41. Pi -- From MathWorld A brief history of notation for pi is given by Castellanos (1988). pi is sometimesknown as ludolph s constant after ludolph van ceulen (15391610), http://mathworld.wolfram.com/Pi.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants Pi ... Pi Pi A real number denoted which is defined as the ratio of a circle 's circumference 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. Spigot (Rabinowitz and Wagon 1995; Arndt and Haenel 2001; Borwein and Bailey 2003, pp. 140-141) and digit-extraction algorithms (the BBP formula ) are known for Pi's continued fraction is given by [3, 7, 15, 1, 292, 1, 1, 1, ...] (Sloane's ). Its Engel expansion is 1, 1, 1, 8, 8, 17, 19, 300, 1991, 2492, ... (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).

42. Pi Digits -- From MathWorld ludolph van ceulen spent much of his life calculating pi to 35 places. Although hedid not live to publish his result, it was inscribed on his gravestone. http://mathworld.wolfram.com/PiDigits.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Number Theory Constants Pi ... Mathematical Records Pi Digits The calculation of the 's digits has occupied mathematicians since the day of the Rhind papyrus (1500 BC). Ludolph van Ceulen spent much of his life calculating to 35 places. Although he did not live to publish his result, it was inscribed on his gravestone. Wells (1986, p. 48) discusses a number of other calculations. The calculation of also figures in the Star Trek episode "Wolf in the Fold," in which Captain Kirk and Mr. Spock force an evil entity (composed of pure energy and which feeds on fear) out of the starship Enterprise 's computer by commanding the computer to "compute to the last digit the value of pi," thus sending the computer into an infinite loop. Al-Kashi of Samarkand computed the sexagesimal digits of as (Sloane's ) using -gons, a value accurate to 17 decimal places (Borwein and Bailey 2003, p. 107).

43. 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.

44. Math Forum: A Chronological Table Of Values Attributed To Pi ludolph van ceulen, 1596, Calculates Pi to 35 decimal places. Machin, 1706,100 decimal places. Lambert, 1766, Proves Pi is irrational http://mathforum.org/isaac/problems/pi2.html

The values of Pi through time A Math Forum Project Table of Contents: Famous Problems Home The Bridges of Konigsberg The Value of Pi Prime Numbers ... Links Person/People Year Value Babylonians ~2000 B.C. Egyptians ~2000 B.C. Chinese ~1200 B.C. Old Testament ~550 B.C. Archimedes ~300 B.C. uses 211875/67441=3.14163 Ptolemy ~200 A.D. Chung Huing ~300 A.D. sqrt(10)=3.16... Wang Fau 263 A.D. Tsu Chung-Chi ~500 A.D. Aryabhatta Brahmagupta sqrt(10) Fibonacci Ludolph van Ceulen Calculates Pi to 35 decimal places Machin 100 decimal places Lambert Proves Pi is irrational Richter 500 decimal places Lindeman Proves Pi is transcendental Ferguson 808 decimal places Pegasus Computer 7,840 decimal places IBM 7090 100,000 decimal places CDC 6600 500,000 decimal places So what happened between 1220 and 1596? Well, in the late 15th century European mathematicians (benefiting from the greater intellectual freedom that came with the end of the Middle Ages) figured out how to express Pi exactly as an infinite product. This facilitated the computation of much better approximations. As time passed, mathematicians made the expressions for Pi as an infinite product or sum more concise, and computational methods improved as well. For example: determined that: John Wallis (1616-1703) showed that: While Euler (1707-1783) derived his famous formula: Today Pi is known to more than 10 billion decimal places.

