersenre. During this time period, young men were encouraged to go into the military or the church. Descartes chose the military and joined the army in 1617 under Prince Maurice of Orange. There was no mention of his sleeping schedule during this time, but it probably changed to accommodate army life. After a couple of years in the army he grew disinterested, but not before he was introduced to a problem that would change the course of his life. One day, while walking along the street, he saw a Dutch sign telling of a geometric problem. He asked Isaac Beeckman, Head of the Dutch College at Dort who was unknown to him at the time, to translate it. It took Descartes just a few hours to solve the problem and a friendship grew between them. (MacTutor)