45. Math Forum - Ask Dr. Math culminating with ludolph van ceulen, who worked on the problem all his life,eventually got a value to 35 places, and had it engraved on his tombstone. http://mathforum.org/library/drmath/view/53906.html

Associated Topics Dr. Math Home Search Dr. Math Numbers that represent pi Date: 08/08/97 From: Edith N. Ferrer Subject: Numbers that represent pi If pi is an inexact and transcendental number, how in the world did we obtain a certain series of numbers to represent pi? In other words, what value circumference did we divide by what value diameter to arrive at the accepted pi value of 3.141592653589 etc....? Please help. Thank you very much. Associated Topics High School Transcendental Numbers Search the Dr. Math Library: Find items containing (put spaces between keywords): Click only once for faster results: [ Choose "whole words" when searching for a word like age. all keywords, in any order at least one, that exact phrase parts of words whole words Submit your own question to Dr. Math Math Forum Home Math Library Quick Reference ... Math Forum Search Ask Dr. Math TM http://mathforum.org/dr.math/

46. The Constant Pi van ceulen restored tombstone, The history of the constant p is often divided with ludolph van ceulen (15401610) 35 decimal places great calculation. http://numbers.computation.free.fr/Constants/Pi/pi.html

Archimedes ' constant p p And he made a molten sea, ten cubits from the one brim to the other; it was round all about ... and a line ot thirty cubits did compass it round about. - Bible, 1 Kings 7:23 This mysterious 3.141592..., which comes in at every door and window, and down every chimney. Augustus De Morgan (1806-1871) Definitions Geometrical definition The constant p (Greek letter pi ) is, classically, defined as the ratio of the circumference p of a circle to its diameter d p p d p r and, as proved by Archimedes of Syracuse (287-212 BC) in his famous Measurement of a Circle , the same constant is also the ratio of the area A enclosed by the circle to the square of its radius r A p r Archimedes Analytical definition In 1934, the German mathematician Edmund Landau (1877-1938) gave a new and analytical definition based on the cosine function cos t t t t 1/3 (take the 3 first terms of the sequence), from the continuity of the cosine function, the equation cos t = has roots. If t is the smallest positive root of this equation

47. The Geometric Period 1596 ludolph van ceulen (15401610, Germany) 20 digits with a polygon of 60.233sides. 1609 ludolph van ceulen 35 digits with a polygon of 262 sides. http://numbers.computation.free.fr/Constants/Pi/pigeometry.html

Click here for a Postscript version of this page and here for a pdf version) The geometric period Up to the Seventeenth Century, approximations of p were obtained by mean of geometrical considerations. Most of the methods were dealing with regular polygons circumscribed about and inscribed in the circle. The perimeter or the area of those polygons were calculated with elementary geometrical rules. During this period the notation p was not used and it was not yet a constant but just a geometrical ratio or even just implicit. Ancient estimations Egypt In one of the oldest mathematical text, the Rhind papyrus (from the name of the Egyptologist Henry Rhind who purchased this document in 1858 at Luxor), the scribe Ahmes copied, around 1650 B.C.E., eighty-five mathematical problems. Among those is given a rule, the problem 48 , to find the area of a circular field of diameter 9: take away 1/9 of the diameter and take the square of the remainder. In modern notation, it becomes A= d d d (A is the area of the field and d it's diameter): so if we use the formula A= p d /4, comes the following approximation

48. Enciclopedia :: 100cia.com Translate this page ludolph van ceulen. (En este momento no hay texto en esta p¡gina. Para iniciarel art­culo, click editar esta p¡gina (http//es.wikipedia. http://100cia.com/enciclopedia/Ludolph_van_Ceulen

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49. Kennislink - 9 December 2002:Nieuw Pi-record ludolph van ceulen schreef in 1583 een boekje Kort claer bewijs dat die nieuweghevonden proportie ludolph van ceulen zette zijn berekeningen voort. http://www.kennislink.nl/web/show?id=92946

50. Kennislink - Van Onze Correspondent:Voer Voor Getallenvreters ludolph van ceulen schreef in 1583 een boekje Kort claer bewijs dat die nieuwe ludolph van ceulen, de Nederlandse wiskundige die in 1596 het getal pi http://www.kennislink.nl/web/show?id=130402

51. 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

52. History Of Pi Many years later, ludolph van ceulen (c. 1610), a German mathematician, gave anestimate that was accurate to 34 decimal places using Archimedes method http://people.bath.ac.uk/slt20/history.html

History of pi The ratio of circumference to diameter is the same for all circles and this has been accepted as "fact" for centuries; at least 4000 years. The search for pi began with the Egyptian and Babylonians at around 2000BC. They noticed that the ratio between the circumference and the diameter of a circle was around 3. The value of pi given in the Rhynd Papyrus (c. 2000 BC) is Various Babylonian and Egyptian writings suggest that each of the values were used in different circumstances. The Bible (c. 950 BC, 1 Kings 7:23) and the Talmud both give the value simply as 3. Archimedes of Syracuse (240 BC), using a 96-sided polygon and his method of exhaustion (involving regular shapes and trigonometry), showed that whilst trying to solve the impossible problem of squaring the circle. The important feature of Archimedes' accomplishment is not that he was able to give such an accurate estimate, but that his methods could be used to get any number of digits of pi. In fact, Archimedes' method of exhaustion would prove to be the basis for nearly all calculations of pi for over 1800 years. Ptolemy of Alexandria's is the next notable pi approximation

53. Science -- Sign In but 400 years ago Dutch mathematician ludolph van ceulen got the ball A memorial stone honoring van ceulen s accomplishment was unveiled 5 July at http://www.sciencemag.org/cgi/content/summary/289/5477/241e

You do not have access to this item: Summary : Computing Pi-oneer, Science You are on the site via Free Public Access. What content can I view with Free Public Access If you have a personal user name and password, please login below. SCIENCE Online Sign In Options For Viewing This Content User Name Password this computer. Help with Sign In If you don't use cookies, sign in here Join AAAS and subscribe to Science for free full access. Sign Up More Info Register for Free Partial Access including abstracts, summaries and special registered free full text content. Register More Info Need More Help? Can't get past this page? Forgotten your user name or password? AAAS Members activate your FREE Subscription

54. Science -- Sign In but 400 years ago Dutch mathematician ludolph van ceulen got the ball rollingwith All those zeroes are part of the denominator In van ceulen s day http://www.sciencemag.org/content/vol289/issue5477/r-samples.shtml

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55. Comments And Explanations In Leiden, he studied with ludolph van ceulen, who was the engineering professor.van ceulen is known for calculating pi to 35 digits. http://www.math.vt.edu/people/renardym/comments.html

Comments and explanations The "recent" part of the information is from the Mathematics Genealogy Project . For the older part, I have relied on biographies; here "advising" needs to be interpreted more broadly than the supervision of doctoral theses. Resources consulted include, among others, Mac Tutor Wikipedia , the Catholic Encyclopedia , the Biographisch-Bibliographisches Kirchenlexikon , the Allgemeine Deutsche Biographie , and the Dictionary of Scientific Biography. The online catalogs of several German university libraries, most notably Halle-Wittenberg, Tuebingen, and Leipzig, were also helpful. Goertler's name is often associated with Ludwig Prandtl. Indeed, he worked under Prandtl during the period following his doctorate. The work on Goertler vortices was done in Prandtl's lab. There were two scientists named Robert Daublebsky von Sterneck, who were father and son. The one in the table is the son; he is known for computational work related to the zeros of the Riemann zeta function. The father was a surveying engineer in the Austrian military. Frischauf is known for his contributions to mountaineering in Slovenia in addition to work in astronomy and cartography. The Oesterreichisches Biographisches Lexikon says he studied mathematics and physics under Moth and Petzval. I was unable to find specifics.

56. O4R:  Underground Pi in a 1596 paper entitled “On the Circle,” Dutch mathematician ludolph vanceulen singlehandedly delivered Figure 2. Pi as per van ceulen (1596). http://www.o4r.org/pf_v4n3/PiUnderground.htm

"How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics..." 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 Portland’s 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 pi’s 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.

57. Einige Der Bedeutenden Mathematiker Translate this page ceulen, ludolph van, 1540-1610. Chomsky Noel, 1928-. Chwarismi Muhammed Ibn Musa Al,~830. Church Alonzo, 1903-. Cohen Paul Joseph, 1934- http://www.zahlenjagd.at/mathematiker.html

Einige der bedeutenden Mathematiker Abel Niels Hendrik Appolonius von Perga ~230 v.Chr. Archimedes von Syrakus 287-212 v.Chr. Babbage Charles Banach Stefan Bayes Thomas Bernoulli Daniel Bernoulli Jakob Bernoulli Johann Bernoulli Nicolaus Bessel Friedrich Wilhelm Bieberbach Ludwig Birkhoff Georg David Bolyai János Bolzano Bernhard Boole George Borel Emile Briggs Henry Brouwer L.E.J. Cantor Georg Ferdinand Carroll Lewis Cassini Giovanni Domenico Cardano Girolamo Cauchy Augustin Louis Cayley Arthur Ceulen, Ludolph van Chomsky Noel Chwarismi Muhammed Ibn Musa Al Church Alonzo Cohen Paul Joseph Conway John Horton Courant Richard D'Alembert Jean Le Rond De Morgan Augustus Dedekind Julius Wilhelm Richard Descartes René Dieudonné Jean Diophantos von Alexandria ~250 v. Chr. Dirac Paul Adrien Maurice Dirichlet Peter Gustav Lejeune Eratosthenes von Kyrene 276-194 v.Chr. Euklid von Alexandria ~300 v.Chr. Euler Leonhard Fatou Pierre Fermat Pierre de Fischer Ronald A Sir Fourier Jean-Baptiste-Joseph Fraenkel Adolf Frege Gottlob Frobenius Ferdinand Georg Galois Evariste Galton Francis Sir Gauß Carl Friedrich Germain Marie-Sophie Gödel Kurt Goldbach Christian Hadamard Jacques Hamilton William Rowan Hausdorff Felix Hermite Charles Heawood Percy Heron von Alexandrien ~60 n.Chr.

58. Actuarial Profession - Library Servuces. Staple Inn, London. Special Books Colle L Arithmetique (1558); ludolph van ceulen, van den Circkel (1596) on compoundinterest; Nicolas Struyck, Uytreekening der kanssen in het speelen, http://www.actuaries.org.uk/Display_Page.cgi?url=/library/inst-lib-si.xml

59. Matematikusok Arcképcsarnoka ludolph van ceulen (1550 01. 28. 1617. 12. 31.) Azóta nevezik a p -tludolph-féle számnak. Síremlékén látható a nevét híressé tevo tizedes tört. http://www.sulinet.hu/ematek/html/ceulen.html

Ludolph van Ceulen Holland erõdítményépítõ, vívómester és matematikus. Munkásságáról: Elõször 20, aztán harmincöt tizedesjegyig kiszámította a p értékét. Azóta nevezik a p -t Ludolph-féle számnak Síremlékén látható a nevét híressé tevõ tizedes tört. (Hollandia, Delft város.) fel vissza fõmenü

60. List Of Scientists By Field ceulen, ludolph van. Ceva, Giovanni. Ceva, Tomasso. Chabry, Laurent. Chadwick,James. Chagas, Carlos Ribeiro Justiniano. Chain, Ernst Boris http://www.indiana.edu/~newdsb/c.html

Cabanis, Pierre-Jean-Georges Cabanis, Pierre-Jean-Georges Cabanis, Pierre-Jean-Georges Cabeo, Niccolo Cabeo, Niccolo Cabeo, Niccolo Cabrera, Blas Cadet de Gassicourt, Charles- Louis Cadet de Gassicourt, Charles- Louis Cadet, Louis-Claude Cagniard de la Tour, Charles Cailletet, Louis Paul Cailletet, Louis Paul Caius, John Calandrelli, Giuseppe Calandrelli, Ignazio Calandrelli, Ignazio Calcidius Caldani, Leopoldo Marcantonio Caldani, Leopoldo Marcantonio Calkins, Gary Nathan Callan, Nicholas Callandreau, Pierre Jean Octave Callendar, Hugh Longbourne Callendar, Hugh Longbourne Callinicos of Heliopolis Callippus Callippus Calmette, Albert Camerarius, Rudolph Jakob Camerarius, Rudolph Jakob Cameron, Angus Ewan Cameron, Angus Ewan Campanella, Tommaso Campani, Giuseppe Campani, Giuseppe Campanus of Novara Campanus of Novara Campbell, Douglas Houghton Campbell, Ian Campbell, Norman Robert Campbell, Norman Robert Campbell, William Wallace Campbell, William Wallace Camper, Peter Camper, Peter Camper, Peter Canano, Giovan Battista Canano, Giovan Battista Cancrin, Franz Ludwig von

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